  For discrete-time survival data, conditional likelihood inference in Cox's
hazard odds model is theoretically desirable but exact calculation is numerical
intractable with a moderate to large number of tied events. Unconditional
maximum likelihood estimation over both regression coefficients and baseline
hazard probabilities can be problematic with a large number of time intervals.
We develop new methods and theory using numerically simple estimating
functions, along with model-based and model-robust variance estimation, in
hazard probability and odds models. For the probability hazard model, we derive
as a consistent estimator the Breslow-Peto estimator, previously known as an
approximation 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 in
addition to the risk sets and covariates, similarly to the conditional
likelihood estimator. Our methods are expected to perform satisfactorily in a
broad range of settings, with small or large numbers of tied events
corresponding to a large or small number of time intervals. The methods are
implemented in the R package dSurvival.
