Home Assignment
Q1. An investigation was conducted to study the average time it took for students to reach to
school. Information about time (in minutes) was collected as <30, 30- 60 and > 60. What
problems, you may encounter in the analysis using such data? (2 marks)
Q2. In a study to examine the risk factors for under-nutrition among children less than 3
years of age (N=1054), the information about immunization status of the children was
missing for 18% of the subjects. Describe and explain the two possible ways to deal with the
missing data (4 marks).
Q3. A IGRAs sero-prevalence survey of Mycobacterium tuberculosis among adults was
conducted in Thar region of Sindh. This survey provides relatively unbiased estimates of
prevalence of Mycobacterium tuberculosis in the adult population of the region. Suppose that the
Mycobacterium tuberculosis status of each subject is approximately independent of each other,
and the true prevalence of Mycobacterium tuberculosis is 0.05. A total of 80 individuals were
surveyed to examine for Mycobacterium tuberculosis. (Total marks 11)
a) Find the exact p-value of getting at most two individuals as IGRAs positive under the hypothesis
that the true prevalence of Mycobacterium tuberculosis is 0.05? (4 marks)
b) Find the p-value of getting at most two individuals as IGRAs positive by using appropriate
approximate methods described by Greenland & Rothman? (5 marks)
c) Comment on the results obtained in part a) and b). (2 marks)
Q4. A researcher computed exact confidence intervals from a 2x2 table with limits of the
confidence interval are between 1.45 and 3.22. Now, she thought that mid-p exact limits are more
appropriate in this scenario, how would you expect these results to be in comparison with exact
confidence intervals? Explain your answer (2 marks)
Q5. The data in the table below are from a case-control study, showing numbers of patients
attending a particular ante-natal clinic in the last 5 years. The aim of the study was to
examine risk factors associated with low birth weight. Cases were defined as women giving
birth to a baby weighing less than 2500 g and were a random sample from all such women
attending the clinic in the past 5 years. Controls were a similarly drawn random sample of
women whose baby weighed at least 2500 g. The risk factors of interest were Ethnic origin,
Number of ante-natal visits in the first trimester of pregnancy and Smoking status during
pregnancy. The data is presented in the table below (17 marks).
Smoked during Cases (birth weight Controls (birth weight Total
pregnancy
<2500 g)
2500+ g)
No
29 (49.0%)
86 (66.0%)
115
Yes
30 (51.0%)
44 (34.0%)
74
Total
59
130
189
a) State the null and alternate hypothesis for the smoking as the exposure in terms of
parameter of the interest (2 mark).
b) State and explain the assumptions for obtaining crude estimate (3 marks).
c) Calculate and interpret the relevant measure of association (2 marks).
d) Calculate 95% confidence interval (4 marks)
e) Using the appropriate formula in your handouts and book, obtain the estimate of
uncertainty in results due to chance and interpret the p-value obtained (6 marks).
Q6. A researcher studied maternal risk factors and pregnancy outcomes. He was particularly
interested in babies that were “Small for Gestational Age (SGA)” as a sign of intrauterine
growth restriction (IUGR). Risk factors that he considered were maternal smoking during
pregnancy and maternal “parity” (number of prior live births).
A sub-sample of 751 subjects from that study was analyzed for the following variables (all
measured at time of study enrolment). (22 marks)
smoker: Mother smoked during pregnancy (0= no, 1= yes);
parity: Number of prior live births (0= none, 1= one, 2= two or more);
nulliparous: Never given birth including mother with first pregnancy i.e. parity = 0
(0= no, 1= yes)
SGA : Baby was small for gestational age at birth (0= no, 1= yes)
The following table present cross-tabulation of “small for gestational age (sga)” by maternal
smoking (smoker) and parity(parity).
a) Construct tables of “small for gestational age (sga)” by maternal smoking during
pregnancy (smoker) overall and within groups defined by nulliparous (Hint: Make 2x2
tables) (6 Marks)
b) The parity level-specific odds ratios for maternal smoking during pregnancy versus small
for gestational age with 95% confidence intervals are given in the following table: (16 marks)
Nulliparous
None
At least one
OR (95% C.I.)
1.69 (0.96, 2.99)
2.27 (1.20, 4.30)
The crude and Mental Haenszel odds ratios for maternal smoking during pregnancy versus small
for gestational age are 1.89 (95% C.I.: 1.24, 2.89) and 1.92 (95% C.I.: 1.26, 2.94) respectively.
The values of test statistic(s) for crude and Nulliparous status adjusted Mantel-Haenszel 2’s are
8.87 (p-value=0.0029) and 9.32 (p-value=0.0023) respectively each with one degree of freedom.
Similarly, the crude odds ratios for maternal smoking versus nulliparous status and small for
gestational age versus nulliparous status are 0.84 (95% C.I.: 0.61, 1.16) and 1.43 (95% C.I.: 0.94,
2.16) respectively. The values of test statistic(s) for these associations using 2 are 1.12 (pvalue=0.2908) and 2.79 (p-value=0.0949) respectively each with one degree of freedom.
i) Is there effect modification by nulliparous status? Provide reasons to support your
answer (3 marks)
ii) Is there confounding by Nulliparous status? Provide reasons to support your answer
along with the criteria for confounding. (3 marks)
iii) Test whether crude estimate is homogeneous across strata? Use α=0.05. Write down all
steps of testing the hypothesis. (10 marks)
Q7. To investigate whether maternal HIV infection was a risk factor for child severe
pneumonia, a case-control study was conducted. There were 266 children with one or more
episodes of severe pneumonia, with a total of 283 episodes. For each of the 283 episodes, the
child was recruited as a case. 283 individually-matched control children were selected from
the demographic surveillance site (DSS) population, with one control child for each case. The
control child was matched on age (in months), sex, and neighborhood, and was selected
within one week of the date that the matched case presented at the health clinic. (20 marks)
The table using discordant and concordant pairs is summarized below:
Case mother HIV negative
Case mother HIV positive
Control mother HIV negative
232
38
Control mother HIV positive
11
2
a) What is the exposure and outcome of interest in the above scenario? (2 marks)
b) Calculate crude and Mantel-Haenszel measures of risk for the association between
maternal HIV and child severe pneumonia, comparing children with HIV positive mothers
to children with HIV negative mothers. Also obtain 95% confidence interval for the MantelHaenszel estimate. (8 marks)
c) Is there any relationship of maternal HIV and child severe pneumonia? Test the
hypothesis at 5% level of significance to support your answer. Write down all steps of
testing the hypothesis. (10 marks)