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Analysis of 2 by 2 tables and two-sample survival data has been widely used.Exact calculation is computational intractable for conditional likelihoodinference in odds ratio models with large marginals in 2 by 2 tables, orpartial likelihood inference in Cox's proportional hazards models withconsiderable tied event times. Approximate methods are often employed, buttheir statistical properties have not been formally studied while taking intoaccount the approximation involved. We develop new methods and theory byconstructing suitable estimating functions while leveraging knowledge fromconditional or partial likelihood inference. We propose a weightedMantel--Haenszel estimator in an odds ratio model such as Cox's discrete-timeproportional hazards model. Moreover, we consider a probability ratio model,and derive as a consistent estimator the Breslow--Peto estimator, which hasbeen regarded as an approximation to partial likelihood estimation in the oddsratio model. We study both model-based and model-robust variance estimation.For the Breslow--Peto estimator, our new model-based variance estimator is nogreater than the commonly reported variance estimator. We present numericalstudies which support the theoretical findings.

Analysis of odds, probability, and hazard ratios: From 2 by 2 tables to two-sample survival data