Predicting the probability of health status for censored cases is of interest. Such prediction is not available by using the popular Tobit model for left censored discrete data. A mixture model with possibility of unhealthy state for censored cases is more appropriate. Considering the health status of censored cases as a latent variable, its value can be imputed by data augmentation methods. Gibbs sampling, Data Augmentation, and Poor Man's Data Augmentation algorithms are developed, and accuracy and convergence are demonstrated along with a comparison with the exact marginal posterior distributions.
Chronic diseases have significant impact on the health status for the censored cases.