STOCKHOLM UNIVERSITY
DEPT OF MATHEMATICS
Div. of Mathematical Statistics
MS 4070
EXAM
23 October 2006
Exam in Epidemiology
23 October 2006 at 9–14
Examiner: Juni Palmgren, tel. 16 45 57, [email protected]
Allowed aid: Formulae and tables supplied with the exam. Pocket calculator.
Return: Thursday 26/10 2006 at 13.30 in room 31, house 6, Kräftriket or by appointment.
The result may also be announced by e-mail for those who wish.
Every correct problem gives 10 points. The limit for Pass (Godkänt) is 45 points and for
Excellent (Väl Godkänt) is 65 points including extra points from the homework assignments.
————————————————
Problem 1
a)
(3 p)
What measures of association can meaningfully be calculated from data in a prospective
follow-up study?
b)
(3 p)
Calculate the odds of failing when the probability of failing is (i) 0.75 (ii) 0.50 (iii) 0.25,
respectively.
c)
(4 p)
In a three year follow-up study the conditional probabilities of failure during the first, second
and third years are 0.05, 0.09, and 0.12, respectively. Calculate the probability of surviving
three years without failing. Calculate also the probability of failing at some time during the
three year follow-up.
Problem 2
Woolf (1955) illustrated his paper on methods for analyzing 2x2 tables with the following data
from a British case-control study of peptic ulcer and blood type. The data are from two large
cities, comparing cases of peptic ulcer with either blood type A or O, with population controls
from these same cities with either blood type A or O.
Epidemiology, 23 October 2006
Blood Type
Group A
Group O
2
Peptic Ulcer
YES
NO
|
1272
9110 | 10382
825
7994 | 8819
------------|
2097
17104 19202
a)
(2 p)
What margin(s) are fixed by design?
b)
(2 p)
What measure(s) of association between blood type and risk of peptic ulcer can meaningfully
be estimated? Give the relevant estimate(s).
c)
(2 p)
Compute a 95% confidence interval for the association between blood type and risk of peptic
ulcer.
d)
(2 p)
Test the null hypothesis of no association between blood type and risk of peptic ulcer.
e)
(2 p)
Describe in words the results and the conclusions of the analysis.
Problem 3
The data for the study in problem 2 were collected in London and Manchester, England. Here
are the separate results for each city:
London
Blood Type
Group A
Group O
Peptic Ulcer
YES
NO
911
4578
579
4219
Manchester
Blood Type
Group A
Group O
Peptic Ulcer
YES
NO
361
4532
246
3775
Consider the following Stata Output
cc ulcer type
[fw=count], by(city)
3
Epidemiology, 23 October 2006
city |
OR [95% Conf. Interval] M-H Weight
-------------+------------------------------------------London
|
1.4500
1.293997
1.624901
257.671 (exact)
Manchester|
1.222
1.030082
1.450677
125.0698 (exact)
-------------+------------------------------------------Crude |
1.3529
1.231923
1.485873
(exact)
M-H combined |
1.3756
1.253122
1.510105
--------------------------------------------------------Test of homogeneity (M-H)
chi2(1) =
2.75 Pr>chi2 = 0.0972
Test that combined OR = 1:
Mantel-Haenszel chi2(1) =
Pr>chi2 =
0.0000
45.21
a)
(3 p)
Consider first the tables separately: What is the odds ratio in London? Is there a statistically significant association in London? And what is the odds ratio in Manchester? Is this
association statistically significant?
b)
(3 p)
Do the associations between blood type and risk of ulcer differ in London and Manchester at
the 5% significance level?
c)
(4 p)
Does city act as a confounder and/or as an effect modifier in this study?
Problem 4
a)
(3 p)
When the risk factor of interest is less common in the population than the disease of interest, which study design (cohort or case-control) is usually more powerful for studying the
association between the risk factor and the disease?
b)
(3 p)
Suppose two investigators are planning case-control studies, and both determine to randomly
select 100 cases and 100 controls from their populations of interest. The first investigator
believes that exposure probabilities in the cases and controls are roughly 0.4 and 0.1, respectively (so an odds ratio of about 6 is expected). The second investigator believes that, in
her situation, the exposure probabilities in the cases and controls are roughly 0.2 and 0.04,
respectively (so that again an odds ratio of about 6 is anticipated). Which study has the
greater power to detect a significant association between the exposure and disease?
c)
(4 p)
A researcher has carried out a case-control study of risk factors for leukaemia among children.
He has been told, by a colleague, that he should be using logistic regression to analyse his
4
Epidemiology, 23 October 2006
data. He remembers, from his days at medical school, how to calculate chi-square significance
tests and relative risks from contingency tables, and he has done this for all the variables
(potential risk factors) in his data set. He comes to you for help, and asks two questions:
1. What is the advantage of using logistic regression rather than simple chi-square tests
and relative risks?
2. How can I interpret the results from a logistic regression analysis obtained from a computer package?
What would you tell him?
Problem 5
Karkavelas et al (1995) give the following survival times (in rank order) for 27 subjects with
a rare form of brain tumor:
10,12,13,15,16,20,20,24,24,26,26,27,39,42,45,45,48,52,58,60,61,62,73,75,77,104,120.
Survival time is recorded as the number of weeks between initiation of cisplantin treatment
and death. No subject was recorded as censored.
a)
(3 p)
Construct a graph (by hand) of the estimated survival function for up to 20 weeks of follow-up.
b)
(3 p)
Construct a graph (by hand) of the estimated hazard function for up to 20 weeks of follow-up.
c)
(4 p)
Divide the time axis into ten week intervals and estimate the failure rate in the first and
second ten week follow-up period.
Problem 6
For the study in problem 5, the cellularity of the tumor is believed to affect survival. High
versus low cellularity was recorded for each tumor and a log hazard ratio of 0.558 (standard
error 0.437) was obtained from fitting a Cox proportional hazards model, comparing survival
of patients with high cellularity tumors to patients with low cellularity tumors.
a)
(5 p)
Describe the Cox proportional hazards model, and interpret the result given above.
b)
(5 p)
Describe the log-rank test for the hypothesis of equal survival experience in the two groups.
Good luck!