Problem on matching, Epidemiology Course VHM 811 at AVC - Fall Semester 2007

This problem follows closely Tables 10.1-4 of Rothman & Greenland (1998). It is intended merely as an illustration of the calculations involved in matching in cohort and case-control studies.

"Consider the hypothetical target population of 2 million individuals given in Table 10-1. Both the exposure and male sex are risk factors for the disease: Within sex, exposed have 10 times the risk of unexposed, and within exposure levels, males have five times the risk of females. There is also substantial confounding, since 90% of the exposed individuals are male and only 10% of the unexposed are male. The crude risk ratio in the target population comparing exposed with unexposed is 33, considerably different from the sex-specific value of 10."

1. Compute the risks within the four groups, and convince yourself that the numbers derived from the table match the description in the above excerpt from Rothman & Greenland (1998).

2. Suppose a cohort study was planned involving 10% of the exposed target population. Work out the desired distribution of individuals onto the four groups after frequency matching for sex, and compute also the expected numbers of cases in each group. Check that the risk ratio is indeed constant within sex, and identical to the crude risk ratio.

3. Suppose a case-control study was planned involving all the cases in the target population and a sample of an equal number of controls, frequency matched to the cases for sex. Work out the desired distribution of individuals onto the four groups, and compute also the expected numbers of cases and controls in each group. Calculate the crude odds-ratio as well as the odds-ratio within each sex, and comment on your finding. Calculate also suitable statistics to substantiate a selection bias for the exposure.