  Analysis of 2 by 2 tables and two-sample survival data has been widely used.
Exact calculation is computational intractable for conditional likelihood
inference in odds ratio models with large marginals in 2 by 2 tables, or
partial likelihood inference in Cox's proportional hazards models with
considerable tied event times. Approximate methods are often employed, but
their statistical properties have not been formally studied while taking into
account the approximation involved. We develop new methods and theory by
constructing suitable estimating functions while leveraging knowledge from
conditional or partial likelihood inference. We propose a weighted
Mantel--Haenszel estimator in an odds ratio model such as Cox's discrete-time
proportional hazards model. Moreover, we consider a probability ratio model,
and derive as a consistent estimator the Breslow--Peto estimator, which has
been regarded as an approximation to partial likelihood estimation in the odds
ratio model. We study both model-based and model-robust variance estimation.
For the Breslow--Peto estimator, our new model-based variance estimator is no
greater than the commonly reported variance estimator. We present numerical
studies which support the theoretical findings.
