An EM algorithm for analyzing right-censored survival data under the semiparametric proportional odds model

The semiparametric proportional odds (PO) model is a popular alternative to Cox’s proportional hazards model for analyzing survival data. Although many approaches have been proposed for this topic in the literature, most of the existing approaches have been found computationally expensive and difficult to implement. In this article, a novel and easy-to-implement approach based on an expectation-maximization (EM) algorithm is proposed for analyzing right-censored data. The EM algorithm involves only solving a low-dimensional estimating equation for the regression parameters and then updating the spline coefficients in simple closed form at each iteration. Our method is robust to initial values, converges fast, and provides the variance estimates in closed form. Simulation studies suggest that the proposed method has excellent performance in estimating both regression parameters and the baseline survival function, even when the right censoring rate is very high. The method is applied to a large dataset about breast cancer survival extracted from the Surveillance, Epidemiology, and End Results (SEER) database maintained by the U.S. National Cancer Institute. This method is now available in R package regPOr for public use.