A Random Pattern-Mixture Model for Longitudinal Data With Dropouts

Pattern-mixture models are frequently used for longitudinal data analysis with dropouts because they do not require explicit specification of the dropout mechanism. These models stratify the data according to time to dropout and formulate a model for each stratum. This usually results in underindentifiability, because we need to estimate many pattern-specific parameters even though the eventual interest is usually on the marginal parameters. In this article we extend this framework to a random pattern-mixture model, where the pattern-specific parameters are treated as nuisance parameters and modeled as random instead of fixed. The pattern is defined according to a surrogate for the dropout process. A constraint is then put on the pattern by linking it to the time to dropout using a random-effects survival model. We assume, conditional on the latent pattern effects, that the longitudinal outcome and the dropout process are independent. This model retains the robustness of the traditional pattern-mixture models, while avoiding the overparameterization problem. When we define each subject as a separate stratum, this model reduces to the shared parameter model. Maximum likelihood estimates are obtained using an EM Newton– Raphson algorithm. We apply the method to the depression data from the Prevention of Suicide in Primary Care Elderly Collaborative Trial (PROSPECT). We show when the dropout information is adjusted for under the proposed model, the treatment seems to reduce depression in the elderly.