An analysis of longitudinal data with nonignorable dropout using the truncated multivariate normal distribution

Abstract

For a vector of multivariate normal when some elements, but not necessarily all, are truncated, we derive the moment generating function and obtain expressions for the first two moments involving the multivariate hazard gradient. To show one of many applications of these moments, we then extend the two-step estimation of censored regression models to longitudinal studies with nonignorable dropout, in the sense that the probability of dropout depends on unobserved, or missing, observations. With nonignorable dropout, direct maximization of the likelihood function can be computationally intensive or even infeasible. The two-step method in such cases can be an adequate substitute. In a set of simulation studies the developed two-step method and the maximum likelihood (ML) method are compared. It turns out that the proposed method preforms at least as well as the ML and provides a convenient alternative that can easily be implemented in standard software.