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

TY - JOUR

T1 - Analysis of odds, probability, and hazard ratios

T2 - From 2 by 2 tables to two-sample survival data

AU - Tan, Zhiqiang

N1 - Funding Information: The research was supported in part by PCORI, United States of America grant ME-1511-32740 . The author thanks two referees for helpful comments. Publisher Copyright: © 2022 Elsevier B.V.

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - Breslow–Peto estimator

KW - Conditional likelihood

KW - Mantel–Haenszel estimator

KW - Model-robust variance estimation

KW - Partial likelihood

KW - Proportional hazards model

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U2 - https://doi.org/10.1016/j.jspi.2022.05.002

DO - https://doi.org/10.1016/j.jspi.2022.05.002

M3 - Article

SN - 0378-3758

VL - 221

SP - 248

EP - 265

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

ER -