Received: 18 October 2020 Revised: 5 April 2021 Accepted: 10 May 2021 DOI: 10.1002/sim.9083 RESEARCH ARTICLE Bayesian sensitivity analyses for longitudinal data with dropouts that are potentially missing not at random: A high dimensional pattern-mixture model Niko A. Kaciroti 1,2 Roderick J.A. Little 1 1 Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, Michigan, USA 2 Department of Pediatrics, Medical School, University of Michigan, Ann Arbor, Michigan, USA Correspondence Niko A. Kaciroti, Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI. Email: nicola@umich.edu Abstract Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern-mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome mea- sure at the follow-up time t k , conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing-data pattern at time t k with that of the observed subjects at time t k . The large number of the sensitiv- ity parameters is reduced by treating them as random with a prior distribution having some pre-specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension. KEYWORDS clinical trials, hypertension, missing data, MNAR future dependent, tipping point analysis, TROPHY trial 1 INTRODUCTION Missing data are a common problem in statistical modeling of longitudinal studies where subjects drop out prematurely before study completion. A wide range of statistical models for analyzing outcomes with missing data is available, with their performance depending on validity of their underlying assumptions. Approaches include pattern-mixture models (PMM), 1,2 selection models (SM), 3-5 and shared-parameter models 6,7 In longitudinal studies, the dropout mechanism is missing not at random (MNAR) if the probability of dropping out at time t depends on y t and/or y t+1 , … , y K . When the probability of dropping out at time t depends on future unobserved values y t+1 , … , y K , the dropout mechanism is future dependent MNAR. 8 When the number of follow-up visits increases, modeling missingness mechanism becomes high dimensional and challenging regardless of the approach used. To deal Abbreviations: MAR, missing at random, MCAR, missing completely at random, MNAR, missing not at random, TROPHY, trial of preventing hypertension. Statistics in Medicine. 2021;40:4609–4628. wileyonlinelibrary.com/journal/sim © 2021 John Wiley & Sons Ltd. 4609