Joint modeling of outcome, observation time, and missingness.

A modeling framework is described for the specific setting of clinical trials in which there is only a single post-randomization response measurement, which may itself be missing, or, for clinical reasons, may be measured before the trial end. Such settings have three simultaneous processes: the outcome itself, the time to measurement, and the occurrence of missing values. A simple latent variable structure within a multivariate Gaussian distribution is used to model them. The full model is strictly nonrandom with respect to the missing value process, and therefore estimability of certain parameters depends on unverifiable assumptions. We use a simulation study to assess the behavior of the maximum likelihood estimators from the model; we then compare and contrast with a simpler last observation carried forward (LOCF) approach that ignores both the time to response and the missingness process, and is commonly used in practice in such settings. The proposed approach is illustrated using data from a trial on the treatment of congestive heart failure, in which the response measurements were obtained by echocardiography.