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Fundamentals of Biostatistics

Bernard Rosner

Chapter 10

Hypothesis Testing: Categorical Data - all with Video Answers

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Chapter Questions

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Problem 1

How many participants need to be enrolled in each group to have a $90 \%$ chance of detecting a significant difference using a two-sided test with $\alpha=.05$ if compliance is perfect?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:55

Problem 2

Answer Problem 10.1 if compliance is as given in Example 10.37.

Tiffany Tran
Tiffany Tran
Numerade Educator
02:12

Problem 3

Answer Problem 10.1 if a one-sided test with power $=$ .8 is used and compliance is perfect.

AG
Ankit Gupta
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Problem 4

Suppose 11,000 men are actually enrolled in each treatment group. What would be the power of such a study if a two-sided test with $\alpha=.05$ were used and compliance is perfect?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:55

Problem 5

Answer Problem 10.4 if compliance is as given in Example 10.37.

Tiffany Tran
Tiffany Tran
Numerade Educator
02:12

Problem 6

What significance test can be used to assess whether there is a relationship between receiving an antibiotic and receiving a bacterial culture while in the hospital?

Brett Donadeo
Brett Donadeo
Numerade Educator
01:19

Problem 7

Perform the test in Problem $10.6,$ and report a $p$ -value.

Kristof Mueller
Kristof Mueller
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02:36

Problem 8

Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug $\mathrm{A}$ is effective, whereas drug $\mathrm{B}$ is ineffective; and for 16 matched pairs drug $B$ is effective, whereas drug $A$ is ineffective.
What test procedure can be used to assess the results?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
03:56

Problem 9

Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug $\mathrm{A}$ is effective, whereas drug $\mathrm{B}$ is ineffective; and for 16 matched pairs drug $B$ is effective, whereas drug $A$ is ineffective.
Perform the test in Problem $10.8,$ and report a $p$ -value. In the same study, if the focus is on the 100 matched pairs consisting of male patients, then the following results are obtained:
for 52 matched pairs both drugs are effective; for 35 matched pairs both drugs are ineffective; for 4 matched pairs drug $\mathrm{A}$ is effective, whereas drug $B$ is ineffective; and for 9 matched pairs drug $\mathrm{B}$ is effective, whereas drug $\mathrm{A}$ is ineffective.

James Kiss
James Kiss
Numerade Educator
06:57

Problem 10

Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug $\mathrm{A}$ is effective, whereas drug $\mathrm{B}$ is ineffective; and for 16 matched pairs drug $B$ is effective, whereas drug $A$ is ineffective.
How many concordant pairs are there among the male matched pairs?

Suzanne W.
Suzanne W.
Numerade Educator
06:57

Problem 11

Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug $\mathrm{A}$ is effective, whereas drug $\mathrm{B}$ is ineffective; and for 16 matched pairs drug $B$ is effective, whereas drug $A$ is ineffective.
How many discordant pairs are there among the male matched pairs?

Suzanne W.
Suzanne W.
Numerade Educator
06:52

Problem 12

Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug $\mathrm{A}$ is effective, whereas drug $\mathrm{B}$ is ineffective; and for 16 matched pairs drug $B$ is effective, whereas drug $A$ is ineffective.
Perform a significance test to assess any differences in effectiveness between the drugs among males. Report a $p$ -value.

Caleb Huber
Caleb Huber
Numerade Educator
02:03

Problem 13

Suppose researchers do an epidemiologic investigation of people entering a sexually transmitted disease clinic. They find that 160 of 200 patients who are diagnosed as having gonorrhea and 50 of 105 patients who are diagnosed as having nongonococcal urethritis have had previous episodes of urethritis.
Are the present diagnosis and prior episodes of urethritis associated?

Prabhakar Kumar
Prabhakar Kumar
Numerade Educator
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Problem 14

A 1980 study investigated the relationship between the use of OCs and the development of endometrial cancer [9]. The researchers found that of 117 endometrial-cancer patients, 6 had used the OC Oracon at some time in their Iives, whereas 8 of the 395 controls had used this agent. Test for an association between the use of Oracon and the incidence of endometrial cancer, using a two-tailed test.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:57

Problem 15

Retinitis pigmentosa is a disease that manifests itself via different genetic modes of inheritance. Cases have been documented with a dominant, recessive, and sex-linked mode of inheritance. It has been conjectured that mode of inheritance is related to the ethnic origin of the individual. Cases of the disease have been surveyed in an English and a Swiss population with the following results: Of 125 English cases, 46 had sex-linked disease, 25 had recessive disease, and 54 had dominant disease. Of 110 Swiss cases, 1 had sex-linked disease, 99 had recessive disease, and 10 had dominant disease.
Do these data show a significant association between ethnic origin and genetic type?

James Kiss
James Kiss
Numerade Educator
01:05

Problem 16

One important aspect of medical diagnosis is its reproducibility. Suppose that two different doctors examine 100 patients for dyspnea in a respiratory-disease clinic and that doctor A diagnosed 15 patients as having dyspnea, doctor B diagnosed 10 patients as having dyspnea, and both doctor $A$ and doctor $B$ diagnosed 7 patients as having dyspnea.
Compute the Kappa statistic and its standard error regarding reproducibility of the diagnosis of dyspnea in this clinic.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
05:46

Problem 17

The conventions of cardiac echocardiography are derived from comprehensive studies performed by technicians and cardiologists. Traditionally, patients are positioned supine (i.e., lying on their back), although there is no evidence to support this practice. Clinicians in the emergency department (ED) are sometimes faced with acutely ill patients who cannot tolerate the supine position. For this reason, a study is planned to compare ultrasound studies performed while a patient is supine vs. while a patient is upright.

Patients $\geq 18$ years of age who present to the ED with chest pain or shortness of breath and consent to the study will be enrolled. Each patient will receive two ultrasound studies, one in the supine position and one in the upright position. The order of administration of the two studies will be at random. Readers will review the images in a blinded manner and assess a number of clinical characteristics. An important endpoint is pericardial effusion (or fluid around the heart). Suppose 50 patients are enrolled in the pilot phase of the study.
(i) For 30 patients it is determined from both images that there is no fluid around the heart.
(ii) For 10 patients it is determined from both images that there is fluid around the heart.
(iii) For 8 patients it is determined from the supine image, but not the upright image, that there is fluid around the heart.
(iv) For 2 patients it is determined from the upright image, but not the supine image, that there is fluid around the heart.
If we focus on patients where there are different results for the supine and upright images [i.e., groups (iii) and (iv) abovel, what test can be performed to assess whether there is a significant difference in determinations for supine
vs. upright images?

Carlos Pinilla
Carlos Pinilla
Numerade Educator
03:42

Problem 18

The conventions of cardiac echocardiography are derived from comprehensive studies performed by technicians and cardiologists. Traditionally, patients are positioned supine (i.e., lying on their back), although there is no evidence to support this practice. Clinicians in the emergency department (ED) are sometimes faced with acutely ill patients who cannot tolerate the supine position. For this reason, a study is planned to compare ultrasound studies performed while a patient is supine vs. while a patient is upright.

Patients $\geq 18$ years of age who present to the ED with chest pain or shortness of breath and consent to the study will be enrolled. Each patient will receive two ultrasound studies, one in the supine position and one in the upright position. The order of administration of the two studies will be at random. Readers will review the images in a blinded manner and assess a number of clinical characteristics. An important endpoint is pericardial effusion (or fluid around the heart). Suppose 50 patients are enrolled in the pilot phase of the study.
(i) For 30 patients it is determined from both images that there is no fluid around the heart.
(ii) For 10 patients it is determined from both images that there is fluid around the heart.
(iii) For 8 patients it is determined from the supine image, but not the upright image, that there is fluid around the heart.
(iv) For 2 patients it is determined from the upright image, but not the supine image, that there is fluid around the heart.
Perform the test in Problem 10.17 and report a $p$ -value (two-tailed). Interpret the results in words.

Issa Dababneh
Issa Dababneh
Numerade Educator
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Problem 19

Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing loss associated with persistent otitis media and prevent recurrences of episodes of otitis media after tubes are inserted. However, acute otormea (a discharge from the external ear indicating inflammation of the extemal or middle ear), where middle ear fluid drains through the tube, is a common side effect with tympanostomy tubes.
A clinical trial was conducted (Van Dongen et al. $[10])$ among children $1-10$ years of age with prior symptoms of otorrhea comparing efficacy of (i) antibiotic eardrops,
(ii) oral antibiotics, and (iii) observation without treatment, referred to below as observation. Children were seen at home by study physicians at 2 weeks and 6 months after randomization. The primary outcome was the presence of otorrhea at 2 weeks observed by study physicians. The results are given in Table 10.22
Provide a point estimate and a $95 \%$ confidence interval for the prevalence of otorrhea at 2 weeks in the observation group.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 20

Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing loss associated with persistent otitis media and prevent recurrences of episodes of otitis media after tubes are inserted. However, acute otormea (a discharge from the external ear indicating inflammation of the extemal or middle ear), where middle ear fluid drains through the tube, is a common side effect with tympanostomy tubes.
A clinical trial was conducted (Van Dongen et al. $[10])$ among children $1-10$ years of age with prior symptoms of otorrhea comparing efficacy of (i) antibiotic eardrops,
(ii) oral antibiotics, and (iii) observation without treatment, referred to below as observation. Children were seen at home by study physicians at 2 weeks and 6 months after randomization. The primary outcome was the presence of otorrhea at 2 weeks observed by study physicians. The results are given in Table 10.22
Provide a point estimate and a $95 \%$ Cl for the prevalence of otorrhea in the ear drop group.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 21

Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing loss associated with persistent otitis media and prevent recurrences of episodes of otitis media after tubes are inserted. However, acute otormea (a discharge from the external ear indicating inflammation of the extemal or middle ear), where middle ear fluid drains through the tube, is a common side effect with tympanostomy tubes.
A clinical trial was conducted (Van Dongen et al. $[10])$ among children $1-10$ years of age with prior symptoms of otorrhea comparing efficacy of (i) antibiotic eardrops,
(ii) oral antibiotics, and (iii) observation without treatment, referred to below as observation. Children were seen at home by study physicians at 2 weeks and 6 months after randomization. The primary outcome was the presence of otorrhea at 2 weeks observed by study physicians. The results are given in Table 10.22
What test can be used to compare the prevalence of otorrhea for the ear drop group vs. the observation group? State the hypotheses to be tested.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 22

Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing loss associated with persistent otitis media and prevent recurrences of episodes of otitis media after tubes are inserted. However, acute otormea (a discharge from the external ear indicating inflammation of the extemal or middle ear), where middle ear fluid drains through the tube, is a common side effect with tympanostomy tubes.
A clinical trial was conducted (Van Dongen et al. $[10])$ among children $1-10$ years of age with prior symptoms of otorrhea comparing efficacy of (i) antibiotic eardrops,
(ii) oral antibiotics, and (iii) observation without treatment, referred to below as observation. Children were seen at home by study physicians at 2 weeks and 6 months after randomization. The primary outcome was the presence of otorrhea at 2 weeks observed by study physicians. The results are given in Table 10.22
Perform the test in Problem 10.21 and report a p-value (two-tailed). Interpret your results in words.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:32

Problem 23

The following data are provided from the SEER Cancer Registries of the National Cancer Institute based on 17 cancer registries in the United States. Data are available for stage of disease at diagnosis for women with breast cancer by age and race as shown in Table 10.23[11]
Test whether the distribution of stage of disease is significantly different between Caucasian and African American women with breast cancer who are younger than 50 years of age. Please provide a $p$ -value (two-tailed). Ignore the unstaged cases in your analysis. The 5 -year survival rates by stage of disease, age at diagnosis, and race are provided in Table 10.24

Amany Waheeb
Amany Waheeb
Numerade Educator
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Problem 24

Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing loss associated with persistent otitis media and prevent recurrences of episodes of otitis media after tubes are inserted. However, acute otormea (a discharge from the external ear indicating inflammation of the extemal or middle ear), where middle ear fluid drains through the tube, is a common side effect with tympanostomy tubes.
A clinical trial was conducted (Van Dongen et al. $[10])$ among children $1-10$ years of age with prior symptoms of otorrhea comparing efficacy of (i) antibiotic eardrops,
(ii) oral antibiotics, and (iii) observation without treatment, referred to below as observation. Children were seen at home by study physicians at 2 weeks and 6 months after randomization. The primary outcome was the presence of otorrhea at 2 weeks observed by study physicians. The results are given in Table 10.22
Test whether the 5-year survival rate for breast cancer is significantly different between African American and Caucasian women who are younger than 50 years of age and have localized disease. Provide a $p$ -value (two-tailed).

