Semiparametric inference in the proportional odds regression model

For fitting the proportional odds regression model with right-censored survival times, we introduce some weighted empirical odds functions. These functions are solutions of some self-consistency equations and have a nice martingale representation. From these functions, several classes of new regression estimators, such as the pseudo-maximum likelihood estimator, martingale residual-based estimators, and minimum distance estimators, are derived. These estimators have desirable properties such as easy computation, asymptotic normality via a martingale analysis, and reliable asymptotic covariance estimation in closed form. Extensive numerical studies show that the minimum La distance estimators have very good finite-sample behaviors compared to existing methods. Results of some simulation studies and applications to a real dataset are given. The weighted odds function-based approach also provides inference on the baseline odds function and some measures for lack-of-fit analysis.