Bayesian Semiparametric Mixture Tobit Models with Left-Censoring Skewness and Covariate Measurement Errors

摘要

Common problems to many longitudinal HIV/AIDS, cancer, vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection (LOD) may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models which can account for a high proportion of censored data should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left-censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left-censoring, skewness and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study.