Subjective prior distributions for modeling longitudinal continuous outcomes with non-ignorable dropout

Abstract

Substance abuse treatment research is complicated by the pervasive problem of non-ignorable missing data-i.e. the occurrence of the missing data is related to the unobserved outcomes. Missing data frequently arise due to early client departure from treatment. Pattern-mixture models (PMMs) are often employed in such situations to jointly model the outcome and the missing data mechanism. PMMs require non-testable assumptions to identify model parameters. Several approaches to parameter identification have therefore been explored for longitudinal modeling of continuous outcomes, and informative priors have been developed in other contexts. In this paper, we describe an expert interview conducted with five substance abuse treatment clinical experts who have familiarity with the therapeutic community modality of substance abuse treatment and with treatment process scores collected using the Dimensions of Change Instrument. The goal of the interviews was to obtain expert opinion about the rate of change in continuous client-level treatment process scores for clients who leave before completing two assessments and whose rate of change (slope) in treatment process scores is unidentified by the data. We find that the experts' opinions differed dramatically from widely utilized assumptions used to identify parameters in the PMM. Further, subjective prior assessment allows one to properly address the uncertainty inherent in the subjective decisions required to identify parameters in the PMM and to measure their effect on conclusions drawn from the analysis.

Figure 1

Prior distributions provided by Experts 1–5 for the slope of the Resident Sharing, Support & Enthusiasm score for those clients whose last assessments were at 1, 3, 6, and 9 months, as noted beneath each box. Prior mode is provided by the dark solid line, the box width reflects the difference between the upper and lower bounds, and the dashed lines are the posterior mean slopes from the data analysis. (Expert 5’s 9-month assessment (far-right hand side) is missing.)

Figure 2

Prior distributions provided by clinical experts 1–5 for the slope of each Dimensions of Change domain for clients who only provided these data at treatment entry. CS=Clarity & Safety; CR=Community Responsibility; RS=Resident Sharing, Support & Enthusiasm. Note that Expert 5’s prior is equivalent to the last observation carried forward (LOCF) assumption for those with only one observation at time 0.

Figure 3

Marginal posterior distributions of the marginal slope (averaged over drop-out time) under sensitivity analyses and subjective prior distributions.

Figure 4

Marginal posterior distributions of β̅₁ under equal weight linear opinion pooling of the five experts’ priors for ${\beta }_1^{(1)}$ .