Regression Analysis of Arbitrarily Censored and Left‐Truncated Data Under the Proportional Odds Model

In survival analysis, the exact times of an event of interest may not always be observed due to the nature of the event and the study design for all subjects but are usually partially observed subject to censoring and truncation in many real-life studies. In this article, we study regression analysis of arbitrarily censored and left-truncated data under a popular semiparametric proportional odds model. A new estimation approach via an expectation and maximization algorithm (EM) is developed based on a novel data augmentation involving exponential and multinomial latent variables. The EM algorithm has appealing features such as being robust to initial values, converging fast, and providing a variance estimate in a simple closed form. The proposed approach has excellent performance and outperforms several existing competing methods, as shown in our simulation studies, and it is further illustrated by two real-life data applications. The proposed method has been incorporated into the R package regPOspline for public use.