Methods for applying partial likelihood analysis of proportional hazards models to interval censored failure times are compared in a simulation study. The Efron approximation is shown to be superior to the Breslow approximation, but both methods tend to break down as the number of tied event times created by interval censoring increases or treatment effects increase. Estimates of treatment effects tend to be biased toward zero for both methods. The Efron method is shown to closely approximate the geometric mean of the partial likelihoods for all possible orderings of tied event times, while the arithmetic mean of all possible likelihoods more closely approximates the results that would be obtained if the exact event times were known. Geometric and arithmetic means of random samples of possible partial likelihoods are considered for situations with larger numbers of tied failure times. Key words: Cox proportional hazards, interval censoring, partial likelihood, tied failure times.