Question

AMA 4351 STATISTICAL EPIDEMIOLOGY Answer any two questions. CAT 2. 5th April 2024 1 hour. Question one (15 marks) 228 patients with advanced lung cancer were recruited in cohort study and followed up for one year or until they died or exited the study for any other reason. A researcher conducted a Cox Proportional Hazard regression analysis. Below are the results. Call: coxph(formula = Surv(time, status) ~ sex + age + ph.ecog, data = lung) n= 227, number of events= 164 (1 observation deleted due to missingness) coef se(coef) z Pr(>|z|) sex -0.552612 0.167739 -3.294 0.000986 * age 0.011067 0.009267 1.194 0.232416 ph.ecog 0.463728 0.113577 4.083 4.45e-05 * --- Signif. codes: 0 '' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 a) Explain two key assumptions made by the researcher when using the Cox Proportional Hazard model. (2 marks) b) From the regression coefficient reported, compute the hazard ratios and their 95% confidence intervals for the three exposure variables and interpret the researcher findings. (5 marks) c) The researcher was interested in testing differences in survival time between male and female patient and obtained the following results N Observed Expected (O-E)^2/E (O-E)^2/V sex=1 138 112 91.6 4.55 10.3 sex=2 90 53 73.4 5.68 10.3 Chisq= 10.3 on 1 degrees of freedom, p= 0.001 Identify the statistical test he could use in the comparison. (2 marks) d) Was there evidence the survival time was different? Explain your answer. (3 marks) e) Show that in Cox proportional hazards model, the Hazard Ratio (HR) is given as: HR(t) := e^?? (3 marks)

          AMA 4351 STATISTICAL EPIDEMIOLOGY
Answer any two questions. CAT 2. 5th April 2024 1 hour.
Question one (15 marks)
228 patients with advanced lung cancer were recruited in cohort study and followed up for one year or until they died or exited the study for any other reason. A researcher conducted a Cox Proportional Hazard regression analysis. Below are the results.
Call:
coxph(formula = Surv(time, status) ~ sex + age + ph.ecog, data = lung)
n= 227, number of events= 164
(1 observation deleted due to missingness)
            coef      se(coef)      z Pr(>|z|)
sex      -0.552612    0.167739 -3.294 0.000986 ***
age       0.011067    0.009267  1.194 0.232416
ph.ecog   0.463728    0.113577  4.083 4.45e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
a) Explain two key assumptions made by the researcher when using the Cox Proportional Hazard model. (2 marks)
b) From the regression coefficient reported, compute the hazard ratios and their 95% confidence intervals for the three exposure variables and interpret the researcher findings. (5 marks)
c) The researcher was interested in testing differences in survival time between male and female patient and obtained the following results
        N Observed Expected (O-E)^2/E (O-E)^2/V
sex=1 138      112     91.6      4.55      10.3
sex=2  90       53     73.4      5.68      10.3
Chisq= 10.3 on 1 degrees of freedom, p= 0.001
Identify the statistical test he could use in the comparison. (2 marks)
d) Was there evidence the survival time was different? Explain your answer. (3 marks)
e) Show that in Cox proportional hazards model, the Hazard Ratio (HR) is given as:
HR(t) := e^?? (3 marks)

AMA 4351 STATISTICAL EPIDEMIOLOGY
Answer any two questions. CAT 2. 5th April 2024 1 hour.
Question one (15 marks)
228 patients with advanced lung cancer were recruited in cohort study and followed up for one year or until they died or exited the study for any other reason. A researcher conducted a Cox Proportional Hazard regression analysis. Below are the results.
Call:
coxph(formula = Surv(time, status) sex + age + ph.ecog, data = lung)
n= 227, number of events= 164
(1 observation deleted due to missingness)
coef se(coef) z Pr(>|z|)
sex -0.552612 0.167739 -3.294 0.000986 ***
age 0.011067 0.009267 1.194 0.232416
ph.ecog 0.463728 0.113577 4.083 4.45e-05 ***
—
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
a) Explain two key assumptions made by the researcher when using the Cox Proportional Hazard model. (2 marks)
b) From the regression coefficient reported, compute the hazard ratios and their 95% confidence intervals for the three exposure variables and interpret the researcher findings. (5 marks)
c) The researcher was interested in testing differences in survival time between male and female patient and obtained the following results
N Observed Expected (O-E)^2/E (O-E)^2/V
sex=1 138 112 91.6 4.55 10.3
sex=2 90 53 73.4 5.68 10.3
Chisq= 10.3 on 1 degrees of freedom, p= 0.001
Identify the statistical test he could use in the comparison. (2 marks)
d) Was there evidence the survival time was different? Explain your answer. (3 marks)
e) Show that in Cox proportional hazards model, the Hazard Ratio (HR) is given as:
HR(t) := e^?? (3 marks)

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