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:21

Problem 25

Suppose a study examines the relative efficacy of penicillin and spectinomycin in treating gonorrhea. Three treatments are considered: (1) penicillin, (2) spectinomycin, low dose, and (3) spectinomycin, high dose. Three possible responses are recorded: (1) positive smear, (2) negative smear, positive culture, (3) negative smear, negative culture. The data in Table 10.25 are obtained.
Is there any relationship between the type of treatment and the response? What form does the relationship take?

Alexander Cheng
Alexander Cheng
Numerade Educator
02:40

Problem 26

Suppose a study examines the relative efficacy of penicillin and spectinomycin in treating gonorrhea. Three treatments are considered: (1) penicillin, (2) spectinomycin, low dose, and (3) spectinomycin, high dose. Three possible responses are recorded: (1) positive smear, (2) negative smear, positive culture, (3) negative smear, negative culture. The data in Table 10.25 are obtained.
Suppose either a positive smear or a positive culture is regarded as a positive response and distinguished from the negative smear, negative culture response. Is there an association between the type of treatment and this measure of response?

Eric Goldman
Eric Goldman
Numerade Educator
03:25

Problem 27

Improving control of blood-glucose levels is an important motivation for the use of insulin pumps by diabetic patients. However, certain side effects have been reported with pump therapy. Table 10.26 provides data on the occurrence of diabetic ketoacidosis (DKA) in patients before and after start of pump therapy [12]
What is the appropriate procedure to test whether the rate of DKA is different before and after start of pump therapy?

Dominador Tan
Dominador Tan
Numerade Educator
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Problem 28

Suppose a study examines the relative efficacy of penicillin and spectinomycin in treating gonorrhea. Three treatments are considered: (1) penicillin, (2) spectinomycin, low dose, and (3) spectinomycin, high dose. Three possible responses are recorded: (1) positive smear, (2) negative smear, positive culture, (3) negative smear, negative culture. The data in Table 10.25 are obtained.
Perform the significance test in Problem 10.27 , and report a $p$ -value.

Victor Salazar
Victor Salazar
Numerade Educator
01:06

Problem 29

A study group of 576 working women $30-49$ years of age who took phenacetin-containing analgesics and a control group of 533 comparably aged women without such intake were identified in 1968 and followed for mortality and morbidity outcomes. One hypothesis to be tested was that phenacetin intake may influence renal (kidney) function and hence have an effect on specific indices of renal morbidity and mortality. The mortality status of these women was determined from 1968 to $1987 .$ The researchers found that 16 of the women in the study group and 1 of the women in the control group died, where at least one cause of death was considered renal [13].
Test for differences in renal mortality between the two groups in either direction, and report a two-tailed $p$ -value. The cohort was also followed for total mortality. The researchers found that 74 women in the study group died, compared with 27 in the control group.

Akhil Choudhary
Akhil Choudhary
Numerade Educator
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Problem 30

A study group of 576 working women $30-49$ years of age who took phenacetin-containing analgesics and a control group of 533 comparably aged women without such intake were identified in 1968 and followed for mortality and morbidity outcomes. One hypothesis to be tested was that phenacetin intake may influence renal (kidney) function and hence have an effect on specific indices of renal morbidity and mortality. The mortality status of these women was determined from 1968 to $1987 .$ The researchers found that 16 of the women in the study group and 1 of the women in the control group died, where at least one cause of death was considered renal [13].
What statistical test should be used to compare the total mortality experience of the study group with that of the control group?

Victor Salazar
Victor Salazar
Numerade Educator
01:06

Problem 31

A study group of 576 working women $30-49$ years of age who took phenacetin-containing analgesics and a control group of 533 comparably aged women without such intake were identified in 1968 and followed for mortality and morbidity outcomes. One hypothesis to be tested was that phenacetin intake may influence renal (kidney) function and hence have an effect on specific indices of renal morbidity and mortality. The mortality status of these women was determined from 1968 to $1987 .$ The researchers found that 16 of the women in the study group and 1 of the women in the control group died, where at least one cause of death was considered renal [13].
Implement the test in Problem $10.30,$ and report a $p$ -value.

Akhil Choudhary
Akhil Choudhary
Numerade Educator
05:25

Problem 32

A study was performed in Lebanon looking at the effect of widowhood on mortality [14] . Each of 151 widowers and 544 widows were matched to a person married at the time of widowhood and of the same age $(\pm 2$ years) and gender. The people in the matched pairs were followed until one member of the matched pair died. The results in Table 10.27 were obtained for those matched pairs in which at least one member had died by 1980 .
Suppose all the matched pairs in Table 10.27 are considered. What method of analysis can be used to test whether there is an association between widowhood and mortality?

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:25

Problem 33

A study was performed in Lebanon looking at the effect of widowhood on mortality [14] . Each of 151 widowers and 544 widows were matched to a person married at the time of widowhood and of the same age $(\pm 2$ years) and gender. The people in the matched pairs were followed until one member of the matched pair died. The results in Table 10.27 were obtained for those matched pairs in which at least one member had died by 1980 .
Implement the test in Problem $10.32,$ and report a $p$ -value.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:25

Problem 34

A study was performed in Lebanon looking at the effect of widowhood on mortality [14] . Each of 151 widowers and 544 widows were matched to a person married at the time of widowhood and of the same age $(\pm 2$ years) and gender. The people in the matched pairs were followed until one member of the matched pair died. The results in Table 10.27 were obtained for those matched pairs in which at least one member had died by 1980 .
Answer the same question as Problem 10.32 considering $36-$ to 45 -year-old males only.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:25

Problem 35

A study was performed in Lebanon looking at the effect of widowhood on mortality [14] . Each of 151 widowers and 544 widows were matched to a person married at the time of widowhood and of the same age $(\pm 2$ years) and gender. The people in the matched pairs were followed until one member of the matched pair died. The results in Table 10.27 were obtained for those matched pairs in which at least one member had died by 1980 .
Implement the test in Problem $10.34,$ and report a $p$ -value.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:25

Problem 36

A study was performed in Lebanon looking at the effect of widowhood on mortality [14] . Each of 151 widowers and 544 widows were matched to a person married at the time of widowhood and of the same age $(\pm 2$ years) and gender. The people in the matched pairs were followed until one member of the matched pair died. The results in Table 10.27 were obtained for those matched pairs in which at least one member had died by 1980 .
Based on all matched pairs, how much power did the study just mentioned have vs. the alternative hypothesis that a widower is twice as likely to die before a married person of the same age and gender, assuming that all age groups are considered?

Raymond Matshanda
Raymond Matshanda
Numerade Educator
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Problem 37

What test procedure can be used to compare the percentage of hens whose pancreatic secretions increased (post-pre) among the five treatment regimens?

Victor Salazar
Victor Salazar
Numerade Educator
01:53

Problem 38

Implement the test procedure in Problem $10.37,$ and report a $p$ -value.

Carolyn Behr-Jerome
Carolyn Behr-Jerome
Numerade Educator
00:39

Problem 39

Answer Problem 10.38 for biliary secretions.

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
00:30

Problem 40

For all hormone groups except saline, different doses of hormones were administered to different groups of hens. Is there a dose-response relationship between the proportion of hens with increasing pancreatic secretions and the hormone dose? This should be assessed separately for each specific active hormone.

Aadit Sharma
Aadit Sharma
Numerade Educator
00:39

Problem 41

Answer Problem 10.40 for biliary secretions.

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
02:18

Problem 42

A secondary prevention trial of lipid lowering is planned in patients with previous myocardial infarction (MI). Patients are to be randomized to either a treatment group receiving diet therapy and cholesterol-lowering drugs or a control group receiving diet therapy and placebo pills. The study endpoint is to be a combined endpoint consisting of either definite fatal coronary heart disease (CHD) or nonfatal MI (i.e., a new nonfatal Ml distinct from previous events). Suppose it is projected that the incidence of combined events among controls is $7 \%$ per year.
What proportion of controls will have events over 5 years? Hint: Assume no deaths due to non-CHD causes. Suppose the treatment benefit is projected to be a reduction in the 5 -year event rate by $30 \%$

Jameson Kuper
Jameson Kuper
Numerade Educator
01:10

Problem 43

A secondary prevention trial of lipid lowering is planned in patients with previous myocardial infarction (MI). Patients are to be randomized to either a treatment group receiving diet therapy and cholesterol-lowering drugs or a control group receiving diet therapy and placebo pills. The study endpoint is to be a combined endpoint consisting of either definite fatal coronary heart disease (CHD) or nonfatal MI (i.e., a new nonfatal Ml distinct from previous events). Suppose it is projected that the incidence of combined events among controls is $7 \%$ per year.
What is the expected event rate in the treated group?

Tyler Moulton
Tyler Moulton
Numerade Educator
02:29

Problem 44

A secondary prevention trial of lipid lowering is planned in patients with previous myocardial infarction (MI). Patients are to be randomized to either a treatment group receiving diet therapy and cholesterol-lowering drugs or a control group receiving diet therapy and placebo pills. The study endpoint is to be a combined endpoint consisting of either definite fatal coronary heart disease (CHD) or nonfatal MI (i.e., a new nonfatal Ml distinct from previous events). Suppose it is projected that the incidence of combined events among controls is $7 \%$ per year.
If the rates in Problems 10.42 and 10.43 are the true rates, how many participants will be needed in each group if a one-sided test with $\alpha=.05$ is to be used and an $80 \%$ chance of finding a significant difference is desired? Investigators expect that not all participants will comply. In particular, they project that $5 \%$ of the treatment group will not comply with drug therapy and that $10 \%$ of the control group will start taking cholesterol-lowering drugs outside the study.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
02:18

Problem 45

A secondary prevention trial of lipid lowering is planned in patients with previous myocardial infarction (MI). Patients are to be randomized to either a treatment group receiving diet therapy and cholesterol-lowering drugs or a control group receiving diet therapy and placebo pills. The study endpoint is to be a combined endpoint consisting of either definite fatal coronary heart disease (CHD) or nonfatal MI (i.e., a new nonfatal Ml distinct from previous events). Suppose it is projected that the incidence of combined events among controls is $7 \%$ per year.
What will be the expected rates in Problems 10.42 and 10.43 if this level of lack of compliance is realized?

Jameson Kuper
Jameson Kuper
Numerade Educator
01:10

Problem 46

A secondary prevention trial of lipid lowering is planned in patients with previous myocardial infarction (MI). Patients are to be randomized to either a treatment group receiving diet therapy and cholesterol-lowering drugs or a control group receiving diet therapy and placebo pills. The study endpoint is to be a combined endpoint consisting of either definite fatal coronary heart disease (CHD) or nonfatal MI (i.e., a new nonfatal Ml distinct from previous events). Suppose it is projected that the incidence of combined events among controls is $7 \%$ per year.
What will be the revised sample size estimate in Problem 10.44 if the lack of compliance is taken into account?

