10.2. Paired Observations from a Highly Stratified Cohort Study
Consider a randomized clinical trial where i = 1,2,...,q centers are randomly selected, and, at each center, one randomly selected patient is placed on treatment, and another randomly selected patient is placed on placebo. Interest lies in whether the patients improve; thus, improvement is the event of interest. Since there are only two observations per center, it is not possible to estimate a center effect (pair effect) without bias. As a general rule, you need each possible outcome to have five observations per explanatory variable in the model for valid estimation to proceed.
Suppose yij = 1 if improvement occurs and yij = 0 if it does not (j = 1 for treatment and j = 2 for the ...
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