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Fundamentals of Biostatistics

Bernard Rosner

Chapter 13

Design and Analysis Techniques for Epidemiologic Studies - all with Video Answers

Educators


Chapter Questions

01:22

Problem 1

In a 1985 study of the relationship between contraceptive use and infertility, 89 of 283 infertile women, compared with 640 of 3833 control (fertile) women, had used an intrauterine device (IUD) at some time in their lives [43].
Use the normal-theory method to test for significant differences in contraceptive-use patterns between the two groups.

Joanna Quigley
Joanna Quigley
Numerade Educator
04:47

Problem 2

Use the contingency-table method to perform the test in Problem 13.1

Eric Mockensturm
Eric Mockensturm
Numerade Educator
00:24

Problem 3

Compare your results in Problems 13.1 and $13.2 .$

Amy Jiang
Amy Jiang
Numerade Educator
01:35

Problem 4

Compute a 95% Cl for the difference in the proportion of women who have ever used IUDs between the infertile and fertile women in Problem 13.1

Marc Lauzon
Marc Lauzon
Numerade Educator
00:35

Problem 5

Compute the OR in favor of ever using an IUD for infertile women vs. fertile women.

Joanna Quigley
Joanna Quigley
Numerade Educator
00:22

Problem 6

Provide a 95\% Cl for the true OR corresponding to your answer to Problem 13.5.

Katelyn Chen
Katelyn Chen
Numerade Educator
00:31

Problem 7

What is the relationship between your answers to Problems 13.2 and 13.6?

Amy Jiang
Amy Jiang
Numerade Educator
05:01

Problem 8

Refer to Problem 10.30 (on page 442 ). Estimate the $R R$ for total mortality of the study group vs. the control group. Provide $95 \%$ confidence limits for the $R R$.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
10:47

Problem 9

Refer to Table 13.8 (on page 656 ).
Perform a significance test to examine the association between OC use and bacteriuria after controlling for age.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
01:17

Problem 10

Refer to Table 13.8 (on page 656 ).
Estimate the OR in favor of bacteriuria for OC users vs. non-OC users after controlling for age.

Mohammed Nadhir
Mohammed Nadhir
Numerade Educator
00:37

Problem 11

Provide a 95% Cl for the OR estimate in Problem 13.10.

Melissa Lupinacci
Melissa Lupinacci
Numerade Educator
00:48

Problem 12

Is the association between bacteriuria and OC use comparable among different age groups? Why or why not?

Neel Faucher
Neel Faucher
Numerade Educator
01:07

Problem 13

Suppose you did not control for age in the preceding analyses. Calculate the crude (unadjusted for age) odds ratio in favor of bacteriuria for OC users vs. non-OC users.

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:28

Problem 14

How do your answers to Problems 13.10 and 13.13 relate to each other? Explain any differences found.

Victor Salazar
Victor Salazar
Numerade Educator
02:35

Problem 15

A study was performed looking at the risk of fractures in three rural lowa communities according to whether their drinking water was "higher calcium," "higher fluorides," or "control" as determined by water samples. Table 13.44 presents data comparing the rate of fractures (over 5 years) between the higher-calcium vs. the control communities for women ages $20-35$ and $55-80$, respectively [44].
CAN'T COPY THE GRAPH
What test can be used to compare the fracture rates in these two communities while controlling for age?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
View

Problem 16

Implement the test in Problem 13.15 , and report a $p$ -value (two-sided).

Victor Salazar
Victor Salazar
Numerade Educator
02:09

Problem 17

Estimate the OR relating higher calcium and fractures while controlling for age.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
01:55

Problem 18

Provide a 95\% Cl for the estimate obtained in Problem 13.17.

Linda Hand
Linda Hand
Numerade Educator
00:50

Problem 19

A study was performed assessing the association between lifetime analgesic intake and change in estimated glomerular filtration rate (GFR) as measured from two blood samples obtained in 1989 and 2000 among 1645 participants in the Nurses' Health Study (Curhan, et al. [45]). GFR is a commonly used index of kidney function with lower levels indicating worse kidney function. The following data were presented relating lifetime intake of acetaminophen (the active ingredient in Tylenol) in grams and a decline of $\geq 30 \%$ in estimated GFR, which is considered a clinically meaningful decline in kidney function (denoted as a case).
CAN'T COPY THE GRAPH
What is the estimated odds ratio for being a case comparing Group D to Group A?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
01:55

Problem 20

Provide a $95 \%$ Cl for the OR computed in Problem 13.19.

Linda Hand
Linda Hand
Numerade Educator
04:05

Problem 21

A logistic regression analysis was run using Stata relating disease status to lifetime acetaminophen intake divided by $100(1 \text { unit }=100 \mathrm{g})$ denoted by ace_100. The results are given in Table 13.46
CAN'T COPY THE TABLE
Estimate the odds ratio for being a case comparing a subject with a lifetime acetaminophen intake of $1100 \mathrm{g}$ vs. a lifetime acetaminophen intake of $100 \mathrm{g}$. Provide a $95 \% \mathrm{Cl}$ for this odds ratio.

Kush Khamesra
Kush Khamesra
Numerade Educator
04:05

Problem 22

A logistic regression analysis was run using Stata relating disease status to lifetime acetaminophen intake divided by $100(1 \text { unit }=100 \mathrm{g})$ denoted by ace_100. The results are given in Table 13.46
CAN'T COPY THE TABLE
Suppose a cutoff for excessive lifetime acetaminophen intake (L) is a level such that the risk of at least a $30 \%$ decline in GFR over 11 years is $\geq 10 \% .$ What is your best estimate of L?

Kush Khamesra
Kush Khamesra
Numerade Educator
01:46

Problem 23

One assumption in Table 13.46 is that the log odds ratio of being a case is a linear function of the lifetime acetaminophen intake. To check this assumption, a second logistic regression was run relating disease status to acetaminophen intake in categories using the categories in Table 13.45 with Group $A$ as the reference and Groups $B, C,$ and $D$ denoted by .lacetam $\sim 300$, lacetam $\sim 1750$, lacetam $\sim 4000$, respectively (see Table 13.47 ).
CAN'T COPY THE TABLE
Estimate the odds ratio for Group C vs. Group A and provide a $95 \%$ Cl. Are the results consistent with those in Problem $13.21 ?$ Why or why not?

Adriano Chikande
Adriano Chikande
Numerade Educator
00:24

Problem 24

Refer to Problem 10.32 (on page 442 ).
Estimate the OR relating widowhood to mortality based on all the data in Table 10.27 (on page 442 ).
CAN'T COPY THE TABLE

Ashley Volpe
Ashley Volpe
Numerade Educator
05:34

Problem 25

Refer to Problem 10.32 (on page 442 ).
Provide a $95 \%$ Cl for the OR.

