An analytic method for the placebo‐based pattern‐mixture model

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Pattern-mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data. The placebo-based pattern-mixture model (Little and Yau, Biometrics 1996; 52:1324-1333) treats missing data in a transparent and clinically interpretable manner and has been used as sensitivity analysis for monotone missing data in longitudinal studies. The standard multiple imputation approach (Rubin, Multiple Imputation for Nonresponse in Surveys, 1987) is often used to implement the placebo-based pattern-mixture model. We show that Rubin's variance estimate of the multiple imputation estimator of treatment effect can be overly conservative in this setting. As an alternative to multiple imputation, we derive an analytic expression of the treatment effect for the placebo-based pattern-mixture model and propose a posterior simulation or delta method for the inference about the treatment effect. Simulation studies demonstrate that the proposed methods provide consistent variance estimates and outperform the imputation methods in terms of power for the placebo-based pattern-mixture model. We illustrate the methods using data from a clinical study of major depressive disorders.