Tyler Moulton
Tyler Moulton
Numerade Educator
02:27

Problem 47

A study was performed among 40 boys in a school in Edinburgh to look at the presence of spermatozoa in urine samples according to age $[15] .$ The boys entered the study at $8-11$ years of age and left the study at $12-18$ years of age. A 24-hour urine sample was supplied every 3 months by each boy. Table 10.28 gives the presence or absence of sperm cells in the urine samples for each boy together with the ages at entrance and exit of the study and the age at the first sperm-positive urine sample.
For all parts of this question, exclude boys who exited this study without 1 sperm-positive urine sample (i.e., boys 8,9,14,25,28,29,30)
Provide a stem-and-leaf plot of the age at first sperm-positive urine specimen.

James Kiss
James Kiss
Numerade Educator
01:44

Problem 48

A study was performed among 40 boys in a school in Edinburgh to look at the presence of spermatozoa in urine samples according to age $[15] .$ The boys entered the study at $8-11$ years of age and left the study at $12-18$ years of age. A 24-hour urine sample was supplied every 3 months by each boy. Table 10.28 gives the presence or absence of sperm cells in the urine samples for each boy together with the ages at entrance and exit of the study and the age at the first sperm-positive urine sample.
For all parts of this question, exclude boys who exited this study without 1 sperm-positive urine sample (i.e., boys 8,9,14,25,28,29,30)
If we assume that all boys have no sperm cells at age $11(11.0 \text { years) and all have sperm cells at age } 18$ then estimate the probability of first developing sperm cells at ages 12 (i.e., between 12.0 and 12.9 years), 13,14,15
$16,$ and 17

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:27

Problem 49

A study was performed among 40 boys in a school in Edinburgh to look at the presence of spermatozoa in urine samples according to age $[15] .$ The boys entered the study at $8-11$ years of age and left the study at $12-18$ years of age. A 24-hour urine sample was supplied every 3 months by each boy. Table 10.28 gives the presence or absence of sperm cells in the urine samples for each boy together with the ages at entrance and exit of the study and the age at the first sperm-positive urine sample.
For all parts of this question, exclude boys who exited this study without 1 sperm-positive urine sample (i.e., boys 8,9,14,25,28,29,30)
Suppose mean age at spermatogenesis = 13.67 years, with standard deviation $=0.89$ years and we assume that the age at spermatogenesis follows a normal distribution. The pediatrician would like to know what is the earliest age (in months) before which $95 \%$ of boys experience spermatogenesis because he or she would like to refer boys who haven't experienced spermatogenesis by this age to a specialist for further follow-up. Can you estimate this age from the information provided in this part of the problem?

James Kiss
James Kiss
Numerade Educator
02:27

Problem 50

A study was performed among 40 boys in a school in Edinburgh to look at the presence of spermatozoa in urine samples according to age $[15] .$ The boys entered the study at $8-11$ years of age and left the study at $12-18$ years of age. A 24-hour urine sample was supplied every 3 months by each boy. Table 10.28 gives the presence or absence of sperm cells in the urine samples for each boy together with the ages at entrance and exit of the study and the age at the first sperm-positive urine sample.
For all parts of this question, exclude boys who exited this study without 1 sperm-positive urine sample (i.e., boys 8,9,14,25,28,29,30)
Suppose we are uncertain whether a normal distribution provides a good fit to the distribution of age at spermatogenesis. Answer this question using the results from Problems $10.47-10.49 .$ (Assume that the large-sample method discussed in this chapter is applicable to these data.)

James Kiss
James Kiss
Numerade Educator
02:35

Problem 51

In the Harvard Medical Practice Study $[16],$ a sample of 31,429 medical records of hospital patients were reviewed to assess the frequency of medical malpractice. Two types of malpractice were identified:
(1) An adverse event was defined as an injury caused by medical management (rather than by the underlying disease).
(2) Negligence was defined as care that fell below the standard expected of physicians in the community.
An approximate $1 \%$ sample of records was reviewed on two different occasions by different review teams. The data in Table 10.29 were obtained.
Are frequencies of reporting of adverse events or negligence comparable in review process A (the original review) and review process B (the re-review)?

Bailey Brooks
Bailey Brooks
Numerade Educator
02:35

Problem 52

In the Harvard Medical Practice Study $[16],$ a sample of 31,429 medical records of hospital patients were reviewed to assess the frequency of medical malpractice. Two types of malpractice were identified:
(1) An adverse event was defined as an injury caused by medical management (rather than by the underlying disease).
(2) Negligence was defined as care that fell below the standard expected of physicians in the community.
An approximate $1 \%$ sample of records was reviewed on two different occasions by different review teams. The data in Table 10.29 were obtained.
Can you assess the reproducibility of adverse events and negligence designations? Which seems to be more reproducible?

Bailey Brooks
Bailey Brooks
Numerade Educator
02:39

Problem 53

A study was performed among subjects with persistent sciatica (El Barzouhi et al. [17]). Sciatica is pain that radiates down the leg and is often caused by a hemiated disk in the lumbar region of the lower back. A randomized trial was conducted comparing an early surgery strategy vs. conservative care for an additional 6 months followed by surgery for patients who did not improve. Of the 267 patients eligible for the study, 131 were randomly assigned to undergo early surgery and 136 to prolonged conservative care. Of the 131 patients in the surgery group, 15 recovered before surgery could be performed. Of the 136 patients in the conservative care group, 54 actually underwent surgery in the first year. Thus, a total of $(131-15)+54=170$ patients actually received surgery and $15+(136-54)=97$ patients received no surgery. The primary results were presented based on treatment actually received.

An MRI was performed at 1 year of follow-up to determine whether disk herniation was present and, if so, the extent of herniation compared to baseline. Definite disk herniation was present for 15 patients who received surgery and for 25 patients who received no surgery.
What test can be performed to compare the prevalence of disk herniation between the patients who received surgery vs. the patients who did not receive surgery?

Sophie Knight
Sophie Knight
Numerade Educator
02:39

Problem 54

A study was performed among subjects with persistent sciatica (El Barzouhi et al. [17]). Sciatica is pain that radiates down the leg and is often caused by a hemiated disk in the lumbar region of the lower back. A randomized trial was conducted comparing an early surgery strategy vs. conservative care for an additional 6 months followed by surgery for patients who did not improve. Of the 267 patients eligible for the study, 131 were randomly assigned to undergo early surgery and 136 to prolonged conservative care. Of the 131 patients in the surgery group, 15 recovered before surgery could be performed. Of the 136 patients in the conservative care group, 54 actually underwent surgery in the first year. Thus, a total of $(131-15)+54=170$ patients actually received surgery and $15+(136-54)=97$ patients received no surgery. The primary results were presented based on treatment actually received.

An MRI was performed at 1 year of follow-up to determine whether disk herniation was present and, if so, the extent of herniation compared to baseline. Definite disk herniation was present for 15 patients who received surgery and for 25 patients who received no surgery.
Perform the test in Problem $10.53,$ and report a twosided $p$ -value.

Sophie Knight
Sophie Knight
Numerade Educator
02:39

Problem 55

A study was performed among subjects with persistent sciatica (El Barzouhi et al. [17]). Sciatica is pain that radiates down the leg and is often caused by a hemiated disk in the lumbar region of the lower back. A randomized trial was conducted comparing an early surgery strategy vs. conservative care for an additional 6 months followed by surgery for patients who did not improve. Of the 267 patients eligible for the study, 131 were randomly assigned to undergo early surgery and 136 to prolonged conservative care. Of the 131 patients in the surgery group, 15 recovered before surgery could be performed. Of the 136 patients in the conservative care group, 54 actually underwent surgery in the first year. Thus, a total of $(131-15)+54=170$ patients actually received surgery and $15+(136-54)=97$ patients received no surgery. The primary results were presented based on treatment actually received.

An MRI was performed at 1 year of follow-up to determine whether disk herniation was present and, if so, the extent of herniation compared to baseline. Definite disk herniation was present for 15 patients who received surgery and for 25 patients who received no surgery.
Interpret the results in Problem 10.54 in words. The investigators also assessed clinical outcomes for the patients at 1 year. They defined a favorable outcome as a complete or nearly complete disappearance of symptoms on a patient-reported Likert scale for global perceived recovery. One of the paradoxes of sciatica is that sometimes patients perceive less pain even if MRI findings have

Sophie Knight
Sophie Knight
Numerade Educator
05:47

Problem 56

not changed. A comparison was made between the patientreported favorable outcome and change in the MRI assessment of extent of nerve root compression (1 yr. vs. baseline). The results were as follows:

Among 224 patients with a favorable outcome, nerve root compression had disappeared completely at 1 year for 169 patients, was present at 1 year but reduced from baseline for 39 patients, and was unchanged or increased from baseline for 16 patients. Among 43 patients with an unfavorable outcome, nerve root compression had disappeared completely at 1 year for 29 patients, was present at 1 year but reduced from baseline for 6 patients, and was unchanged or increased from baseline for 8 patients.
What test can be performed to assess the association between change in nerve root compression and clinical outcome?

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
05:47

Problem 57

not changed. A comparison was made between the patientreported favorable outcome and change in the MRI assessment of extent of nerve root compression (1 yr. vs. baseline). The results were as follows:

Among 224 patients with a favorable outcome, nerve root compression had disappeared completely at 1 year for 169 patients, was present at 1 year but reduced from baseline for 39 patients, and was unchanged or increased from baseline for 16 patients. Among 43 patients with an unfavorable outcome, nerve root compression had disappeared completely at 1 year for 29 patients, was present at 1 year but reduced from baseline for 6 patients, and was unchanged or increased from baseline for 8 patients.
Perform the test in Problem 10.56 , and report a two-sided $p$ -value.

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
05:47

Problem 58

not changed. A comparison was made between the patientreported favorable outcome and change in the MRI assessment of extent of nerve root compression (1 yr. vs. baseline). The results were as follows:

Among 224 patients with a favorable outcome, nerve root compression had disappeared completely at 1 year for 169 patients, was present at 1 year but reduced from baseline for 39 patients, and was unchanged or increased from baseline for 16 patients. Among 43 patients with an unfavorable outcome, nerve root compression had disappeared completely at 1 year for 29 patients, was present at 1 year but reduced from baseline for 6 patients, and was unchanged or increased from baseline for 8 patients.
Interpret the results in Problem 10.57 in words.

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
02:07

Problem 59

Members of several tennis clubs in the greater Boston area were surveyed. Each participant was asked whether he or she had ever had tennis elbow and, if so, how many episodes. An attempt was made to enroll roughly an equal number of participants with at least one episode of tennis elbow (the cases) and participants with no episodes of tennis elbow (the controls). The interviewer asked the participants about other possibly related factors, including demographic factors (e.g., age, gender) and characteristics of their tennis racquet (e.g., string type of racquet used, material(s) of racquet). This type of study is a case-control study and also can be considered as an observational study. It is distinctly different from a clinical trial, in which treatments are assigned at random. Because of randomization, participants receiving different treatments in a clinical trial will, on average, tend to be comparable. In an observational study, we are interested in relating risk factors to disease outcomes. However, it is difficult to make causal inferences (e.g.. "wood racquets cause tennis elbow") because participants are not assigned to a type of racquet at random. Indeed, if we find differences in the frequency of tennis elbow by type of racquet, there may be some other variable(s) that are related to both tennis elbow and to the type of racquet that are more direct "causes" of tennis elbow. Nevertheless, observational studies are useful in obtaining important clues as to disease etiology. One interesting aspect of observational studies is that there are often no prior leads as to which risk factors are even associated with disease. Therefore, investigators tend to ask many questions about possible risk factors without having a firm idea as to which risk factors are really important.
In this problem, act like a detective and look at each risk factor in the data set separately and relate this risk factor to tennis elbow. How you define tennis elbow is somewhat arbitrary. You may want to compare participants with $1+$ episodes of tennis elbow vs. participants with no episodes. Or you may want to focus specifically on participants with multiple episodes of tennis elbow, or perhaps create a graded scale according to the number of episodes of tennis elbow (e.g., 0 episodes, 1 episode, 2+ episodes), etc. In this exercise, consider each risk factor separately. In Chapter $13,$ we will discuss logistic regression methods, where we will be able to study the effects of more than one risk factor simultaneously on disease.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:19

Problem 60

For children with one affected ear at baseline, compare the efficacy of the two study medications.

