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Keywords: Exact tests, Bayesian imputation, Imputation models, Missing-at-random (MAR), Missing-not-at-random (MNAR), Multiple imputation, Informative missing data mechanism, Prediction models, Randomization tests, Rare disease, Tipping point analysis.
Missing data are common or nearly unavoidable in clinical trials. Due to uncertainty regarding the mechanistic basis of missing data, statistical inference that ignores missing data may not be reliable as associated potential bias is not accounted for. Despite the availability of well known multiple imputation (MI) methodology and off-the-shelf statistical software procedures for handling a particular missing data classification, i.e., missing-at-random (MAR), approaches to more serious issues of potentially missing-not-at-random (MNAR) mechanisms are elusive. Existing procedures following a pattern-mixture approach apply to a single model type for each variable according to its distribution. In reality nearly all adequate and well-controlled clinical trials devote substantial efforts to collect patient disposition information on reasons for missing observations and dropouts, and so the use of a single model may be inadequate. We propose MI procedures by which different imputation methods are used to account for different reasons of missing observations or dropouts. In particular, we propose a Bayesian MI method for missing baseline values, which are critical for change from baseline analysis. To ensure robust inference, especially for rare disease applications with small sample size, we develop exact (i.e., permutation or re-randomization) tests with the proposed MI procedures. The exact tests include a tipping point sensitivity analysis for MNAR data. The exact tests also address the problem that the imputed data are unconditionally dependent on the observed data, which makes results from existing sampling theory or model based inference uninterpretable.