Isotonic Estimation of Additive Covariate Effects Under Proportional Hazard Models

In this paper, we generalize the isotonic proportional hazards model to include multiple continuous covariates with an unspecified baseline hazard function where the effect of the covariate on a failure rate is monotone but otherwise unspecified. In particular, we study the additive isotonic structure of multiple covariates, assuming the monotonic effects of the covariates are separated and linearly added to the semiparametric proportional hazards model. We propose an efficient computation by implementing the pseudo iterative convex minorant algorithm in the cycling algorithm. The algorithm is extended to a model with multiple time-dependent covariates. In simulation studies, our proposed method shows a decrease in bias and variance as the sample size increases. Additionally, we will demonstrate the practical utility of our methodology using data from a cardiovascular study.