Eric Goldman
Eric Goldman
Numerade Educator
02:44

Problem 61

In children with two affected ears at baseline, compare the efficacy of the two study medications, treating the response at 14 days as a graded scale (two cleared ears, one cleared ear, no cleared ears).

John Barone
John Barone
Numerade Educator
00:48

Problem 62

For children with two affected ears, test the hypothesis that responses to the study medications for the first and second ears are independent.

Lucas Finney
Lucas Finney
Numerade Educator
01:02

Problem 63

Death of a patient in the hospital is a high-priority medical outcome. Some hospital deaths may be due to inadequate care and are potentially preventable. An adverse event during a hospital stay is defined as a problem of any nature and seriousness experienced by a patient during his or her stay in the hospital that is potentially attributable to clinical or administrative management rather than the underlying disease. A study in a hospital in Granada, Spain, assessed whether there was a relationship between adverse events and deaths during hospital stay $[18] .$ In this study, 524 cases (i.e., people who died in the hospital) were identified between January $1,1990,$ and January $1,1991 .$ For each case, a control patient was matched on admission diagnosis and admission date. A retrospective chart review determined occurrence of adverse events among all cases and controls. There were 299 adverse events occurring among the cases and 225 among the controls. Among the 299 cases in which an adverse event occurred, 126 of their corresponding matched controls also had an adverse event.
What method of analysis can be used to compare the proportion of adverse events between cases and controls?

Akhil Choudhary
Akhil Choudhary
Numerade Educator
01:02

Problem 64

Death of a patient in the hospital is a high-priority medical outcome. Some hospital deaths may be due to inadequate care and are potentially preventable. An adverse event during a hospital stay is defined as a problem of any nature and seriousness experienced by a patient during his or her stay in the hospital that is potentially attributable to clinical or administrative management rather than the underlying disease. A study in a hospital in Granada, Spain, assessed whether there was a relationship between adverse events and deaths during hospital stay $[18] .$ In this study, 524 cases (i.e., people who died in the hospital) were identified between January $1,1990,$ and January $1,1991 .$ For each case, a control patient was matched on admission diagnosis and admission date. A retrospective chart review determined occurrence of adverse events among all cases and controls. There were 299 adverse events occurring among the cases and 225 among the controls. Among the 299 cases in which an adverse event occurred, 126 of their corresponding matched controls also had an adverse event.
Implement the method suggested in Problem 10.63 and report a two-tailed $p$ -value.

Akhil Choudhary
Akhil Choudhary
Numerade Educator
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Problem 65

A topic of current interest is whether abortion is a risk factor for breast cancer. One issue is whether women who have had abortions are comparable to women who have not had abortions in terms of other breast-cancer risk factors. One of the best-known breast-cancer risk factors is parity (i.e., number of children), with parous women with many children having about a $30 \%$ lower risk of breast cancer than nulliparous women (i.e., women with no children). Hence, it is important to assess whether the parity distributions of women with and without previous abortions are comparable. The data in Table 10.30 were obtained from the Nurses' Health Study on this issue.
What test can be performed to compare the parity distribution of women with and without induced abortions?

Roee Shalom
Roee Shalom
Numerade Educator
View

Problem 66

A topic of current interest is whether abortion is a risk factor for breast cancer. One issue is whether women who have had abortions are comparable to women who have not had abortions in terms of other breast-cancer risk factors. One of the best-known breast-cancer risk factors is parity (i.e., number of children), with parous women with many children having about a $30 \%$ lower risk of breast cancer than nulliparous women (i.e., women with no children). Hence, it is important to assess whether the parity distributions of women with and without previous abortions are comparable. The data in Table 10.30 were obtained from the Nurses' Health Study on this issue.
Implement the test in Problem $10.65,$ and report a two-tailed $p$ -value. Suppose that with each additional child, breast-cancer risk is reduced by $10 \%$ (i.e., women with 1 child have a risk of breast cancer that is $90 \%$ of that of a nulliparous woman of the same age; women with 2 children have a risk that is $.9^{2}$ or $81 \%$ of that of a nulliparous woman, etc.). (For the purposes of this problem, consider women with 4+ births as having exactly 4 births.)

Roee Shalom
Roee Shalom
Numerade Educator
View

Problem 67

A topic of current interest is whether abortion is a risk factor for breast cancer. One issue is whether women who have had abortions are comparable to women who have not had abortions in terms of other breast-cancer risk factors. One of the best-known breast-cancer risk factors is parity (i.e., number of children), with parous women with many children having about a $30 \%$ lower risk of breast cancer than nulliparous women (i.e., women with no children). Hence, it is important to assess whether the parity distributions of women with and without previous abortions are comparable. The data in Table 10.30 were obtained from the Nurses' Health Study on this issue.
Suppose there is no causal effect of induced abortion on breast cancer. Based on the parity distribution in the two groups, would women with induced abortion be expected to have the same, higher, or lower risk of breast cancer? If higher or lower, by how much? (Assume that the age distributions are the same between women who have or have not had previous abortions.)

Roee Shalom
Roee Shalom
Numerade Educator
03:53

Problem 68

A 5 -year study among 601 participants with retinitis pigmentosa assessed the effects of high-dose vitamin A (15,000 IU per day) and vitamin $E(400$ IU per day) on the course of their disease. One issue is to what extent supplementation with vitamin A affected their serum-retinol levels. The serum-retinol data in Table 10.31 were obtained over
3 years of follow-up among 73 males taking 15,000 IU/day of vitamin A (vitamin A group) and among 57 males taking
75 IU/day of vitamin A (the trace group; this is a negligible amount compared with usual dietary intake of 3000 IU/day).
What test can be used to assess whether mean serum retinol has increased over 3 years among subjects in the vitamin A group?

Mark Tingey
Mark Tingey
Numerade Educator
03:33

Problem 69

A 5 -year study among 601 participants with retinitis pigmentosa assessed the effects of high-dose vitamin A (15,000 IU per day) and vitamin $E(400$ IU per day) on the course of their disease. One issue is to what extent supplementation with vitamin A affected their serum-retinol levels. The serum-retinol data in Table 10.31 were obtained over
3 years of follow-up among 73 males taking 15,000 IU/day of vitamin A (vitamin A group) and among 57 males taking
75 IU/day of vitamin A (the trace group; this is a negligible amount compared with usual dietary intake of 3000 IU/day).
Can the test be implemented based on the data just presented? Why or why not? If yes, implement the test and report a two-tailed $p$ -value.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
10:51

Problem 70

A 5 -year study among 601 participants with retinitis pigmentosa assessed the effects of high-dose vitamin A (15,000 IU per day) and vitamin $E(400$ IU per day) on the course of their disease. One issue is to what extent supplementation with vitamin A affected their serum-retinol levels. The serum-retinol data in Table 10.31 were obtained over
3 years of follow-up among 73 males taking 15,000 IU/day of vitamin A (vitamin A group) and among 57 males taking
75 IU/day of vitamin A (the trace group; this is a negligible amount compared with usual dietary intake of 3000 IU/day).
One assumption of the test in Problem 10.68 is that the distribution of serum retinol is approximately normal. To verify this assumption, the investigators obtained a frequency distribution of serum retinol at year 0 among males in the vitamin A group, with data as shown in Table 10.32

Robin Corrigan
Robin Corrigan
Numerade Educator
10:00

Problem 71

One interesting aspect of the study described in Problem 10.68 is to assess changes in other parameters as a result of supplementation with vitamin A. One quantity of interest is the level of serum triglycerides. Researchers found that among 133 participants in the vitamin A group (males and females combined) who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 15$ were above the upper limit of normal at each of their last 2 consecutive study visits. Similarly, among 138 participants in the trace group who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 2$ were above the upper limit of normal at each of their last two consecutive study visits [19]
What proportion of people in each group developed abnormal triglyceride levels over the course of the study? Are these proportions measures of prevalence, incidence, or neither?

Ryan Mcalister
Ryan Mcalister
Numerade Educator
01:51

Problem 72

One interesting aspect of the study described in Problem 10.68 is to assess changes in other parameters as a result of supplementation with vitamin A. One quantity of interest is the level of serum triglycerides. Researchers found that among 133 participants in the vitamin A group (males and females combined) who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 15$ were above the upper limit of normal at each of their last 2 consecutive study visits. Similarly, among 138 participants in the trace group who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 2$ were above the upper limit of normal at each of their last two consecutive study visits [19]
What test can be performed to compare the percentage of participants who developed abnormal triglyceride levels between the vitamin A group and the trace group?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
01:51

Problem 73

One interesting aspect of the study described in Problem 10.68 is to assess changes in other parameters as a result of supplementation with vitamin A. One quantity of interest is the level of serum triglycerides. Researchers found that among 133 participants in the vitamin A group (males and females combined) who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 15$ were above the upper limit of normal at each of their last 2 consecutive study visits. Similarly, among 138 participants in the trace group who were in the normal range at baseline $(<2.13 \mu \mathrm{mol} / \mathrm{L}), 2$ were above the upper limit of normal at each of their last two consecutive study visits [19]
Implement the test in Problem $10.72,$ and report a two-tailed $p$ -value.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
02:46

Problem 74

A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird feeders were set up with different types of sunflower seeds, one with a black oil seed and one with a striped seed. The bird feeders were observed for a 1 -hour period for each of 12 days over a 1 -month period. The number of birds of different species who ate seeds from a specific bird feeder was counted for each bird feeder for each of a number of species of birds. (The data for this problem were supplied by David Rosner.)
On the first day of testing, 1 titmouse ate the black oil seeds and 4 titmice ate the striped seeds. Of the goldfinches, 19 ate the black oil seeds and 5 ate the striped seeds.
What test can be performed to assess whether the feeding preferences of titmice and goldfinches are comparable on the first day of testing?

Bryan Meares
Bryan Meares
Numerade Educator
02:46

Problem 75

A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird feeders were set up with different types of sunflower seeds, one with a black oil seed and one with a striped seed. The bird feeders were observed for a 1 -hour period for each of 12 days over a 1 -month period. The number of birds of different species who ate seeds from a specific bird feeder was counted for each bird feeder for each of a number of species of birds. (The data for this problem were supplied by David Rosner.)
On the first day of testing, 1 titmouse ate the black oil seeds and 4 titmice ate the striped seeds. Of the goldfinches, 19 ate the black oil seeds and 5 ate the striped seeds.
Implement the test in Problem $10.74,$ and report a $p$ -value.

