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

TL;DR

This paper introduces new statistical methods for analyzing 2x2 tables and two-sample survival data, addressing computational challenges and providing more accurate variance estimations for common estimators.

Contribution

It develops novel estimators and variance estimation techniques for odds ratio and hazard ratio models, improving accuracy and theoretical understanding.

Findings

The weighted Mantel–Haenszel estimator is proposed for odds ratio models.

The Breslow–Peto estimator is shown to be consistent for probability ratio models.

New variance estimators are more accurate and theoretically justified.

Abstract

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.