Uma Kumari
Uma Kumari
Numerade Educator
View

Problem 26

A study was conducted in Wales relating blood-pressure and blood-lead levels [46]. It was reported that 4 of 455 men with blood-lead levels $\leq 11 \mu g / 100$ mL had elevated SBP $(\geq 160$$\mathrm{mm} \mathrm{Hg}$ ), whereas 16 of 410 men with blood-lead levels $\geq 12$ $\mu \mathrm{g} / 100 \mathrm{mL}$ also had elevated SBP. It was also reported that 6 of 663 women with blood-lead levels $\leq 11 \mu g / 100$ mL had elevated SBP, whereas 1 of 192 women with blood-lead levels $\geq 12 \mu g / 100$ mL had elevated SBP.
CAN'T COPY THE TABLE
What is an appropriate procedure to test the hypothesis that there is an association between blood pressure and blood lead, while controlling for sex?

Victor Salazar
Victor Salazar
Numerade Educator
08:56

Problem 27

Implement the procedure in Problem $13.26,$ and report a $p$ -value.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
View

Problem 28

A study was conducted in Wales relating blood-pressure and blood-lead levels [46]. It was reported that 4 of 455 men with blood-lead levels $\leq 11 \mu g / 100$ mL had elevated SBP $(\geq 160$$\mathrm{mm} \mathrm{Hg}$ ), whereas 16 of 410 men with blood-lead levels $\geq 12$ $\mu \mathrm{g} / 100 \mathrm{mL}$ also had elevated SBP. It was also reported that 6 of 663 women with blood-lead levels $\leq 11 \mu g / 100$ mL had elevated SBP, whereas 1 of 192 women with blood-lead levels $\geq 12 \mu g / 100$ mL had elevated SBP.
CAN'T COPY THE TABLE
Estimate the OR relating blood pressure to blood lead, and provide a $95 \%$ Cl about this estimate.

Victor Salazar
Victor Salazar
Numerade Educator
08:36

Problem 29

Aminoglycoside antibiotics are particularly useful clinically in the treatment of serious gram-negative bacterial infections among hospitalized patients. Despite their potential for toxicity, as well as the continued development of newer antimicrobial agents of other classes, it seems likely that the clinical use of aminoglycosides will continue to be widespread. The choice of a particular aminoglycoside antibiotic for a given patient depends on several factors, including the specific clinical situation, differences in antimicrobial spectrum and cost, and risks of side effects, particularly nephrotoxicity and auditory toxicity. Many randomized, controlled trials have been published that compare the various aminoglycoside antibiotics with respect to efficacy, nephrotoxicity, and, to a lesser extent, auditory toxicity. These individual trials have varied widely with respect to their design features and their conclusions. A major limitation to their interpretability is that the majority of the individual trials have lacked an adequate sample size to detect the small-to-moderate differences between treatment groups that are most plausible. As a result, the individual trials published to date have generally not permitted firm conclusions, especially concerning the relative potential for toxicity of aminoglycosides. In these circumstances, one method to estimate the true effects of these agents more precisely is to conduct an overview, or meta-analysis, of the data from all randomized trials. In this way, a true increase in risk could emerge that otherwise would not be apparent in any single trial due to small sample size. Therefore, a quantitative overview of the results of all published randomized controlled trials that assessed the efficacy and toxicity of individual aminoglycoside antibiotics was undertaken.
Forty-five randomized clinical trials, published between June 1975 and September $1985,$ were identified that compared two or more of five aminoglycoside antibiotics:
amikacin, gentamicin, netilmicin, sisomicin, and tobramycin. Thirty-seven of these trials could provide data suitable for comparative purposes.
The specific endpoints of interest were efficacy, nephrotoxicity, and auditory toxicity (ototoxicity). Efficacy was defined as bacterial or clinical response to treatment as reported in each individual trial. Nephrotoxicity was defined as the percentage of toxic events to the kidney reported, regardless of whether the published paper suggested some explanation other than the use of the study drug, such as use of another potentially nephrotoxic agent, or the presence of an underlying disease affecting kidney function. Auditory toxicity was defined as reported differences between pre- and post-treatment audiograms.
The data are organized into three Data Sets: EFF.DAT, all NEPHRO.DAT, and OTO.DAT, all at www.cengagebrain.com. A separate record is presented for each antibiotic studied for each endpoint. The format is given in the files EFF.DOC, III NEPHRO.DOC, and OTO.DOC at www.cengagebrain.com.
Columns $1-8:$ Study name
10-11: Study number (number on reference list)
13: Endpoint $(1=\text { efficacy } ; 2=$ nephrotoxicity; $3=\text { ototoxicity })$
15: antibiotic ( $1=$ amikacin; $2=$ gentamicin; $3=$ netilmicin; $4=$ sisomicin; $5=$ tobramycin)
17-19: Sample size
21-23: Number cured (for efficacy) or number with side effect (for nephrotoxicity or ototoxicity)
Refer to Data Set NEPHRO.DAT at www.cengagebrain.com.
Use methods of meta-analysis to assess whether there are differences in nephrotoxicity between each pair of antibiotics. Obtain point estimates and $95 \%$ Cls for the $O R$ and provide a two-sided $p$ -value.

Sana Riaz
Sana Riaz
Numerade Educator
08:36

Problem 30

Aminoglycoside antibiotics are particularly useful clinically in the treatment of serious gram-negative bacterial infections among hospitalized patients. Despite their potential for toxicity, as well as the continued development of newer antimicrobial agents of other classes, it seems likely that the clinical use of aminoglycosides will continue to be widespread. The choice of a particular aminoglycoside antibiotic for a given patient depends on several factors, including the specific clinical situation, differences in antimicrobial spectrum and cost, and risks of side effects, particularly nephrotoxicity and auditory toxicity. Many randomized, controlled trials have been published that compare the various aminoglycoside antibiotics with respect to efficacy, nephrotoxicity, and, to a lesser extent, auditory toxicity. These individual trials have varied widely with respect to their design features and their conclusions. A major limitation to their interpretability is that the majority of the individual trials have lacked an adequate sample size to detect the small-to-moderate differences between treatment groups that are most plausible. As a result, the individual trials published to date have generally not permitted firm conclusions, especially concerning the relative potential for toxicity of aminoglycosides. In these circumstances, one method to estimate the true effects of these agents more precisely is to conduct an overview, or meta-analysis, of the data from all randomized trials. In this way, a true increase in risk could emerge that otherwise would not be apparent in any single trial due to small sample size. Therefore, a quantitative overview of the results of all published randomized controlled trials that assessed the efficacy and toxicity of individual aminoglycoside antibiotics was undertaken.
Forty-five randomized clinical trials, published between June 1975 and September $1985,$ were identified that compared two or more of five aminoglycoside antibiotics:
amikacin, gentamicin, netilmicin, sisomicin, and tobramycin. Thirty-seven of these trials could provide data suitable for comparative purposes.
The specific endpoints of interest were efficacy, nephrotoxicity, and auditory toxicity (ototoxicity). Efficacy was defined as bacterial or clinical response to treatment as reported in each individual trial. Nephrotoxicity was defined as the percentage of toxic events to the kidney reported, regardless of whether the published paper suggested some explanation other than the use of the study drug, such as use of another potentially nephrotoxic agent, or the presence of an underlying disease affecting kidney function. Auditory toxicity was defined as reported differences between pre- and post-treatment audiograms.
The data are organized into three Data Sets: EFF.DAT, all NEPHRO.DAT, and OTO.DAT, all at www.cengagebrain.com. A separate record is presented for each antibiotic studied for each endpoint. The format is given in the files EFF.DOC, III NEPHRO.DOC, and OTO.DOC at www.cengagebrain.com.
Columns $1-8:$ Study name
10-11: Study number (number on reference list)
13: Endpoint $(1=\text { efficacy } ; 2=$ nephrotoxicity; $3=\text { ototoxicity })$
15: antibiotic ( $1=$ amikacin; $2=$ gentamicin; $3=$ netilmicin; $4=$ sisomicin; $5=$ tobramycin)
17-19: Sample size
21-23: Number cured (for efficacy) or number with side effect (for nephrotoxicity or ototoxicity)
Refer to Data Set OTO.DAT at www.cengagebrain.com.
Answer the question in Problem 13.29 to assess whether there are differences in ototoxicity between each pair of antibiotics.

