Estimating Regression Parameters in an Extended Proportional Odds Model

Abstract

The proportional odds model may serve as a useful alternative to the Cox proportional hazards model to study association between covariates and their survival functions in medical studies. In this article, we study an extended proportional odds model that incorporates the so-called “external” time-varying covariates. In the extended model, regression parameters have a direct interpretation of comparing survival functions, without specifying the baseline survival odds function. Semiparametric and maximum likelihood estimation procedures are proposed to estimate the extended model. Our methods are demonstrated by Monte Carlo simulations, and applied to a landmark randomized clinical trial of a short-course nevirapine (NVP) for mother-to-child transmission (MTCT) of human immunodeficiency virus type-1 (HIV-1). Additional application includes an analysis of the well-known Veterans Administration (VA) lung cancer trial.

KEY WORDS:

• Counting process
• Estimating function
• HIV/AIDS
• Maximum likelihood estimation
• Semiparametric model
• Time-varying covariate

Acknowledgments

Chen's research was partially supported by grants from the National Institute of Allergy and Infectious Diseases (NIH/NIAID R01 AI089341, R01 AI78835) and the National Cancer Institute (NIH/NCI P01 CA053996), Hu's research was partially supported by the University of Utah's Study Design and Biostatistics Center, with funding in part from the Public Health Services research grant numbers UL1-RR025764 and C06-RR11234 and from the National Center for Research Resources, and Zhao's research was partially supported by grants from the National Institute of Mental Health (NIH/NIMH R01 MH 084621) and the National Cancer Institute (NIH/NCI R01 CA 119225). The authors thank the editor, an associate editor, and two referees for their valuable comments that helped improve a previous version of the article.