An empirical evaluation of the use of conditional and unconditional likelihoods for case-control data

Abstract

A Monte Carlo study is made of conditional and unconditional likelihoods in the analysis of case-control data where the underlying disease incidence is assumed to follow a logistic model. Results indicate that the full likelihood may yield estimates of relative risk that are unacceptably biased upwards for strata with fewer than 20 cases and 20 controls. The simulations support the need for better approximations to the conditional likelihood. With 1 to R matched studies the bias of the full likelihood is excessive for R less than 10, suggesting the general use of the conditional likelihood. In matched pair studies the conditional likelihood tends to underestimate the true risk when there are fewer than 50 pairs.