Sana Riaz
Sana Riaz
Numerade Educator
08:36

Problem 31

Aminoglycoside antibiotics are particularly useful clinically in the treatment of serious gram-negative bacterial infections among hospitalized patients. Despite their potential for toxicity, as well as the continued development of newer antimicrobial agents of other classes, it seems likely that the clinical use of aminoglycosides will continue to be widespread. The choice of a particular aminoglycoside antibiotic for a given patient depends on several factors, including the specific clinical situation, differences in antimicrobial spectrum and cost, and risks of side effects, particularly nephrotoxicity and auditory toxicity. Many randomized, controlled trials have been published that compare the various aminoglycoside antibiotics with respect to efficacy, nephrotoxicity, and, to a lesser extent, auditory toxicity. These individual trials have varied widely with respect to their design features and their conclusions. A major limitation to their interpretability is that the majority of the individual trials have lacked an adequate sample size to detect the small-to-moderate differences between treatment groups that are most plausible. As a result, the individual trials published to date have generally not permitted firm conclusions, especially concerning the relative potential for toxicity of aminoglycosides. In these circumstances, one method to estimate the true effects of these agents more precisely is to conduct an overview, or meta-analysis, of the data from all randomized trials. In this way, a true increase in risk could emerge that otherwise would not be apparent in any single trial due to small sample size. Therefore, a quantitative overview of the results of all published randomized controlled trials that assessed the efficacy and toxicity of individual aminoglycoside antibiotics was undertaken.
Forty-five randomized clinical trials, published between June 1975 and September $1985,$ were identified that compared two or more of five aminoglycoside antibiotics:
amikacin, gentamicin, netilmicin, sisomicin, and tobramycin. Thirty-seven of these trials could provide data suitable for comparative purposes.
The specific endpoints of interest were efficacy, nephrotoxicity, and auditory toxicity (ototoxicity). Efficacy was defined as bacterial or clinical response to treatment as reported in each individual trial. Nephrotoxicity was defined as the percentage of toxic events to the kidney reported, regardless of whether the published paper suggested some explanation other than the use of the study drug, such as use of another potentially nephrotoxic agent, or the presence of an underlying disease affecting kidney function. Auditory toxicity was defined as reported differences between pre- and post-treatment audiograms.
The data are organized into three Data Sets: EFF.DAT, all NEPHRO.DAT, and OTO.DAT, all at www.cengagebrain.com. A separate record is presented for each antibiotic studied for each endpoint. The format is given in the files EFF.DOC, III NEPHRO.DOC, and OTO.DOC at www.cengagebrain.com.
Columns $1-8:$ Study name
10-11: Study number (number on reference list)
13: Endpoint $(1=\text { efficacy } ; 2=$ nephrotoxicity; $3=\text { ototoxicity })$
15: antibiotic ( $1=$ amikacin; $2=$ gentamicin; $3=$ netilmicin; $4=$ sisomicin; $5=$ tobramycin)
17-19: Sample size
21-23: Number cured (for efficacy) or number with side effect (for nephrotoxicity or ototoxicity)
Refer to Data Set EFF.DAT at www.cengagebrain.com.
Answer the question in Problem 13.29 to assess whether there are differences in efficacy between each pair of antibiotics.

Sana Riaz
Sana Riaz
Numerade Educator
02:18

Problem 32

A recent study compared the use of percutaneous transluminal coronary angioplasty (PTCA) with medical therapy in the treatment of single-vessel coronary-artery disease. A total of 105 patients were randomly assigned to PTCA and 107 to medical therapy. Over a period of 6 months, Ml occurred in 5 patients in the PTCA group and 3 patients in the medical-therapy group.
Estimate the $R R$ of $\mathrm{Ml}$ for patients assigned to PTCA vs. patients assigned to medical therapy, and provide a $95 \%$ Cl for this estimate.
At the 6 -month clinic visit, 61 of 96 patients seen in the PTCA group and 47 of 102 patients seen in the medicaltherapy group were angina free.

Jameson Kuper
Jameson Kuper
Numerade Educator
01:03

Problem 33

Answer Problem 13.32 for the endpoint of being angina free at 6 months.

Raj Bala
Raj Bala
Numerade Educator
02:46

Problem 34

Refer to Problem 10.59 (on page 445 ). In this problem, we Lescribed Data Set TENNIS1.DAT (at www.cengagebrain .com), which is an observational study relating episodes of tennis elbow to other risk factors.
Use logistic-regression methods to compare participants with $1+$ episodes of tennis elbow vs. participants with
0 episodes of tennis elbow, considering multiple risk factors in the same model.

James Kiss
James Kiss
Numerade Educator
01:58

Problem 35

Refer to Problem 10.59 (on page 445 ). In this problem, we described Data Set TENNIS1.DAT (at www.cengagebrain .com), which is an observational study relating episodes of tennis elbow to other risk factors.
Use linear-regression methods to predict the number of episodes of tennis elbow as a function of several risk factors in the same model.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:30

Problem 36

A drug company proposes to introduce a new antihypertensive agent that is aimed at elderly hypertensive participants with prior heart disease. Because this is a high-risk group, the company is hesitant to withhold antihypertensive therapy from these patients and instead proposes an equivalence study comparing the new agent (drug A) with the current antihypertensive therapy used by those participants. Hence, the participants will be randomized to either maintenance of their current therapy or replacement of their current therapy with drug A. Suppose the endpoint is total cardiovascular disease (CVD) mortality, and it is assumed that under their current therapy $15 \%$ of participants will die of CVD over the next 5 years.
Suppose drug A will be considered equivalent to the current therapy if the 5 -year CVD mortality is not worse than 20\%. How many participants must be enrolled in the study to ensure at least an $80 \%$ chance of demonstrating equivalence if equivalence will be based on a one-sided $95 \% \mathrm{Cl}$ approach, an equal number of subjects are randomized to drug $A$ and current therapy, and the underlying mortality rates of the two therapies are the same?

