Survival estimation through the cumulative hazard function with monotone natural cubic splines

In this paper we explore the estimation of survival probabilities via a smoothed version of the survival function, in the presence of censoring. We investigate the fit of a natural cubic spline on the cumulative hazard function under appropriate constraints. Under the proposed technique the problem reduces to a restricted least squares one, leading to convex optimization. The approach taken in this paper is evaluated and compared via simulations to other known methods such as the Kaplan Meier and the logspline estimator. Our approach is easily extended to address estimation of survival probabilities in the presence of covariates when the proportional hazards model assumption holds. In this case the method is compared to a restricted cubic spline approach that involves maximum likelihood. The proposed approach can be also adjusted to accommodate left censoring.