Bryan Meares
Bryan Meares
Numerade Educator
03:04

Problem 76

One assumption in the entire experiment is that the feeding preferences of the same species of bird remain the same over time. To test this assumption, the data for goldfinches were separated by the 6 different days on which they were observed (they were not observed at all for the other 6 days). For 2 of the 6 days small numbers of goldfinches were observed (2 on one day and 1 on another day). Thus, data from these two days were also not included. The results for the remaining 4 days are shown in Table 10.3310.76 What test can be used to assess whether the feeding preference of goldfinches are the same on different days?
What test can be used to assess whether the feeding preference of goldfinches are the same on different days?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
08:09

Problem 77

One assumption in the entire experiment is that the feeding preferences of the same species of bird remain the same over time. To test this assumption, the data for goldfinches were separated by the 6 different days on which they were observed (they were not observed at all for the other 6 days). For 2 of the 6 days small numbers of goldfinches were observed (2 on one day and 1 on another day). Thus, data from these two days were also not included. The results for the remaining 4 days are shown in Table 10.33
Implement the test in Problem $10.76,$ and report a $p$ -value.

Ryan Mcalister
Ryan Mcalister
Numerade Educator
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Problem 78

The Physicians' Health Study was a randomized doubleblind placebo-controlled trial of beta-carotene (50 mg every other day). In $1982,$ the study enrolled 22,071 male physicians ages $40-84$. The participants were followed until December $31,1995,$ for the development of new cancers (malignant neoplasms). The results reported [20] are shown in Table 10.34
What test can be used to compare cancer incidence rates between the two treatment groups?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
View

Problem 79

The Physicians' Health Study was a randomized doubleblind placebo-controlled trial of beta-carotene (50 mg every other day). In $1982,$ the study enrolled 22,071 male physicians ages $40-84$. The participants were followed until December $31,1995,$ for the development of new cancers (malignant neoplasms). The results reported [20] are shown in Table 10.34
Implement the test in Problem $10.78,$ and report a two-tailed $p$ -value.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
View

Problem 80

The Physicians' Health Study was a randomized doubleblind placebo-controlled trial of beta-carotene (50 mg every other day). In $1982,$ the study enrolled 22,071 male physicians ages $40-84$. The participants were followed until December $31,1995,$ for the development of new cancers (malignant neoplasms). The results reported [20] are shown in Table 10.34
The expectation before the study started was that beta-carotene might prevent $10 \%$ of incident cancers relative to placebo. How much power did the study have to detect an effect of this magnitude if a two-sided test is used with $\alpha=.05$ and we assume that the true incidence rate in the placebo group is the same as the observed incidence rate and that compliance with study medications is perfect?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:03

Problem 81

A common assumption is that the gender distributions of successive offspring are independent. To test this assumption, birth records were collected from the first 5 births in 51,868 families. For families with exactly 5 children, Table 10.35 shows a frequency distribution of the number of male offs pring (from Data Set SEXRAT.DAT; see p. 110).
Suppose the investigators doubt the probability of a male birth is exactly $50 \%$ but are willing to assume the gender distributions of successive offspring are independent.
What is the best estimate of the probability of a male offspring based on the observed data?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
03:03

Problem 82

A common assumption is that the gender distributions of successive offspring are independent. To test this assumption, birth records were collected from the first 5 births in 51,868 families. For families with exactly 5 children, Table 10.35 shows a frequency distribution of the number of male offs pring (from Data Set SEXRAT.DAT; see p. 110).
Suppose the investigators doubt the probability of a male birth is exactly $50 \%$ but are willing to assume the gender distributions of successive offspring are independent.
What is the probability of $0,1,2,3,4,$ and 5 male offspring out of 5 births based on the estimate in Problem $10.81 ?$

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
01:54

Problem 83

A common assumption is that the gender distributions of successive offspring are independent. To test this assumption, birth records were collected from the first 5 births in 51,868 families. For families with exactly 5 children, Table 10.35 shows a frequency distribution of the number of male offs pring (from Data Set SEXRAT.DAT; see p. 110).
Suppose the investigators doubt the probability of a male birth is exactly $50 \%$ but are willing to assume the gender distributions of successive offspring are independent.
Test the hypothesis that the gender distributions of successive offspring are independent based on the model in Problem $10.82 .$ What are your conclusions concerning the hypothesis?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:58

Problem 84

Nighttime bladder control is an important developmental milestone, with failure dependent on age. Continence is usually achieved between 4 and 6 years of age, but an important minority of children experience delays in success. A longitudinal study was conducted in Britain in which nighttime bedwetting was assessed at ages $4,6,8,9,11,$ and 15 years among 3272 children in the Medical Research Council's 1946 National Survey of Health [21]. The following data were presented. There were 1362 boys and 1313 girls who reported no bedwetting at any of the six ages just listed. Consider this as the control group. There were 6 boys and 2 girls who reported no bedwetting at ages $4,6,$ and 8 but reported some bedwetting at both ages 9 and $11 .$ Consider this as the case group. Ignore children with any other pattern of bedwetting over the six ages.
What test can be used to assess whether the percentage of cases among boys is significantly different from the percentage of cases among girls?

Qudsiya Anis
Qudsiya Anis
Numerade Educator
00:22

Problem 85

Nighttime bladder control is an important developmental milestone, with failure dependent on age. Continence is usually achieved between 4 and 6 years of age, but an important minority of children experience delays in success. A longitudinal study was conducted in Britain in which nighttime bedwetting was assessed at ages $4,6,8,9,11,$ and 15 years among 3272 children in the Medical Research Council's 1946 National Survey of Health [21]. The following data were presented. There were 1362 boys and 1313 girls who reported no bedwetting at any of the six ages just listed. Consider this as the control group. There were 6 boys and 2 girls who reported no bedwetting at ages $4,6,$ and 8 but reported some bedwetting at both ages 9 and $11 .$ Consider this as the case group. Ignore children with any other pattern of bedwetting over the six ages.
Implement the test in Problem $10.84,$ and report a two-tailed $p$ -value.

Simon Sauvageau
Simon Sauvageau
Numerade Educator
04:00

Problem 86

A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and $15.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area or
ii. a late start group, where dialysis was initiated when their GFR was 5.0 to $7.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area.The primary outcome was total mortality. There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years.
What test can be used to compare the mortality rates in the two groups?

Stanley Enemuo
Stanley Enemuo
Numerade Educator
04:00

Problem 87

A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and $15.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area or
ii. a late start group, where dialysis was initiated when their GFR was 5.0 to $7.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area.The primary outcome was total mortality. There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years.
Implement the test in Problem $10.86,$ and report a two-sided $p$ -value. In planning the study it was anticipated that 400 subjects would be enrolled per group and that the 3 -year mortality risk would be $36 \%$ in the late start group and $26 \%$ in the early start group.

Stanley Enemuo
Stanley Enemuo
Numerade Educator
04:00

Problem 88

A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and $15.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area or
ii. a late start group, where dialysis was initiated when their GFR was 5.0 to $7.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area.The primary outcome was total mortality. There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years.
How much power would the study have if it had occurred under the planned mortality rates and sample size?
One issue is that not all the late start patients actually started dialysis when their GFR was between 5.0 and 7.0 . Indeed, $75 \%$ of the late start patients initiated dialysis at a GFR $>7.0$ due to symptoms.

Stanley Enemuo
Stanley Enemuo
Numerade Educator
04:00

Problem 89

A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and $15.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area or
ii. a late start group, where dialysis was initiated when their GFR was 5.0 to $7.0 \mathrm{mL}$ per minute per $1.73 \mathrm{m}^{2}$ of body surface area.The primary outcome was total mortality. There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years.
If we assume that these $75 \%$ of patients had a mortality rate that was the average of the early start and late start groups (i.e., $31 \%$ ), then how much power did the study actually have under the same assumptions as in Problem 10.88?

Stanley Enemuo
Stanley Enemuo
Numerade Educator
02:44

Problem 90

Acute OTM early in infancy may be an important predictor of subsequent morbidity, including psychological and educational difficulties. A study was performed among high-risk infants who had already experienced either a single episode of acute OTM prior to the age of 6 months or two or more episodes before 12 months of life [23] Children were randomized to one of three treatment groups,
(a) amoxicillin (AMX), (b) sulfisoxazole (SUL), or (c) placebo (PLA), and their parents were told to administer the drug daily for a 6 -month period (even in the absence of symptoms). If children had an acute OTM episode during the study period, they received the best antibiotic care, regardless of their study-drug group. The results were as shown in Table 10.36
What test can be used to compare the percentage of children who were acute OTM-free between the AMX group and the PLA group?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
01:10

Problem 91

Acute OTM early in infancy may be an important predictor of subsequent morbidity, including psychological and educational difficulties. A study was performed among high-risk infants who had already experienced either a single episode of acute OTM prior to the age of 6 months or two or more episodes before 12 months of life [23] Children were randomized to one of three treatment groups,
(a) amoxicillin (AMX), (b) sulfisoxazole (SUL), or (c) placebo (PLA), and their parents were told to administer the drug daily for a 6 -month period (even in the absence of symptoms). If children had an acute OTM episode during the study period, they received the best antibiotic care, regardless of their study-drug group. The results were as shown in Table 10.36
Perform the test in Problem $10.90,$ and report a twotailed $p$ -value. The children were followed for an additional 6 months after the study-drug period (first 6 months) was over. The results reported concerning acute OTM experience over the entire
12-month period are shown in Table 10.37 .

Tyler Moulton
Tyler Moulton
Numerade Educator
02:44

Problem 92

Acute OTM early in infancy may be an important predictor of subsequent morbidity, including psychological and educational difficulties. A study was performed among high-risk infants who had already experienced either a single episode of acute OTM prior to the age of 6 months or two or more episodes before 12 months of life [23] Children were randomized to one of three treatment groups,
(a) amoxicillin (AMX), (b) sulfisoxazole (SUL), or (c) placebo (PLA), and their parents were told to administer the drug daily for a 6 -month period (even in the absence of symptoms). If children had an acute OTM episode during the study period, they received the best antibiotic care, regardless of their study-drug group. The results were as shown in Table 10.36
Perform a test to compare the percentage acute OTM-free in the AMX group vs. the PLA group over the second 6 months of the study among children who were acute OTM-free after the first 6 months. Report a two-tailed $p$ -value.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
06:24

Problem 93

Smallpox vaccine is highly effective in immunizing against smallpox when given as late as 2 to 3 days after exposure. Smallpox vaccine is in short supply and is currently available in different dosages. A randomized double-blind study was performed to compare the efficacy of undiluted vaccine vs. different doses of diluted vaccine [24] One definition of clinical success was the formation of a vesicle at the inoculation site 7 to 9 days after vaccination. The results from the trial are shown in Table 10.38.
Perform a test to compare the success rate of undiluted vaccine vs. 1: 100 diluted vaccine. Report a two-tailed $p$ -value.

Daniel Caproni
Daniel Caproni
Numerade Educator
06:24

Problem 94

Smallpox vaccine is highly effective in immunizing against smallpox when given as late as 2 to 3 days after exposure. Smallpox vaccine is in short supply and is currently available in different dosages. A randomized double-blind study was performed to compare the efficacy of undiluted vaccine vs. different doses of diluted vaccine [24] One definition of clinical success was the formation of a vesicle at the inoculation site 7 to 9 days after vaccination. The results from the trial are shown in Table 10.38.
Perform a test to assess whether the success rate is a function of the $\log _{10}$ (dilution ratio). Report a two-tailed $p$ -value. [Note: For the 1: 10 group, $\log _{10}$ (dilution ratio) $=$ $\left.\log _{10}(1 / 10)=-1, \ldots, \text { etc. }\right]$
A more quantitative measure of efficacy was the cytotoxic T-cell response. The results are shown in Table 10.39

Daniel Caproni
Daniel Caproni
Numerade Educator
02:24

Problem 95

What test can be used to compare the cytotoxic T-cell response of the undiluted group vs. the 1: 100 diluted group?