Jorge Villanueva
Jorge Villanueva
Numerade Educator
03:30

Problem 37

A drug company proposes to introduce a new antihypertensive agent that is aimed at elderly hypertensive participants with prior heart disease. Because this is a high-risk group, the company is hesitant to withhold antihypertensive therapy from these patients and instead proposes an equivalence study comparing the new agent (drug A) with the current antihypertensive therapy used by those participants. Hence, the participants will be randomized to either maintenance of their current therapy or replacement of their current therapy with drug A. Suppose the endpoint is total cardiovascular disease (CVD) mortality, and it is assumed that under their current therapy $15 \%$ of participants will die of CVD over the next 5 years.
Suppose in the actual study that 200 participants are randomized to each group. Forty-four participants who receive drug $A$ and 35 participants who receive current therapy die of $\mathrm{CVD}$ in the next 5 years. Can the treatments be considered equivalent? Why or why not?

Jorge Villanueva
Jorge Villanueva
Numerade Educator
10:02

Problem 38

How much power did the study described in Problem 13.37 have of demonstrating equivalence under the assumptions in Problem $13.36 ?$

Ernest Castorena
Ernest Castorena
Numerade Educator
04:05

Problem 39

Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study [47]. Several potential risk factors, such as age, blood pressure, and cigarette smoking, are of interest and need to be controlled for simultaneously. Therefore, a multiple logistic-regression model was fitted to these data, as shown in Table 13.48 .
Assess the statistical significance of the individual risk factors.

Kush Khamesra
Kush Khamesra
Numerade Educator
View

Problem 40

Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study [47]. Several potential risk factors, such as age, blood pressure, and cigarette smoking, are of interest and need to be controlled for simultaneously. Therefore, a multiple logistic-regression model was fitted to these data, as shown in Table 13.48 .
What do these statistical tests mean in this instance?

Shu Naito
Shu Naito
Numerade Educator
06:29

Problem 41

Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study [47]. Several potential risk factors, such as age, blood pressure, and cigarette smoking, are of interest and need to be controlled for simultaneously. Therefore, a multiple logistic-regression model was fitted to these data, as shown in Table 13.48 .
Compute the OR relating the additional risk of sudden death per 100 -centiliter (cL) decrease in vital capacity after adjustment for the other risk factors.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:38

Problem 42

Provide a $95 \%$ Cl for the estimate in Problem 13.41 .

Gaurav Kalra
Gaurav Kalra
Numerade Educator
07:11

Problem 43

Refer to Data Set HORMONE.DAT at www.cengagebrain .com.
Use logistic-regression methods to assess whether presence of biliary secretions during the second period (any or none) is related to the type of hormone used during the second period.

Cyrielle Lorio
Cyrielle Lorio
Numerade Educator
02:06

Problem 44

Refer to Data Set HORMONE.DAT at www.cengagebrain .com.
Answer the same question as in Problem 13.43 for the presence of pancreatic secretions.

VS
Vivek Singh
Numerade Educator
View

Problem 45

Refer to Data Set HORMONE.DAT at www.cengagebrain-com.
Use logistic-regression methods to assess whether the presence of biliary secretions during the second period is related to dose of hormone used during the second period (do separate analyses for each active hormonehormones $2-5$ ).

Shu Naito
Shu Naito
Numerade Educator
11:25

Problem 46

Answer the same question as in Problem 13.45 for the presence of pancreatic secretions.

Asma Venkitta
Asma Venkitta
Numerade Educator
06:37

Problem 47

Refer to Data Set EAR.DAT (see Table 3.12 (on page 69), also www.cengagebrain.com).
Consider a subject "cured" if (1) the subject is a unilateral case and the ear clears by 14 days or (2) the subject is a bilateral case and both ears are clear by 14 days. Run a logistic regression with outcome variable = cured and independent variables (1) antibiotic, (2) age, and (3) type of case (unilateral or bilateral). Assess goodness of fit of the model you obtain.

James Kiss
James Kiss
Numerade Educator
06:37

Problem 48

Refer to Data Set EAR.DAT (see Table 3.12 (on page 69), also www.cengagebrain.com).
Use correlated binary data methods to relate clearance of an ear by 14 days to antibiotic type and age. Use the ear as the unit of analysis. (Hint: Use generalized estimating equation methods.)

James Kiss
James Kiss
Numerade Educator
01:05

Problem 49

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Assess whether there are significant treatment effects regarding pain during maximum activity.

Robin Corrigan
Robin Corrigan
Numerade Educator
05:55

Problem 50

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Asses whether there are significant treatment effects regarding pain 12 hours after maximum activity.

Stephen Hobbs
Stephen Hobbs
Numerade Educator
18:39

Problem 51

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Assess whether there are significant treatment effects regarding pain on an average day.

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
05:54

Problem 52

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Assess whether there are significant carry-over effects for the endpoint in Problem 13.49

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:59

Problem 53

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Assess whether there are significant carry-over effects for the endpoint in Problem 13.50 .

Kayleah Tsai
Kayleah Tsai
Numerade Educator
00:59

Problem 54

Refer to Data Set TENNIS2.DAT at www.cengagebrain .com.
Assess whether there are significant carry-over effects for the endpoint in Problem 13.51.

Kayleah Tsai
Kayleah Tsai
Numerade Educator
02:10

Problem 55

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49.
Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods.
Assess whether there are any significant treatment or carry-over effects of SBP or DBP in study 1.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:00

Problem 56

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49.
Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods.
Answer Problem 13.55 for study 2.

Noah Musser
Noah Musser
Numerade Educator
02:00

Problem 57

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49.
Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods.
Answer Problem 13.55 for study 3.

Noah Musser
Noah Musser
Numerade Educator
02:10

Problem 58

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49.
Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods.
Suppose we are planning a new study similar in design to study $1 .$ How many participants do we need to study to detect an underlying 3 -mm Hg treatment effect for SBP with 80\% power assuming there is no carry-over effect and we perform a two-sided test with $\alpha=.05$ ?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
04:13

Problem 59

Answer Problem 13.58 for an underlying 2-mm Hg treatment effect for DBP.

Nicholas Sacco
Nicholas Sacco
Numerade Educator
06:00

Problem 60

Answer Problem 13.58 for a new study similar in design to study 2.

Nicholas Sacco
Nicholas Sacco
Numerade Educator
01:04

Problem 61

Answer Problem 13.59 for a new study similar in design to study 2.

