MCMC-based estimation methods for continuous longitudinal data with non-random (non)-monotone missingness

Abstract

The analysis of incomplete longitudinal data requires joint modeling of the longitudinal outcomes (observed and unobserved) and the response indicators. When non-response does not depend on the unobserved outcomes, within a likelihood framework, the missingness is said to be ignorable, obviating the need to formally model the process that drives it. For the non-ignorable or non-random case, estimation is less straightforward, because one must work with the observed data likelihood, which involves integration over the missing values, thereby giving rise to computational complexity, especially for high-dimensional missingness. The stochastic EM algorithm is a variation of the expectation–maximization (EM) algorithm and is particularly useful in cases where the E (expectation) step is intractable. Under the stochastic EM algorithm, the E-step is replaced by an S-step, in which the missing data are simulated from an appropriate conditional distribution. The method is appealing due to its computational simplicity. The SEM algorithm is used to fit non-random models for continuous longitudinal data with monotone or non-monotone missingness, using simulated, as well as case study, data. Resulting SEM estimates are compared with their direct likelihood counterparts wherever possible.