Asma Venkitta
Asma Venkitta
Numerade Educator
03:04

Problem 96

Perform the test mentioned in Problem $10.95,$ and report a two-tailed $p$ -value. What is your conclusion regarding the effectiveness of the undiluted in contrast to the 1: 100 diluted vaccine?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:44

Problem 97

It is fairly well known that perception of weight by adolescents does not always agree with actual weight. What is less clear is whether perception of weight differs by gender. For this purpose, a study was performed among students in a local high school, where students provided their actual height and weight by self-report. The following data were obtained from 286 students $(143 \text { boys and } 143$ girls). (The data for this problem were provided by Laura Rosner.) The students were classified as underweight if their bodymass index (BMI) $\left(\mathrm{kg} / \mathrm{m}^{2}\right)$ was less than $18.0 \mathrm{kg} / \mathrm{m}^{2}$, as normal if their BMI was $\geq 18.0$ and $<25.0,$ and overweight if their BMI was $\geq 25.0$. Based on these criteria, 17 of the girls were underweight, 113 were of normal weight, and 13 were overweight. For the boys, 7 were underweight, 115 were of normal weight, and 21 were overweight.
What test procedure can be used to assess whether the weight status of boys significantly differs from girls?

Carson Merrill
Carson Merrill
Numerade Educator
02:44

Problem 98

It is fairly well known that perception of weight by adolescents does not always agree with actual weight. What is less clear is whether perception of weight differs by gender. For this purpose, a study was performed among students in a local high school, where students provided their actual height and weight by self-report. The following data were obtained from 286 students $(143 \text { boys and } 143$ girls). (The data for this problem were provided by Laura Rosner.) The students were classified as underweight if their bodymass index (BMI) $\left(\mathrm{kg} / \mathrm{m}^{2}\right)$ was less than $18.0 \mathrm{kg} / \mathrm{m}^{2}$, as normal if their BMI was $\geq 18.0$ and $<25.0,$ and overweight if their BMI was $\geq 25.0$. Based on these criteria, 17 of the girls were underweight, 113 were of normal weight, and 13 were overweight. For the boys, 7 were underweight, 115 were of normal weight, and 21 were overweight.
Perform the test procedure in Problem 10.97 , and provide a two-tailed $p$ -value.

Carson Merrill
Carson Merrill
Numerade Educator
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Problem 99

One issue in comparing BMI between groups is the underlying distribution of BMI. The mean BMI of the 143 boys was 21.8 with $s d=3.4 .$ The distribution of BMI was as shown in Table $10.40 .$
What test procedure can be used to assess whether the distribution of BMI among the boys is normal?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
04:24

Problem 100

One issue in comparing BMI between groups is the underlying distribution of BMI. The mean BMI of the 143 boys was 21.8 with $s d=3.4 .$ The distribution of BMI was as shown in Table $10.40 .$
Perform the test procedure in Problem 10.99. Provide a $p$ -value. (Assume that BMI is measured exactly with no measurement error; thus, the range $20-22.9$ includes all values $\geq 20$ and $<23$, etc.)

James Kiss
James Kiss
Numerade Educator
03:40

Problem 101

A case-control study was performed of renal-cell carcinoma (RCC) (kidney cancer) [25]. The purpose of the study was to look at environmental risk factors for RCC and to assess whether genetic factors modify the role of environmental risk factors. There were a total of 113 cases and 256 controls studied.
The participants were subdivided into "slow acetylators" and "rapid acetylators" according to the NAT2 genotype. The hypothesis was that slow acetylators might metabolize potentially toxic substances more slowly than rapid acetylators and show different relationships with environmental risk factors such as smoking. Table 10.41 presents data for slow acetylators according to the number of cigarettes smoked per day.
Test for the association between the number of cigarettes smoked per day and RCC among slow acetylators. (Report a two-tailed $p$ -value.)

Qudsiya Anis
Qudsiya Anis
Numerade Educator
00:33

Problem 102

Answer the question in Problem 10.101 for rapid acetylators. Report a two-tailed $p$ -value.

Ahmed Genedy
Ahmed Genedy
Numerade Educator
00:26

Problem 103

Do you think that genetic factors influence the relationship between smoking and RCC based on the preceding data? Why or why not?

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
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Problem 104

The effect of using postmenopausal hormones (PMH) on health outcomes is controversial. Most previous data collected have been from observational studies, and users of PMH may selectively differ from nonusers in ways that are difficult to quantify (e.g., more health conscious, more physician visits in which disease outcomes can be identified). A clinical trial was planned to randomize postmenopausal women to either PMH use or no PMH use and follow them for disease outcomes over a 10 -year period. One outcome of special interest was breast cancer. Suppose the incidence rate of breast cancer among postmenopausal 50-year-old women who do not use PMH is 200 per $10^{5}$ women per year. Suppose also it is hypothesized that PMH increases the incidence of breast cancer by 20\%.
How many women need to be studied in each group (equal sample size per group) to have an $80 \%$ probability of detecting a significant difference if a two-sided test is used with a type I error of $5 \% ?$

Shu Naito
Shu Naito
Numerade Educator
View

Problem 105

The effect of using postmenopausal hormones (PMH) on health outcomes is controversial. Most previous data collected have been from observational studies, and users of PMH may selectively differ from nonusers in ways that are difficult to quantify (e.g., more health conscious, more physician visits in which disease outcomes can be identified). A clinical trial was planned to randomize postmenopausal women to either PMH use or no PMH use and follow them for disease outcomes over a 10 -year period. One outcome of special interest was breast cancer. Suppose the incidence rate of breast cancer among postmenopausal 50-year-old women who do not use PMH is 200 per $10^{5}$ women per year. Suppose also it is hypothesized that PMH increases the incidence of breast cancer by 20\%.
Suppose that 20,000 women are recruited in each group in the actual study. How much power would the study have under the same assumptions just given?

Shu Naito
Shu Naito
Numerade Educator
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Problem 106

The effect of using postmenopausal hormones (PMH) on health outcomes is controversial. Most previous data collected have been from observational studies, and users of PMH may selectively differ from nonusers in ways that are difficult to quantify (e.g., more health conscious, more physician visits in which disease outcomes can be identified). A clinical trial was planned to randomize postmenopausal women to either PMH use or no PMH use and follow them for disease outcomes over a 10 -year period. One outcome of special interest was breast cancer. Suppose the incidence rate of breast cancer among postmenopausal 50-year-old women who do not use PMH is 200 per $10^{5}$ women per year. Suppose also it is hypothesized that PMH increases the incidence of breast cancer by 20\%.
One problem with the design is that about 20\% of the women who are randomized to PMH will not comply (i.e., will go off PMH during the trial). In addition, $10 \%$ of the participants in the control group will go on PMH on their own during the study. How much power will the study have under these revised assumptions under the simplifying assumption that this lack of compliance occurs at the beginning of the study and 20,000 women are recruited for each treatment group?

Shu Naito
Shu Naito
Numerade Educator
02:13

Problem 107

Researchers collected the following data concerning comparability of diagnoses of schizophrenia obtained from primary-care physician report as compared with proxy report (from spouses). Data were collected concerning 953 people (referred to as index subjects). The researchers found that schizophrenia was identified as present on 115 physician reports and 124 proxy reports. Both physician and proxy informants identified 34 people as positive, and they are included among the 115 and 124 individuals described.
If the physician report is considered the gold standard, what is the sensitivity and specificity of proxy reports of schizophrenia? Suppose neither the physician report nor the proxy report is considered the gold standard.

Lucas Finney
Lucas Finney
Numerade Educator
02:13

Problem 108

Researchers collected the following data concerning comparability of diagnoses of schizophrenia obtained from primary-care physician report as compared with proxy report (from spouses). Data were collected concerning 953 people (referred to as index subjects). The researchers found that schizophrenia was identified as present on 115 physician reports and 124 proxy reports. Both physician and proxy informants identified 34 people as positive, and they are included among the 115 and 124 individuals described.
Compare the percentage of subjects identified as schizophrenic by physician report with those so identified by proxy report. Perform a hypothesis test, and report a twotailed $p$ -value.

Lucas Finney
Lucas Finney
Numerade Educator
02:13

Problem 109

Researchers collected the following data concerning comparability of diagnoses of schizophrenia obtained from primary-care physician report as compared with proxy report (from spouses). Data were collected concerning 953 people (referred to as index subjects). The researchers found that schizophrenia was identified as present on 115 physician reports and 124 proxy reports. Both physician and proxy informants identified 34 people as positive, and they are included among the 115 and 124 individuals described.
Suppose there is no difference in the percentage of subjects identified as schizophrenic by physician and by proxy informants. Does this mean the two sources of information are the same for each individual? Why or why not?

Lucas Finney
Lucas Finney
Numerade Educator
02:13

Problem 110

Researchers collected the following data concerning comparability of diagnoses of schizophrenia obtained from primary-care physician report as compared with proxy report (from spouses). Data were collected concerning 953 people (referred to as index subjects). The researchers found that schizophrenia was identified as present on 115 physician reports and 124 proxy reports. Both physician and proxy informants identified 34 people as positive, and they are included among the 115 and 124 individuals described.
In a reproducibility study, researchers contacted the 953 spouses a second time 1 year later and asked them again whether the index subject was schizophrenic. There were 112 positive reports of schizophrenia obtained, of which 89 were positive on both first and second report. Compute an index of reproducibility for proxy report of schizophrenia based on these data, and provide an interpretation of what it means.

Lucas Finney
Lucas Finney
Numerade Educator
02:34

Problem 111

There were early reports that people with extensive sun exposure had a reduced risk of colorectal cancer incidence. Garland and Garland [26] hypothesized that vitamin D status accounted for this inverse association. To further study this hypothesis, a case-control study was performed relating blood levels of vitamin $D$ to the occurrence of colorectal adenoma, a precursor to colorectal cancer (Fedirko et al. [27]). Data from two case-control studies were combined, one from Minnesota (the CPRU Study) and the other from the Carolinas (the MAP Study). All patients underwent elective colonoscopy, during which the presence of adenoma was determined. In addition, patients provided a blood sample and their 25 (OH) vitamin $D_{3}$ levels were determined. Henceforth, we will refer to $25(\mathrm{OH})$ vitamin $\mathrm{D}_{3}$ levels as just vitamin $D_{3}$. since vitamin $D_{3}$ varies by season of the
What test can be performed to assess whether cases tend to have lower levels of vitamin $D_{3}$ than controls?

Lucas Finney
Lucas Finney
Numerade Educator
02:34

Problem 112

There were early reports that people with extensive sun exposure had a reduced risk of colorectal cancer incidence. Garland and Garland [26] hypothesized that vitamin D status accounted for this inverse association. To further study this hypothesis, a case-control study was performed relating blood levels of vitamin $D$ to the occurrence of colorectal adenoma, a precursor to colorectal cancer (Fedirko et al. [27]). Data from two case-control studies were combined, one from Minnesota (the CPRU Study) and the other from the Carolinas (the MAP Study). All patients underwent elective colonoscopy, during which the presence of adenoma was determined. In addition, patients provided a blood sample and their 25 (OH) vitamin $D_{3}$ levels were determined. Henceforth, we will refer to $25(\mathrm{OH})$ vitamin $\mathrm{D}_{3}$ levels as just vitamin $D_{3}$. since vitamin $D_{3}$ varies by season of the
Implement the test in Problem 10.111 , and report a two-sided $p$ -value.