Raj Bala
Raj Bala
Numerade Educator
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Problem 62

A longitudinal study was conducted among children in the Greater Boston Otitis Media Study [48]. Based on all doctor visits during the first year of life, children were classified as having $1+$ episodes vs. 0 episodes of otitis media (OTM). A separate classification was performed for the right and left ears. Several risk factors were studied as possible predictors of OTM. One such risk factor was a sibling history of ear infection, with relevant data displayed in Table 13.50 .
Assess whether a sibling history of ear infection is associated with OTM incidence in the first year of life.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 63

A longitudinal study was conducted among children in the Greater Boston Otitis Media Study [48]. Based on all doctor visits during the first year of life, children were classified as having $1+$ episodes vs. 0 episodes of otitis media (OTM). A separate classification was performed for the right and left ears. Several risk factors were studied as possible predictors of OTM. One such risk factor was a sibling history of ear infection, with relevant data displayed in Table 13.50 .
Provide a $95 \%$ Cl for the true difference in incidence rates for children with siblings between those with and without a sibling history of ear infection.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 64

Answer the questions in Problems 13.67 and 13.63 using generalized estimating equation methods, and compare results with the solution to Problems $13.62-13.63$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:33

Problem 65

Consider Data Set EAR.DAT (see Table 3.12 on page 69). Suppose we use the ear as the unit of analysis, where the outcome is a success if an ear clears by 14 days and a failure otherwise.
Compare the percentage of cleared ears between the cefaclor-treated and the amoxicillin-treated groups. Report a two-tailed $p$ -value.

Ahmed Genedy
Ahmed Genedy
Numerade Educator
01:08

Problem 66

Consider Data Set EAR.DAT (see Table 3.12 on page 69). Suppose we use the ear as the unit of analysis, where the outcome is a success if an ear clears by 14 days and a failure otherwise.
Compare the percentage of cleared ears among children $2-5$ years of age vs. the percentage of cleared ears among children $<2$ years of age. Report a two-tailed $p$ -value.

Ahmed Genedy
Ahmed Genedy
Numerade Educator
02:03

Problem 67

Consider Data Set EAR.DAT (see Table 3.12 on page 69). Suppose we use the ear as the unit of analysis, where the outcome is a success if an ear clears by 14 days and a failure otherwise.
Compare the percentage of cleared ears among children 6+ years of age vs. the percentage of cleared ears among children $<2$ years of age. Report a two-tailed $p$ -value.

Marc Lauzon
Marc Lauzon
Numerade Educator
03:04

Problem 68

A logistic-regression analysis similar to that presented in Example 13.73 (on page 743 ) was run relating breast-cancer incidence in $1980-1984$ to calorie-adjusted total fat (heretofore referred to as total fat intake) as reported on a 1980 FFQ. In addition, age in 5 -year categories and alcohol in categories $(0,0.1-4.9,5.0-14.9,15+\mathrm{g} / \text { day })$ were also controlled for. The regression coefficient for a 10 -g/day increase in total fat intake was -0.163 with standard error $=0.135$.
Obtain a point estimate and a $95 \%$ Cl for the relative risk of breast cancer comparing women whose total fat intake differs by $10 \mathrm{g} /$ day.

Lynn Larson
Lynn Larson
Numerade Educator
02:01

Problem 69

A logistic-regression analysis similar to that presented in Example 13.73 (on page 743 ) was run relating breast-cancer incidence in $1980-1984$ to calorie-adjusted total fat (heretofore referred to as total fat intake) as reported on a 1980 FFQ. In addition, age in 5 -year categories and alcohol in categories $(0,0.1-4.9,5.0-14.9,15+\mathrm{g} / \text { day })$ were also controlled for. The regression coefficient for a 10 -g/day increase in total fat intake was -0.163 with standard error $=0.135$.
Use the data for total fat to fit the linear regression of DR total fat intake on FFQ total fat intake. Obtain the regression coefficient, standard error, and $p$ -value from this regression.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
06:12

Problem 70

A logistic-regression analysis similar to that presented in Example 13.73 (on page 743 ) was run relating breast-cancer incidence in $1980-1984$ to calorie-adjusted total fat (heretofore referred to as total fat intake) as reported on a 1980 FFQ. In addition, age in 5 -year categories and alcohol in categories $(0,0.1-4.9,5.0-14.9,15+\mathrm{g} / \text { day })$ were also controlled for. The regression coefficient for a 10 -g/day increase in total fat intake was -0.163 with standard error $=0.135$.
Using the results from Problems 13.68 and 13.69 obtain an estimate of the $R R$ of breast cancer, comparing women who differ by 10 g/day on total fat intake on the DR, assuming age and alcohol intake have no measurement error and are not correlated with total fat intake.

James Kiss
James Kiss
Numerade Educator
02:47

Problem 71

Obtain a 95\% Cl for the point estimate in Problem 13.70.

Linda Hand
Linda Hand
Numerade Educator
01:08

Problem 72

Compare the measurement-error-corrected $R R$ and Cl in Problems 13.70 and 13.71 with the uncorrected $R R$ and $\mathrm{Cl}$ in Problem 13.68.

Robert Huber
Robert Huber
Numerade Educator
08:48

Problem 73

In the study presented in Example 13.75 (p. 748 ), other hormones were considered in addition to plasma estradiol. Table 13.51 presents the uncorrected relative-risk estimates and $95 \%$ Cls for several other hormones [34].
Obtain the uncorrected logistic-regression coefficients and standard errors for each of the hormones in Table 13.51.

Heather Duong
Heather Duong
Numerade Educator
01:44

Problem 74

The hormones in Table 13.51 were also included in the reproducibility study mentioned in Example 13.75 [36]. The intraclass correlation coefficient and sample size used for each hormone are given in Table 13.52.
Obtain the measurement-error-corrected logisticregression coefficient and standard error for each of the hormones in Table 13.51.

Heather Duong
Heather Duong
Numerade Educator
06:54

Problem 75

In the study presented in Example 13.75 (p. 748 ), other hormones were considered in addition to plasma estradiol. Table 13.51 presents the uncorrected relative-risk estimates and $95 \%$ Cls for several other hormones [34].
Using the results from Problem $13.74,$ obtain a measurement-error-corrected OR and $95 \%$ Cl for each of the hormones.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
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Problem 76

In the study presented in Example 13.75 (p. 748 ), other hormones were considered in addition to plasma estradiol. Table 13.51 presents the uncorrected relative-risk estimates and $95 \%$ Cls for several other hormones [34].
How do the results from Problem 13.75 compare with the results in Table $13.51 ?$

Shu Naito
Shu Naito
Numerade Educator
01:37

Problem 77

Refer to Data Set LEAD.DAT at www.cengagebrain.com. One goal of the study was to assess the effect of lead level in 1972 (variable name LD72) on neurological and psychological measures of health, while controlling for age and sex. One problem is that lead-level data in 1972 are incomplete for some children (coded as 99 ).
Use the complete-case method to relate lead levels in 1972 to full-scale 10 score (variable name IQF), while controlling for age and sex.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:58

Problem 78

Repeat the analysis in Problem 13.77 using multiple-imputation methods.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
16:05

Problem 79

Compare your results in Problems 13.77 and 13.78.

