Bayesian nonparametric analysis of longitudinal studies in the presence of informative missingness

Abstract

In longitudinal clinical trials, one often encounters missingness which is thought to be non-ignorable. It is well-known that non-ignorable missingness introduces fundamental identifiability issues, resulting in intention-to-treat effects being unidentified; the best one can do is to conduct a sensitivity analysis to assess how much of the inference is being driven by missingness. We introduce a Bayesian nonparametric framework for conducting inference in the presence of non-ignorable, non-monotone missingness. This framework focuses on the specification of an auxiliary prior, which we refer to as a working prior, on the space of complete data generating mechanisms. This prior is not used to conduct inference, but instead is used to induce a prior on the observed data generating mechanism, which is then used in conjunction with an identifying restriction to conduct inference. Advantages of this approach include a flexible modeling framework, access to simple computational methods, strong theoretical support, straightforward sensitivity analysis, and its applicability to non-monotone missingness.

A Sensitivity Analysis Approach for Informative Dropout Using Shared Parameter Models

“…The general approach for sensitivity analysis proposed here is similar in spirit to the framework proposed by Linero and Daniels (2015) and Linero (2017), where a flexible 'working model' for the joint distribution of the complete longitudinal outcomes and the dropout time is specified and identifying restrictions are then applied when performing sensitivity analyses with the extrapolation distribution. The typical SPM can be thought of as the 'working model' described in these articles.…”

“…The typical SPM can be thought of as the 'working model' described in these articles. Here, however, we recommend performing sensitivity analysis grounded off the extrapolation distribution from the 'working model', unlike anchoring at the MAR restrictions as done in Linero and Daniels (2015) and Linero (2017).…”

Bayesian Approaches for Missing Not at Random Outcome Data: The Role of Identifying Restrictions

“…A generic approach to modeling the observed data is to specify a working model (Linero, 2017;Linero and Daniels, 2015;Daniels and Linero, 2015). One then implicitly obtains a model for the observed data p(y r , r) = ∫ p ⋆ (y, r) dy −r .…”

Missingness Mechanism that Incorporated Joint Modeling of Longitudinal Data with Monotone Dropout

“…In the ARMD data, the parameters stated above represent the dependence on level and increment, and these quantities are likely to be much less strongly correlated than are y ij and y i,j−1 . The MNAR model is rewritten as in equation (15) logit[p(D i = j|y ij−1 , y ij )] = −1.81 − 0.01(y i,j + y i,j−1 ) + 0.03(y ij − y i,j−1 ),…”

“…There are avoidance of assumptions by these methods about the full-data distribution, and the parametric model for the missingness given the outcome (reference as to the missing data mechanism) is specified and, it is optional for semiparametric model [13]. Different methods have been proposed using likelihood-based methods which are flexible for the semiparametric approaches and allow flexibility of sensitivity analysis [38,14,15]. Some of those works have bayesian approach, but also include proposals related to frequentist framework [34].…”