Exploring the varying covariate effects in proportional odds models with censored data

In this article, we consider a proportional odds model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable for analysis of right-censored data. A local maximum likelihood approach is presented to estimate nonlinear interactions (the coefficient functions) and the baseline function. The proposed estimators are shown to be consistent and asymptotically normal with the asymptotic variance estimated consistently. Also, we develop local profile likelihood ratio method to construct confidence region of coefficient functions. Simulation studies are conducted to evaluate the performances of the proposed estimators, and compare the normal approximation based confidence regions and local profile likelihood ratio based confidence regions. The method is illustrated with Stanford heart transplant data.