Gordon  Ayadju
Gordon Ayadju
Numerade Educator
02:35

Problem 80

A study of raloxifene and incidence of fractures was conducted among women with evidence of osteoporosis. The women were initially divided into two groups: those with and those without pre-existing fractures. The women were then randomized to raloxifene or placebo and followed for 3 years to determine the incidence of new vertebral fractures, with the results shown in Table 13.53 .
Among those with no pre-existing fractures, test whether raloxifene affects the incidence of new fractures.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:35

Problem 81

A study of raloxifene and incidence of fractures was conducted among women with evidence of osteoporosis. The women were initially divided into two groups: those with and those without pre-existing fractures. The women were then randomized to raloxifene or placebo and followed for 3 years to determine the incidence of new vertebral fractures, with the results shown in Table 13.53 .
Among those with no pre-existing fractures, compute the relative risk of new fractures among those randomized to raloxifene vs. placebo, along with its associated $95 \%$ Cl.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:35

Problem 82

A study of raloxifene and incidence of fractures was conducted among women with evidence of osteoporosis. The women were initially divided into two groups: those with and those without pre-existing fractures. The women were then randomized to raloxifene or placebo and followed for 3 years to determine the incidence of new vertebral fractures, with the results shown in Table 13.53 .
Test the association of study agent with new fractures combining both groups of those with and without preexisting fractures.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:35

Problem 83

A study of raloxifene and incidence of fractures was conducted among women with evidence of osteoporosis. The women were initially divided into two groups: those with and those without pre-existing fractures. The women were then randomized to raloxifene or placebo and followed for 3 years to determine the incidence of new vertebral fractures, with the results shown in Table 13.53 .
Combining both groups, compute the standardized RR for raloxifene vs. placebo and new fractures.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:35

Problem 84

A study of raloxifene and incidence of fractures was conducted among women with evidence of osteoporosis. The women were initially divided into two groups: those with and those without pre-existing fractures. The women were then randomized to raloxifene or placebo and followed for 3 years to determine the incidence of new vertebral fractures, with the results shown in Table 13.53 .
Is pre-existing fracture a confounder in these data?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:24

Problem 85

Suppose that 200 obese $(\mathrm{BMl} \geq 25)$ children and 500 normal-weight (BMI $<25$ ) children are identified in a school-based screening for hypertension. Eighteen of the obese children and 10 of the normal-weight children are hypertensive.
What type of study is this?

DG
David Gold
Numerade Educator
03:01

Problem 86

Suppose that 200 obese $(\mathrm{BMl} \geq 25)$ children and 500 normal-weight (BMI $<25$ ) children are identified in a school-based screening for hypertension. Eighteen of the obese children and 10 of the normal-weight children are hypertensive.
What is the $R R$ for hypertension? What is a $95 \%$ Cl associated with this estimate?

Niamat Khuda
Niamat Khuda
Numerade Educator
02:24

Problem 87

Suppose that 200 obese $(\mathrm{BMl} \geq 25)$ children and 500 normal-weight (BMI $<25$ ) children are identified in a school-based screening for hypertension. Eighteen of the obese children and 10 of the normal-weight children are hypertensive.
Suppose that $30 \%$ of children are obese by the above definition. What percent of hypertension is attributable to obesity? Provide a $95 \%$ Cl associated with this estimate.

DG
David Gold
Numerade Educator
01:30

Problem 88

An important issue is whether there are racial differences in hypertension among children. We define hypertension as being above the 95 th percentile for either systolic blood pressure (SBP) or diastolic blood pressure (DBP) among children of the same age, height, and sex. since some of the children were observed at multiple visits, a GEE model was run of hypertension on ethnic group. There were three ethnic groups considered: Caucasian, African American, and Hispanic. The results among boys are given in Table 13.54.
What is the estimated OR for hypertension comparing Hispanic boys vs. Caucasian boys? (Call this OR, ) What is a $95 \%$ Cl for this estimate?

Tyler Moulton
Tyler Moulton
Numerade Educator
19:22

Problem 89

One issue is that BMI, which may vary among ethnic groups, is positively related to hypertension. Hence, a second logistic regression model was run, as shown in Table 13.55.
What is the estimated OR for hypertension comparing Hispanic boys vs. Caucasian boys based on the results in Table 13.55 ? (Call this $\mathrm{O} R_{2}$ ) Provide a $95 \%$ Cl for this estimate. What is the difference in interpretation between $\mathrm{O} R_{1}$ and $\mathrm{O} R_{2} ?$

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
19:22

Problem 90

One issue is that BMI, which may vary among ethnic groups, is positively related to hypertension. Hence, a second logistic regression model was run, as shown in Table 13.55 .
Suppose the average BMl of Hispanic boys is higher than that for Caucasian boys. Is BMI a confounder of the association between ethnic group and hypertension? If so, is it a positive or negative confounder?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
02:30

Problem 91

One assumption of the model in Table 13.55 is that the association between hypertension and ethnic group would be the same for all levels of BMI. To test this assumption a third logistic model was run as presented in Table 13.56.
Is BMI an effect modifier of the association between hypertension and ethnic group? Why or why not?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
19:22

Problem 92

One assumption of the model in Table 13.55 is that the association between hypertension and ethnic group would be the same for all levels of BMI. To test this assumption a third logistic model was run as presented in Table 13.56.
What is the estimated ÖR for hypertension comparing Hispanic vs. Caucasian boys with BMI = 25 kg/m ^ (call this $\mathrm{O} R_{3}$ )?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
02:18

Problem 93

A study was performed relating baldness pattern to MI (heart attack) among men in the Atherosclerosis Risk in Communities (ARIC) study [49]. Baldness pattern and prevalent MI were determined at the same examination during the period $1996-1998$. Baldness was categorized into 5 categories (none/frontal/mild vertex/moderate vertex/severe vertex). For this example, we focus on the comparison of severe vertex baldness to no baldness. The data in Table 13.57 were reported by age group.
What type of study was this?

James Kiss
James Kiss
Numerade Educator
07:10

Problem 94

A study was performed relating baldness pattern to MI (heart attack) among men in the Atherosclerosis Risk in Communities (ARIC) study [49]. Baldness pattern and prevalent MI were determined at the same examination during the period $1996-1998$. Baldness was categorized into 5 categories (none/frontal/mild vertex/moderate vertex/severe vertex). For this example, we focus on the comparison of severe vertex baldness to no baldness. The data in Table 13.57 were reported by age group.
What is the estimated OR for Ml comparing men with severe vertex baldness vs. no baldness after controlling for age?

Angela Chemidlin
Angela Chemidlin
Numerade Educator
07:10

Problem 95

A study was performed relating baldness pattern to MI (heart attack) among men in the Atherosclerosis Risk in Communities (ARIC) study [49]. Baldness pattern and prevalent MI were determined at the same examination during the period $1996-1998$. Baldness was categorized into 5 categories (none/frontal/mild vertex/moderate vertex/severe vertex). For this example, we focus on the comparison of severe vertex baldness to no baldness. The data in Table 13.57 were reported by age group.
Is there a significant association between Ml and severe vertex baldness after controlling for age? Please report a two-tailed $p$ -value.

