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.
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