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For discrete-time survival data, conditional likelihood inference in Cox'shazard odds model is theoretically desirable but exact calculation is numericalintractable with a moderate to large number of tied events. Unconditionalmaximum likelihood estimation over both regression coefficients and baselinehazard probabilities can be problematic with a large number of time intervals.We develop new methods and theory using numerically simple estimatingfunctions, along with model-based and model-robust variance estimation, inhazard probability and odds models. For the probability hazard model, we deriveas a consistent estimator the Breslow-Peto estimator, previously known as anapproximation to the conditional likelihood estimator in the hazard odds model.For the odds hazard model, we propose a weighted Mantel-Haenszel estimator,which satisfies conditional unbiasedness given the numbers of events inaddition to the risk sets and covariates, similarly to the conditionallikelihood estimator. Our methods are expected to perform satisfactorily in abroad range of settings, with small or large numbers of tied eventscorresponding to a large or small number of time intervals. The methods areimplemented in the R package dSurvival.

Consistent and robust inference in hazard probability and odds models with discrete-time survival data