Likelihood Calculations for Matched Case-Control Studies and Survival Studies with Tied Death Times

A recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case-control studies and survival studies with tied death times. An example with seven parameters and ten large strata, the largest of which contains 29 cases and 52 controls, illustrates the feasibility of the conditional maximum likelihood solution. These methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate of the common odds ratio for several 2×2 tables.