Angela Chemidlin
Angela Chemidlin
Numerade Educator
07:10

Problem 96

A study was performed relating baldness pattern to MI (heart attack) among men in the Atherosclerosis Risk in Communities (ARIC) study [49]. Baldness pattern and prevalent MI were determined at the same examination during the period $1996-1998$. Baldness was categorized into 5 categories (none/frontal/mild vertex/moderate vertex/severe vertex). For this example, we focus on the comparison of severe vertex baldness to no baldness. The data in Table 13.57 were reported by age group.
What is the OR between Ml and severe vertex baldness in (i) men $\leq 60$ and (ii) men $>60$ ? If these are the true ORs, is age an effect modifier of the association between baldness and MI? Why or why not?

Angela Chemidlin
Angela Chemidlin
Numerade Educator
01:22

Problem 97

Use logistic regression methods to assess the association between Ml and severe vertex baldness while controlling for age. Compare your results to those in Problem 13.95.

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
07:10

Problem 98

A study was performed relating baldness pattern to MI (heart attack) among men in the Atherosclerosis Risk in Communities (ARIC) study [49]. Baldness pattern and prevalent MI were determined at the same examination during the period $1996-1998$. Baldness was categorized into 5 categories (none/frontal/mild vertex/moderate vertex/severe vertex). For this example, we focus on the comparison of severe vertex baldness to no baldness. The data in Table 13.57 were reported by age group.
Suppose we wish to perform another study of the association between Ml and severe vertex baldness while controlling for age. We will use a two-sided test with $\alpha=$ 0.05 and wish a power of 0.80 to detect an $\mathrm{OR}=1.5 .$ How many subjects do we need?

Angela Chemidlin
Angela Chemidlin
Numerade Educator
01:00

Problem 99

Refer to Data Set SWISS.DAT www.cengagebrain.com.
Use methods of longitudinal data analysis to compare the rates of change in serum creatinine over time by treatment group.

Alexander Cheng
Alexander Cheng
Numerade Educator
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Problem 100

Compare your results with those obtained using ordinary ANOVA methods based on slopes in Problem 12.49 (on page 625 ).

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 101

Refer to Table 13.7 (on page 655 ).
Assess the crude association between MI and OC use without taking age into account (provide a two-tailed $p$ -value).

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 102

Refer to Table 13.7 (on page 655 ).
Assess the association between Ml and OC use after controlling for age (provide a two-tailed $p$ -value).

Victor Salazar
Victor Salazar
Numerade Educator
02:44

Problem 103

Refer to Table 13.7 (on page 655 ).
Estimate the OR between OC use and Ml after controlling for age, and provide a $95 \%$ Cl about this estimate.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:05

Problem 104

Refer to Table 13.7 (on page 655 ).
Is there evidence of effect modification of the OC-MI relationship by age?

James Kiss
James Kiss
Numerade Educator
07:48

Problem 105

Refer to Table 13.7 (on page 655 ).
Suppose we wish to perform another study of the association between OC use and MI and will control for age. Set up a logistic regression based on the data in Table $13.7,$ and use the results to estimate the sample size needed for the new study. Assume that the underlying ageadjusted $\mathrm{OR}=2.0$ and we will conduct a two-sided test with $\alpha=0.05$ and power $=0.80$.

Neel Faucher
Neel Faucher
Numerade Educator
03:53

Problem 106

Refer to Table 10.27 (on page 442 ).
Estimate the OR between widowhood and mortality, and provide a $95 \%$ Cl about this estimate.

Kami Dupree
Kami Dupree
Numerade Educator
03:48

Problem 107

A case-control study was performed early in the Nurses' Health Study (NHS) to assess the possible association between oral contraceptive (OC) use and ovarian cancer [50]. Forty seven ovarian cancer cases were identified at or before baseline (1976). For each case, 10 controls matched by year of birth and with intact ovaries at the time of the index woman's diagnosis were randomly chosen from questionnaire respondents free from ovarian cancer. The data in Table 13.58 were presented.
Use logistic regression methods to assess whether there is an association between ovarian cancer risk and duration of OC use while controlling for age. Provide a two-sided $p$ -value. Assume that the average duration of use in the $<3$ years group $=1.5$ years and in the $3+$ years group $=4$ years. Also, provide an estimate of the OR relating ovarian cancer risk per year of use of $\mathrm{OCs}$ and a $95 \%$ Cl.

Bryan Luo
Bryan Luo
Numerade Educator
03:48

Problem 108

A case-control study was performed early in the Nurses' Health Study (NHS) to assess the possible association between oral contraceptive (OC) use and ovarian cancer [50]. Forty seven ovarian cancer cases were identified at or before baseline (1976). For each case, 10 controls matched by year of birth and with intact ovaries at the time of the index woman's diagnosis were randomly chosen from questionnaire respondents free from ovarian cancer. The data in Table 13.58 were presented.
Use logistic regression methods to assess whether there is an association between ever use of OCs and ovarian cancer risk, while controlling for age. Also, provide an estimate of the $\mathrm{O} R$ and a $95 \%$ Cl about this estimate.

Bryan Luo
Bryan Luo
Numerade Educator
02:24

Problem 109

The data in Table 13.59 were presented relating body mass index (BMI) to progression of advanced age-related macular degeneration (AMD), a common eye disease in the elderly that results in significant visual loss [51] .
What is the attributable risk ( $A R$ ) of high BMI $(\geq 25)$ for progression of AMD?

DG
David Gold
Numerade Educator
07:47

Problem 110

The data in Table 13.59 were presented relating body mass index (BMI) to progression of advanced age-related macular degeneration (AMD), a common eye disease in the elderly that results in significant visual loss [51] .
Provide a $95 \%$ Cl about this estimate.

Ahmad Reda
Ahmad Reda
Numerade Educator
03:58

Problem 111

The Women's Health Study randomly assigned 39,876 initially healthy women ages 45 years or older to receive either $100 \mathrm{mg}$ of aspirin on alternate days or placebo and monitored them for 10 years for a major cardiovascular event $[52] .$ Table 13.60 shows the results stratified by age at randomization.
Use logistic regression methods to characterize the relationship between aspirin assignment and the odds of $\mathrm{CVD}$, by doing the following.
Obtain the crude OR estimate, and provide a $95 \%$ Cl for the crude OR.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
05:10

Problem 112

The Women's Health Study randomly assigned 39,876 initially healthy women ages 45 years or older to receive either $100 \mathrm{mg}$ of aspirin on alternate days or placebo and monitored them for 10 years for a major cardiovascular event $[52] .$ Table 13.60 shows the results stratified by age at randomization.
Use logistic regression methods to characterize the relationship between aspirin assignment and the odds of $\mathrm{CVD}$, by doing the following.
Test the null hypothesis of no association between aspirin assignment and CVD.

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
05:14

Problem 113

The Women's Health Study randomly assigned 39,876 initially healthy women ages 45 years or older to receive either $100 \mathrm{mg}$ of aspirin on alternate days or placebo and monitored them for 10 years for a major cardiovascular event $[52] .$ Table 13.60 shows the results stratified by age at randomization.
Use logistic regression methods to characterize the relationship between aspirin assignment and the odds of $\mathrm{CVD}$, by doing the following.
Evaluate whether age confounds the CVDaspirin relationship by using dummy variables for age categories; calculate the age-adjusted OR estimate and $95 \%$ Cl.

