Maximum Likelihood Estimation in a Semicontinuous Survival Model with Covariates Subject to Detection Limits

Semicontinuous data are common in biological studies, occurring when a variable is continuous over a region but has a point mass at one or more points. In the motivating Genetic and Inflammatory Markers of Sepsis (GenIMS) study, it was of interest to determine how several biomarkers subject to detection limits were related to survival for patients entering the hospital with community acquired pneumonia. While survival times were recorded for all individuals in the study, the primary endpoint of interest was the binary event of 90-day survival, and no patients were lost to follow-up prior to 90 days. In order to use all of the available survival information, we propose a two-part regression model where the probability of surviving to 90 days is modeled using logistic regression and the survival distribution for those experiencing the event prior to this time is modeled with a truncated accelerated failure time model. We assume a series of mixture of normal regression models to model the joint distribution of the censored biomarkers. To estimate the parameters in this model, we suggest a Monte Carlo EM algorithm where multiple imputations are generated for the censored covariates in order to estimate the expectation in the E-step and then weighted maximization is applied to the observed and imputed data in the M-step. We conduct simulations to assess the proposed model and maximization method, and we analyze the GenIMS data set.