Bias and efficiency in logistic analyses of stratified case-control studies

Two approaches to the estimation of the parameters in the logistic model applied to the analysis of stratum matched case-control studies are compared. It is shown that the "unconditional likelihood method' gives estimates of odds ratios which may be severely exaggerated if the stratum sizes are not large; however, if stratum sizes are not small the "conditional likelihood method' is computationally prohibitive. The use of small stratum sizes (e.g., 1-to-1 matching) leads to some loss of efficiency if the matching is irrelevant but it is shown that the loss is small for odds ratios up to at least 3. There would seem to be strong arguments for the routine use of matched designs as the reduction in confounding bias produced by such matching may be considerable whereas there is only a small loss in efficiency compared with unmatched designs.