Analysis of crossover designs for longitudinal binary data with ignorable and nonignorable dropout

Longitudinal binary data in crossover designs with missing data due to ignorable and nonignorable dropout is common. This paper evaluates available conditional and marginal models and establishes the relationship between the conditional and marginal parameters with the primary objective of comparing the treatment mean effects. We perform extensive simulation studies to investigate these models under complete data and the selection models under missing data with different parametric distributions and missingness patterns and mechanisms. The generalized estimating equations and the generalized linear mixed-effects models with pseudo-likelihood estimation are advocated for valid and robust inference. We also propose a controlled multiple imputation method as a sensitivity analysis of the missing data assumption. Lastly, we implement the proposed models and the sensitivity analysis in two real data examples with binary data.

Reference-based pattern-mixture models for analysis of longitudinal binary data

Pattern-mixture model (PMM)-based controlled imputations have become a popular tool to assess the sensitivity of primary analysis inference to different post-dropout assumptions or to estimate treatment effectiveness. The methodology is well established for continuous responses but less well established for binary responses. In this study, we formulate the copy-reference and jump-to-reference PMMs for longitudinal binary data using a multivariate probit model with latent variables. We discuss the maximum likelihood, Bayesian, and multiple imputation methods for estimating the treatment effect under the specified PMM. Simulation studies are conducted to evaluate the performance of these methods. These methods are also illustrated using data from a bipolar mania study.