Bayesian Variable Selection for Longitudinal Substance Abuse Treatment Data Subject to Informative Censoring

Summary: Measuring the process of care in substance abuse treatment requires analysing repeated client assessments at critical time points during treatment tenure. Assessments are frequently censored because of early departure from treatment. Most analyses accounting for informative censoring define the censoring time to be that of the last observed assessment. However, if missing assessments for those who remain in treatment are attributable to logistical reasons rather than to the underlying treatment process being measured, then the length of stay in treatment might better characterize censoring than would time of measurement. Bayesian variable selection is incorporated in the conditional linear model to assess whether time of measurement or length of stay better characterizes informative censoring. Marginal posterior distributions of the trajectory of treatment process scores are obtained that incorporate model uncertainty. The methodology is motivated by data from an on-going study of the quality of care in in-patient substance abuse treatment.