The Stochastic EM algorithm for censored mixed models

The stochastic EM algorithm is an MCMC method for approximating the regular EM algo- rithm in missing data situations where the E-step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying a complete data MLE to a single simulation of the complete data conditional on the observed data. Similarly to other MCMC methods, the final estimate is the mean of the iterative sequence after a suitable burn-in period. The method will be considered for censored mixed models, a computationally challenging context. The stochastic EM algorithm is particularly simple to apply to either linear or nonlinear mixed models with censoring. All that is required is a routine to simulate censored multinormal observations, and a routine to fit the desired uncensored mixed model. An application will be presented involving repeated measures of HIV viral load subject to left censoring caused by a lower detection limit of the assay. The analysis provides insights into sources of variation in the rate of increase of viral load after loss of viral suppression. It is found that crude methods ignoring the censoring are biased compared to the stochastic EM results.