Four methods for modifying partial likelihood analysis of proportional hazards models to deal with interval censored event times are compared via 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 increase or treatment effects increase. Estimated treatment effects tend to be biased toward zero for both methods. The Efron approximation 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 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. In the second part of the presentation, interval censored event time data where members of a cohort may provide correlated response times, and different cohorts may be subjected to different inspection schedules are discussed. Initially any correlation among response times is ignored and a multinomial model for the counts observed in the inspection intervals is used. Non-homogeneous inspection schedules require estimation methods for incompletely classified multinomial data. Robust variance estimation is used to obtain consistent estimates of covariance matrices for parameter estimates. Parametric models for multinomial probabilities are also considered, and tests for comparing the fit of nested models are developed. An application to modeling the development rate of bean leaf beetle eggs is discussed.