Jessica Waggener
Jessica Waggener
Numerade Educator
03:58

Problem 114

The Women's Health Study randomly assigned 39,876 initially healthy women ages 45 years or older to receive either $100 \mathrm{mg}$ of aspirin on alternate days or placebo and monitored them for 10 years for a major cardiovascular event $[52] .$ Table 13.60 shows the results stratified by age at randomization.
Use logistic regression methods to characterize the relationship between aspirin assignment and the odds of $\mathrm{CVD}$, by doing the following.
Evaluate whether age is an effect modifier of the relationship between aspirin and CVD.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:15

Problem 115

The data file BLOOD.DAT (www.cengagebrain.com) contains data from a case-control study assessing several plasma risk factors for breast cancer. The women were matched approximately by age at the blood draw, fasting status and, if possible, current PMH use at the time of the blood draw. There was 1 case and either 1 or 2 controls per matched set, although some of the matched sets are incomplete due to missing data. The matching variable is matchid.
Use logistic regression methods to assess the association between testosterone and breast cancer risk after controlling for age at the blood draw and current PMH use and taking the matching into account. Perform the analysis in two ways:
Treat testosterone as a continuous variable (suitably transformed if necessary).

Carson Merrill
Carson Merrill
Numerade Educator
03:15

Problem 116

The data file BLOOD.DAT (www.cengagebrain.com) contains data from a case-control study assessing several plasma risk factors for breast cancer. The women were matched approximately by age at the blood draw, fasting status and, if possible, current PMH use at the time of the blood draw. There was 1 case and either 1 or 2 controls per matched set, although some of the matched sets are incomplete due to missing data. The matching variable is matchid.
Use logistic regression methods to assess the association between testosterone and breast cancer risk after controlling for age at the blood draw and current PMH use and taking the matching into account. Perform the analysis in two ways:
Treat testosterone as a categorical variable in quartiles, with the 1 st quartile as the reference group.

Carson Merrill
Carson Merrill
Numerade Educator
00:45

Problem 117

Discuss your results from Problems 13.115 and 13.116.

Michelle Nguyen
Michelle Nguyen
Numerade Educator
01:20

Problem 118

Results from a population-based case-control study of ovarian cancer were recently reported from the North Carolina Case-Control Study based on data collected from $1999-2008[53] .$ Cases were women with ovarian cancer who were ages $20-74$ from 48 North Carolina counties; controls were frequency matched by age and race and were recruited from the same geographic regions using randomdigit dialing. Controls could not have a bilateral oophorectomy. The data in Table 13.61 were reported concerning the association between age at menarche (age when periods begin) and ovarian cancer.
For both Caucasians and African Americans (seperately), estimate the OR between late age at menarche $(\geq 12)$ and ovarian cancer risk and provide a $95 \%$ Cl about these estimate.
Two logistic models were run with Stata Version 11 using these data. For the 1 st model (Table 13.62 ) we fit $\operatorname{Logit}(p)=\alpha+\beta_{1} x_{1}+\beta_{2} x_{2}$
where $x_{1}=$ age at menarche (1 represents $\geq 12,0$ represents $<12$ ),
$\mathrm{x}_{2}=$ race $(1=\text { African American, } \mathrm{O}=\text { Caucasian })$ For the 2 nd model (Table 13.63 ) we fit $\operatorname{Logit}(p)=\alpha+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}$

Hossam Mohamed
Hossam Mohamed
Numerade Educator
02:32

Problem 119

Results from a population-based case-control study of ovarian cancer were recently reported from the North Carolina Case-Control Study based on data collected from $1999-2008[53] .$ Cases were women with ovarian cancer who were ages $20-74$ from 48 North Carolina counties; controls were frequency matched by age and race and were recruited from the same geographic regions using randomdigit dialing. Controls could not have a bilateral oophorectomy. The data in Table 13.61 were reported concerning the association between age at menarche (age when periods begin) and ovarian cancer.
Estimate the OR for the association between age at menarche and ovarian cancer after controlling for race, and provide a $95 \%$ Cl about this estimate.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
View

Problem 120

What does the variable $\beta_{1}$ mean in the 2 nd $10^{-}$ gistic regression (Table 13.63 )? How does it differ from the meaning of $\beta,$ in the 1 st logistic regression (Table 13.62)?

Shu Naito
Shu Naito
Numerade Educator
03:48

Problem 121

Results from a population-based case-control study of ovarian cancer were recently reported from the North Carolina Case-Control Study based on data collected from $1999-2008[53] .$ Cases were women with ovarian cancer who were ages $20-74$ from 48 North Carolina counties; controls were frequency matched by age and race and were recruited from the same geographic regions using randomdigit dialing. Controls could not have a bilateral oophorectomy. The data in Table 13.61 were reported concerning the association between age at menarche (age when periods begin) and ovarian cancer.
Assess whether the effect of age at menarche is different for Caucasian vs. African American women. Report a $p$ -value (two-tailed).

Bryan Luo
Bryan Luo
Numerade Educator
01:01

Problem 122

The data set WALES.DAT contains familial data on blood pressure (bp) in two-communities in South Wales (the Rhondda Fach and the Vale of Glamorgan). Subjects were seen at 4 visits from the mid 1950 s to the early 1960 s. For this problem we will focus on bp among adults (age $\geq 30$ ) at the first visit. To standardize bp for age and sex, we will use the z-score approach within 10 -year age-sex groups (i.e., age $30-39$ males/40-49 males/50-59 males/60+ males/30-39 females/40-49 females/50-59 females/60+ females) where
Systolic bp (SBP) z-score $=\frac{\mathrm{SBP}-\text { mean SBP within an age-sex group }}{\text { sd SBP within an age-sex group }}$
We then group SBP z-score for ease of interpretation as follows:
SBP z-score group $=2$ if SBP z-score $\geq 1.0$
$=1$ if $\operatorname{SBP} z-$ score $\geq 0.5$ and $<1.0$
$=0$ if $\mathrm{SBP} z$ -score $<0.5$ and not missing.
Use polytomous logistic regression with group $=0$ as the reference group to assess the association between SBP z-score group and the following variables:
(a) BMI, (b) height, (c) region (i.e., Rhondda Fach vs. Vale of Glamorgan), (d) occupation (treat occupation codes of $5-9$ as missing for this analysis). Of particular interest is the comparison of group $=2$ vs. group $=0$

Tyler Moulton
Tyler Moulton
Numerade Educator
02:27

Problem 123

Use ordinal logistic regression to assess the association between SBP z-score group and the same variables in Problem 13.122.

Bryan Luo
Bryan Luo
Numerade Educator
01:04

Problem 124

Compare your results in Problems 13.122 and 1 3.1 23.

Carson Merrill
Carson Merrill
Numerade Educator
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Problem 125

Repeat the analyses in Problems $13.122-13.124$ using diastolic bp (DBP) z score group defined in the same manner as SBP z-score group.

Victor Salazar
Victor Salazar
Numerade Educator