Bayesian pattern mixture models for missing data in longitudinal studies

Juan Abellan- Andres, Trial Biostatistician, Grünenthal

Here we briefly present the pattern mixture model (PMM) approach to address the analysis of missing not-at-random (MNAR) data in longitudinal clinical trials with discrete monotone dropout pattern. In this setting, the data model p(y | ) is obtained by averaging over the dropout patterns p(y | )=d p(y, d | )=d p(y | d, )p(d | ).

PMMs are typically under-identified because p(ymis | yobs d, ) cannot be estimated from the data. Therefore identifying constraints are needed in order to fit the model to the data. Modeling strategies that allow to split p(y,d | )=p(y | d, )p(d | ) into identified and unidentified components are particularly appealing as they allow detection of a subset s of (unidentified) sensitivity parameters that can be used to assess departure from the missing at random (MAR) hypothesis. In particular we will focus on two constraining methods: the so-called interior family constraints such as complete case missing value (CCMV), nearest-neighbor missing value (NNMV) and available case missing value (ACMV); and the ‘-method’ whereby s = h(M, ), that is, the unidentified parameters s are assumed to be a function h (that may represent the missing mechanism) of the subset M of identified parameters and a set of parameters  representing the potential departure from MAR.

The inferential process is set within the Bayesian paradigm. We will illustrate the approach with a real case study on chronic pain, a Phase III randomized, double-blind placebo-controlled trial to assess the efficacy of a new compound. Subjects were followed over 15 weeks and the dropout rate in the two arms was ~40%. Flat priors were assigned to the different model parameters and posterior samples were obtained using Markov chain Monte Carlo techniques. The results allow to assess departure from MAR and the sensitivity to the choice of the constraining method.