Lucas Finney
Lucas Finney
Numerade Educator
02:34

Problem 113

There were early reports that people with extensive sun exposure had a reduced risk of colorectal cancer incidence. Garland and Garland [26] hypothesized that vitamin D status accounted for this inverse association. To further study this hypothesis, a case-control study was performed relating blood levels of vitamin $D$ to the occurrence of colorectal adenoma, a precursor to colorectal cancer (Fedirko et al. [27]). Data from two case-control studies were combined, one from Minnesota (the CPRU Study) and the other from the Carolinas (the MAP Study). All patients underwent elective colonoscopy, during which the presence of adenoma was determined. In addition, patients provided a blood sample and their 25 (OH) vitamin $D_{3}$ levels were determined. Henceforth, we will refer to $25(\mathrm{OH})$ vitamin $\mathrm{D}_{3}$ levels as just vitamin $D_{3}$. since vitamin $D_{3}$ varies by season of the
Interpret the results (i.e., do cases have higher, lower, or the same vitamin $D_{3}$ levels as controls?).

Lucas Finney
Lucas Finney
Numerade Educator
02:24

Problem 114

10.114 Compare the percentage of Caucasian and African American women who are overweight. Report a two-tailed $p$ -value. A more exact classification of BMI is as follows: $ < 25$ is normal; $\geq 25, < 30$ is overweight; $\geq 30$ is obese.

DG
David Gold
Numerade Educator
02:05

Problem 115

Compare the distribution of BMI between Caucasian and African American women using this finer classification. Report a two-tailed $p$ -value.

Lucas Finney
Lucas Finney
Numerade Educator
01:38

Problem 116

Suppose we are planning a clinical trial and expect a $20 \%$ success rate in the active group and a $10 \%$ success rate in the placebo group. We expect to enroll 100 participants in each group and are interested in the power of the study.
Perform a simulation study, and generate 100 participants from a binomial distribution with $p=.2$ and 100 participants from a binomial distribution with $p=.1 .$ Test to determine whether the observed sample proportion of successes are significantly different, using a two-sided test with $\alpha=.05$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
View

Problem 117

Suppose we are planning a clinical trial and expect a $20 \%$ success rate in the active group and a $10 \%$ success rate in the placebo group. We expect to enroll 100 participants in each group and are interested in the power of the study.
Repeat the Problem 10.116 simulation 1000 times, and compute the proportion of simulations in which a significant difference is found (i.e., an estimate of the power of the study).

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:29

Problem 118

What should the theoretical power be for the exer cise in Problem $10.117 ?$ How do the estimated power anc theoretical power compare?

Mayukh Banik
Mayukh Banik
Numerade Educator
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Problem 119

Aminoglycosides are powerful broad-spectrum antibiotics used for gram-negative infections often in seriously ill patients. For example, the drugs are often prescribed for drug-resistant tuberculosis as recommended by the World Health Organization. However, these drugs have serious side effects, including irreversible hearing loss referred to as ototoxicity. The most commonly prescribed aminoglycoside is gentamicin. A clinical trial was set up in China to assess whether the addition of aspirin to a standard regimen of gentamicin would have an effect on the incidence of ototoxicity [28]. There were 195 patients enrolled in a prospective, randomized, double-blind clinical trial. Of these, 106 patients were randomized to a twice daily regimen of $80-160$ mg of gentamicin plus placebo and 89 patients were randomized to receive the same regimen of gentamicin $+3 \mathrm{g}$ of aspirin (ASA) daily.
(i) What is a prospective study? What are its advantages?
(ii) What is a randomized study? What are its advantages?
(iii) What is a double-blind study? Are there advantages vs. other approaches? After 2 weeks of treatment, 14 of the placebo patients and
3 of the ASA patients developed clinically significant hearing loss.

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 120

Aminoglycosides are powerful broad-spectrum antibiotics used for gram-negative infections often in seriously ill patients. For example, the drugs are often prescribed for drug-resistant tuberculosis as recommended by the World Health Organization. However, these drugs have serious side effects, including irreversible hearing loss referred to as ototoxicity. The most commonly prescribed aminoglycoside is gentamicin. A clinical trial was set up in China to assess whether the addition of aspirin to a standard regimen of gentamicin would have an effect on the incidence of ototoxicity [28]. There were 195 patients enrolled in a prospective, randomized, double-blind clinical trial. Of these, 106 patients were randomized to a twice daily regimen of $80-160$ mg of gentamicin plus placebo and 89 patients were randomized to receive the same regimen of gentamicin $+3 \mathrm{g}$ of aspirin (ASA) daily.
Implement a test to assess whether the incidence of hearing loss is different between the groups. State clearly which test you are using, and report a two-sided $p$ -value.

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 121

Aminoglycosides are powerful broad-spectrum antibiotics used for gram-negative infections often in seriously ill patients. For example, the drugs are often prescribed for drug-resistant tuberculosis as recommended by the World Health Organization. However, these drugs have serious side effects, including irreversible hearing loss referred to as ototoxicity. The most commonly prescribed aminoglycoside is gentamicin. A clinical trial was set up in China to assess whether the addition of aspirin to a standard regimen of gentamicin would have an effect on the incidence of ototoxicity [28]. There were 195 patients enrolled in a prospective, randomized, double-blind clinical trial. Of these, 106 patients were randomized to a twice daily regimen of $80-160$ mg of gentamicin plus placebo and 89 patients were randomized to receive the same regimen of gentamicin $+3 \mathrm{g}$ of aspirin (ASA) daily.
Interpret the results of your test in Problem 10.120 . Suppose another research group wishes to replicate the findings of this study. The investigators conservatively estimate that the incidence of hearing loss will be $10 \%$ in a gentamicin + placebo group and $5 \%$ in a gentamicin $+\mathrm{ASA}$ group and plan to enroll an equal number of subjects in each group.

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 122

Aminoglycosides are powerful broad-spectrum antibiotics used for gram-negative infections often in seriously ill patients. For example, the drugs are often prescribed for drug-resistant tuberculosis as recommended by the World Health Organization. However, these drugs have serious side effects, including irreversible hearing loss referred to as ototoxicity. The most commonly prescribed aminoglycoside is gentamicin. A clinical trial was set up in China to assess whether the addition of aspirin to a standard regimen of gentamicin would have an effect on the incidence of ototoxicity [28]. There were 195 patients enrolled in a prospective, randomized, double-blind clinical trial. Of these, 106 patients were randomized to a twice daily regimen of $80-160$ mg of gentamicin plus placebo and 89 patients were randomized to receive the same regimen of gentamicin $+3 \mathrm{g}$ of aspirin (ASA) daily.
How many subjects need to be enrolled in total in the study if (1) the investigators want to have a $90 \%$ chance of detecting a significant difference using a two-sided test with $\alpha=.05$ and (2) it is anticipated that $5 \%$ of the enrolled subjects will not complete the study?

Victor Salazar
Victor Salazar
Numerade Educator
02:54

Problem 123

The standard screening test for Down's syndrome is based on a combination of maternal age and the level of serum alpha-fetoprotein. Using this test $80 \%$ of Down's syndrome cases can be identified, while $5 \%$ of normals are detected as positive.
What is the sensitivity and specificity of the test? Suppose that 1 out of 500 infants are born with Down's syndrome.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
04:49

Problem 124

The standard screening test for Down's syndrome is based on a combination of maternal age and the level of serum alpha-fetoprotein. Using this test $80 \%$ of Down's syndrome cases can be identified, while $5 \%$ of normals are detected as positive.
What precentage of infants who test positive using the test will actually have Down's syndrome?
A new test is proposed that may be better or worse than the standard test. To assess their relative efficacy, a pilot study is conducted where both tests are used on the same subjects and compared with the true diagnosis. Let $+$
$=$ correct assessment, $-=$ incorrect assessment. The results are given in Table 10.44

Bryan Valdivia
Bryan Valdivia
Numerade Educator
03:16

Problem 125

A new test is proposed that may be better or worse than the standard test. To assess their relative efficacy, a pilot study is conducted where both tests are used on the same subjects and compared with the true diagnosis. Let $+$
$=$ correct assessment, $-=$ incorrect assessment. The results are given in Table 10.44
Thus, for 82 infants, both tests make the correct classification, for 3 infants both tests make the wrong classification, for 5 infants the standard test makes the correct diagnosis while the new test does not, and for 10 infants the new test makes the correct diagnosis while the standard test does not.
Perform a hypothesis test to compare the accuracy of the two tests, and report a two-sided $p$ -value.

Jameson Kuper
Jameson Kuper
Numerade Educator
05:14

Problem 126

Thus, for 82 infants, both tests make the correct classification, for 3 infants both tests make the wrong classification, for 5 infants the standard test makes the correct diagnosis while the new test does not, and for 10 infants the new test makes the correct diagnosis while the standard test does not.
Suppose the investigators plan a larger study comparing the two tests. How many infants need to be tested to have an $80 \%$ probability of finding a significant difference using a two-sided test with $\alpha=0.05$ if the proportion of test results in the four groups in Table 10.44 are considered to be the true proportions?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:43

Problem 127

Dry eye is the most prevalent form of ocular discomfort and irritation, with approximately 20 million people in the United States having mild to moderate dry eye. A small clinical trial was performed to compare the effectiveness of an active drug vs. placebo for relieving symptoms of dry eye. Specifically, patients were randomized to either active drug or placebo for 2 weeks. They then came for a clinic visit where they were exposed to a chamber with a controlled adverse environment (CAE) for 90 minutes (with low humidity intended to exacerbate symptoms of dry eye). The patients were then asked to report their degree of discomfort while in the CAE using the following scale: $(0=\text { none, } 1=$ intermittent awareness, $2=$ constant awareness, $3=$ intermittent discomfort, $4=$ constant discomfort). The results by treatment group are shown in Table 10.45
What is the difference between a nominal and ordinal categorical variable? What type of variable is ocular discomfort?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
00:43

Problem 128

Dry eye is the most prevalent form of ocular discomfort and irritation, with approximately 20 million people in the United States having mild to moderate dry eye. A small clinical trial was performed to compare the effectiveness of an active drug vs. placebo for relieving symptoms of dry eye. Specifically, patients were randomized to either active drug or placebo for 2 weeks. They then came for a clinic visit where they were exposed to a chamber with a controlled adverse environment (CAE) for 90 minutes (with low humidity intended to exacerbate symptoms of dry eye). The patients were then asked to report their degree of discomfort while in the CAE using the following scale: $(0=\text { none, } 1=$ intermittent awareness, $2=$ constant awareness, $3=$ intermittent discomfort, $4=$ constant discomfort). The results by treatment group are shown in Table 10.45
Treating ocular discomfort as a nominal scale, assess whether significant differences in ocular discomfort exist between active drug and placebo patients. Report a $p$ -value (two-tailed). (Hint: Assume that large sample methods are appropriate for the data.) Interpret the results.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
02:08

Problem 129

Dry eye is the most prevalent form of ocular discomfort and irritation, with approximately 20 million people in the United States having mild to moderate dry eye. A small clinical trial was performed to compare the effectiveness of an active drug vs. placebo for relieving symptoms of dry eye. Specifically, patients were randomized to either active drug or placebo for 2 weeks. They then came for a clinic visit where they were exposed to a chamber with a controlled adverse environment (CAE) for 90 minutes (with low humidity intended to exacerbate symptoms of dry eye). The patients were then asked to report their degree of discomfort while in the CAE using the following scale: $(0=\text { none, } 1=$ intermittent awareness, $2=$ constant awareness, $3=$ intermittent discomfort, $4=$ constant discomfort). The results by treatment group are shown in Table 10.45
Treating ocular discomfort as an ordinal scale, assess whether significant differences in ocular discomfort exist between active and placebo patients. Report a $p$ -value (two-tailed). (Hint: Assume that large sample methods are appropriate for these data.) Interpret the results.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:43

Problem 130

A study was performed relating neonatal blood-pressure level to neonatal taste responsiveness (Zinner et al. [29]). To assess salt taste responsiveness, infants 2 to 4 days old were offered 3 solutions via nipple cannulas containing
(i) water, (ii) water + 0.1 molar salt, and (iii) water + 0.3 molar salt. Infant blood pressure was measured separately with a Physiometrics machine at $2-4$ days of age. A comparison was made between the mean number of sucks per burst of sucking (MSB) on (water + 0.3 molar salt) minus the MSB on water alone $=\Delta$ MSB. If $\Delta \mathrm{MSB} \leq-10,$ it was considered an aversive response; if $\Delta \mathrm{MSB}>0$, it was considered a preferential response; otherwise, it was considered a neutral response. For the purposes of this question, the neutral response infants were eliminated and we compare the distribution of diastolic blood pressure between the aversive and preferential response infants. The results are given in Table 10.46
We wish to test whether there is an association between salt taste response and DBP quintile.
State the null and alternative hypotheses to be tested to answer this question in statistical terms.

