Nonignorable dropout models for longitudinal binary data with random effects: An application of Monte Carlo approximation through the Gibbs output

The analysis of longitudinal data with nonignorable dropout remains an active area in biostatistics research. Nonignorable dropout (ND) refers to the type of dropout when the probability of dropout depends on the missing observations at or after the time of dropout. Failure to account for such dependence may result in biased inference. Motivated by a methadone clinic data of longitudinal binary observations with dropouts, we propose a conditional first order autoregressive (AR1) logit model for the outcome measurements. The model is further extended to incorporate random effects in order to account for the population heterogeneity and intra-cluster correlation. The purposed models account for the dropout mechanism by a separate logit model in some covariates and missing outcomes for the binary dropout indicators. For model implementation, we proposed a likelihood approach through Monte Carlo approximation to the Gibbs output that evaluates the complicated likelihood function for the random effect ND model without tear. Finally simulation studies are performed to evaluate the biases on the parameter estimates of the outcome model for different dropout mechanisms.