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An Extended Proportional Odds Model with Time-Varying Covariates
*Nan Hu, University of Washington 

Keywords: Counting process; Estimating function; HIV/AIDS clinical trial; Logistic regression; Semiparametric model; Time-to-event outcome

The proportional odds model has been used as an alternative to the Cox proportional hazard model to study associations between time-independent covariates and survival functions in medical studies. Additionally, one may also be interested in studying an interaction between these covariates and time, or would want to include the ovariates that are potentially time-varying in the proportional odds model. In this article, we hence study an extended proportional odds model with time-varying covariates. In this extended model, regression parameters has a direct interpretation of comparing survival functions, while the baseline survival odds function is unspecified. To estimate the regression parameters, we first develop a simple closed-form estimator for the baseline odds function, and then derive a log-rank type of quasi partial score equations. Monte-Carlo simulations are conducted to assess the validity of our proposed inference procedure. This methodology is motivated by 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 analysis of a well-known Veterans Administration (VA) Lung Cancer Trial.