Nick Johnson
Nick Johnson
Numerade Educator
05:36

Problem 131

A study was performed relating neonatal blood-pressure level to neonatal taste responsiveness (Zinner et al. [29]). To assess salt taste responsiveness, infants 2 to 4 days old were offered 3 solutions via nipple cannulas containing
(i) water, (ii) water + 0.1 molar salt, and (iii) water + 0.3 molar salt. Infant blood pressure was measured separately with a Physiometrics machine at $2-4$ days of age. A comparison was made between the mean number of sucks per burst of sucking (MSB) on (water + 0.3 molar salt) minus the MSB on water alone $=\Delta$ MSB. If $\Delta \mathrm{MSB} \leq-10,$ it was considered an aversive response; if $\Delta \mathrm{MSB}>0$, it was considered a preferential response; otherwise, it was considered a neutral response. For the purposes of this question, the neutral response infants were eliminated and we compare the distribution of diastolic blood pressure between the aversive and preferential response infants. The results are given in Table 10.46
We wish to test whether there is an association between salt taste response and DBP quintile.
What is the expected number of infants in DBP quintile 2 with a preferential salt taste response under the null hypothesis?

Jon Southam
Jon Southam
Numerade Educator
01:43

Problem 132

A study was performed relating neonatal blood-pressure level to neonatal taste responsiveness (Zinner et al. [29]). To assess salt taste responsiveness, infants 2 to 4 days old were offered 3 solutions via nipple cannulas containing
(i) water, (ii) water + 0.1 molar salt, and (iii) water + 0.3 molar salt. Infant blood pressure was measured separately with a Physiometrics machine at $2-4$ days of age. A comparison was made between the mean number of sucks per burst of sucking (MSB) on (water + 0.3 molar salt) minus the MSB on water alone $=\Delta$ MSB. If $\Delta \mathrm{MSB} \leq-10,$ it was considered an aversive response; if $\Delta \mathrm{MSB}>0$, it was considered a preferential response; otherwise, it was considered a neutral response. For the purposes of this question, the neutral response infants were eliminated and we compare the distribution of diastolic blood pressure between the aversive and preferential response infants. The results are given in Table 10.46
We wish to test whether there is an association between salt taste response and DBP quintile.
What test procedure can be used to test the hypotheses in Problem $10.130 ?$

Nick Johnson
Nick Johnson
Numerade Educator
01:43

Problem 133

A study was performed relating neonatal blood-pressure level to neonatal taste responsiveness (Zinner et al. [29]). To assess salt taste responsiveness, infants 2 to 4 days old were offered 3 solutions via nipple cannulas containing
(i) water, (ii) water + 0.1 molar salt, and (iii) water + 0.3 molar salt. Infant blood pressure was measured separately with a Physiometrics machine at $2-4$ days of age. A comparison was made between the mean number of sucks per burst of sucking (MSB) on (water + 0.3 molar salt) minus the MSB on water alone $=\Delta$ MSB. If $\Delta \mathrm{MSB} \leq-10,$ it was considered an aversive response; if $\Delta \mathrm{MSB}>0$, it was considered a preferential response; otherwise, it was considered a neutral response. For the purposes of this question, the neutral response infants were eliminated and we compare the distribution of diastolic blood pressure between the aversive and preferential response infants. The results are given in Table 10.46
We wish to test whether there is an association between salt taste response and DBP quintile.
Use a computer program to implement this test procedure and report a two-tailed $p$ -value.

Nick Johnson
Nick Johnson
Numerade Educator
01:38

Problem 134

A study was performed relating neonatal blood-pressure level to neonatal taste responsiveness (Zinner et al. [29]). To assess salt taste responsiveness, infants 2 to 4 days old were offered 3 solutions via nipple cannulas containing
(i) water, (ii) water + 0.1 molar salt, and (iii) water + 0.3 molar salt. Infant blood pressure was measured separately with a Physiometrics machine at $2-4$ days of age. A comparison was made between the mean number of sucks per burst of sucking (MSB) on (water + 0.3 molar salt) minus the MSB on water alone $=\Delta$ MSB. If $\Delta \mathrm{MSB} \leq-10,$ it was considered an aversive response; if $\Delta \mathrm{MSB}>0$, it was considered a preferential response; otherwise, it was considered a neutral response. For the purposes of this question, the neutral response infants were eliminated and we compare the distribution of diastolic blood pressure between the aversive and preferential response infants. The results are given in Table 10.46
We wish to test whether there is an association between salt taste response and DBP quintile.
What are your overall conclusions based on your results?

Dominador Tan
Dominador Tan
Numerade Educator
View

Problem 135

Antithrombotic drugs are used after coronary stenting to prevent stent thrombosis. A study was performed to compare the efficacy and safety of three antithrombotic drug regimens after coronary stenting: aspirin alone, aspirin $+$ warfarin, and aspirin + ticlopidine [30]. Patients were randomly assigned to one of the three regimens. The primary endpoint was any of the following outcomes: (a) death, (b) revascularization of the target lesion, or (c) angiographic evidence of thrombosis or Ml within 30 days.
What is the principal benefit(s) of assigning patients randomly to the treatment regimens? The results for the primary endpoint are given in Table 10.47 .

Lainey Roebuck
Lainey Roebuck
Numerade Educator
00:26

Problem 136

What test can be used to compare event rates among the three groups?

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
00:44

Problem 137

State the hypotheses to be tested under the null and alternative hypotheses

Kari Hasz
Kari Hasz
Numerade Educator
00:33

Problem 138

Implement the test in Problem 10.136 , and report a p-value (two-tailed).

Ahmed Genedy
Ahmed Genedy
Numerade Educator
03:40

Problem 139

A case-control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were $70-$ to 79 -year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups $(1,2,3,4,$
5, 6), with 6 being the highest risk and 1 being the lowest risk. The data in Table 10.48 were obtained relating the risk score to case/control status.
What test can be performed to study the association between case/control status and risk score? Specifically, we are interested in testing whether cases tend to have consistently higher risk scores or consistently lower risk scores than controls.

Qudsiya Anis
Qudsiya Anis
Numerade Educator
04:03

Problem 140

A case-control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were $70-$ to 79 -year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups $(1,2,3,4,$
5, 6), with 6 being the highest risk and 1 being the lowest risk. The data in Table 10.48 were obtained relating the risk score to case/control status.
Perform the test in Problem $10.139,$ and report a $p$ -value (two-tailed). Another use for the risk score is to compute a prevalence estimate of AMD for women with different risk scores. In the general population, the prevalence of AMD among $70-$ to 79-year-old women is .025.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
07:35

Problem 141

A case-control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were $70-$ to 79 -year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups $(1,2,3,4,$
5, 6), with 6 being the highest risk and 1 being the lowest risk. The data in Table 10.48 were obtained relating the risk score to case/control status.
What is the estimated prevalence of AMD among women with a risk score in group $1 ?$ In group 6 ? Hint Use Bayes' Theorem.

Georgiann Andersen
Georgiann Andersen
Numerade Educator
07:35

Problem 142

A case-control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were $70-$ to 79 -year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups $(1,2,3,4,$
5, 6), with 6 being the highest risk and 1 being the lowest risk. The data in Table 10.48 were obtained relating the risk score to case/control status.
What is the relative risk for AMD among women in group 6 compared with women in group $1 ?$ What does the relative risk mean in words?

Georgiann Andersen
Georgiann Andersen
Numerade Educator
01:26

Problem 143

asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms.
How many subjects should be recruited in each group (same number per group) to have a $90 \%$ chance of detecting a significant difference using a two-sided test with $\alpha=.05 ?$

Nick Johnson
Nick Johnson
Numerade Educator
01:26

Problem 144

Asthma is an important health problem for inner-city children, frequently resulting in hospital admission if symptoms become exacerbated. It is well known that compliance of children with asthma medication is often poor. Also, many household allergens (e.g., roaches) worsen asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms.
Suppose that 50 households are randomized per group. How much power would the study have under the above assumptions? The results of the study were as follows: 14 of the 50 active intervention children had an improvement in symptoms compared with 6 of the 50 control intervention children.

Nick Johnson
Nick Johnson
Numerade Educator
01:26

Problem 145

Asthma is an important health problem for inner-city children, frequently resulting in hospital admission if symptoms become exacerbated. It is well known that compliance of children with asthma medication is often poor. Also, many household allergens (e.g., roaches) worsen asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms.
What test can be used to compare the results in the active and control groups?

Nick Johnson
Nick Johnson
Numerade Educator
01:26

Problem 146

Asthma is an important health problem for inner-city children, frequently resulting in hospital admission if symptoms become exacerbated. It is well known that compliance of children with asthma medication is often poor. Also, many household allergens (e.g., roaches) worsen asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms.
Perform the test in Problem 10.145 , and report a $p$ -value (two-tailed).

Nick Johnson
Nick Johnson
Numerade Educator
07:23

Problem 147

The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline [31]. Retinopathies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max $=56$ months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up - severity level at baseline). An ordinal grading scale was used to evaluate change: $2+$ levels better, 1 level better, no change, 1 level worse, ..., 5+ levels worse. The outcome data by treatment group are given in Table 10.49.
The primary outcome for the study was worsening by 2 or more levels.
What test can be used to compare the two treatment groups on the primary endpoint?

Bon Zapata
Bon Zapata
Numerade Educator
07:23

Problem 148

The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline [31]. Retinopathies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max $=56$ months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up - severity level at baseline). An ordinal grading scale was used to evaluate change: $2+$ levels better, 1 level better, no change, 1 level worse, ..., 5+ levels worse. The outcome data by treatment group are given in Table 10.49.
The primary outcome for the study was worsening by 2 or more levels.
Implement the test in Problem 10.147 , and provide
a $p$ -value (two-tailed).
A more efficient method of analysis would leave the change in retinopathy level in its raw form without grouping the data

Bon Zapata
Bon Zapata
Numerade Educator
00:26

Problem 149

What test can be used to compare the two groups if this more efficient method is used?

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
00:33

Problem 150

Implement the test in Problem $10.149,$ and provide a $p$ -value (two-tailed).

Ahmed Genedy
Ahmed Genedy
Numerade Educator
00:48

Problem 151

Reanalyze the data in Table 10.49 using the Wilcoxon rank sum test.

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
01:30

Problem 152

Compare your results in Problems 10.149 and $10.151 .$ Which do you think is a better method of analysis?

Tyler Moulton
Tyler Moulton
Numerade Educator