Empirical Bayes MCMC estimation for modeling treatment processes, mechanisms of change, and clinical outcomes in small samples.

Abstract

The current analysis demonstrates the use of empirical Bayes (EB) estimation methods with data-derived prior parameters for studying clinically intricate process-mechanism-outcome linkages using structural equation modeling (SEM) with small samples. The data were obtained from a small subsample of 23 families receiving Functional Family Therapy (FFT) for adolescent substance abuse during a completed randomized clinical trial. Two or 3 video-recorded FFT sessions were randomly selected for each family. The middle 20-min portion of each session was observed and coded. An SEM examining the influence of a select set of observed therapist behaviors on pre- to posttreatment change in mother reports of family functioning and, in turn, pre- to posttreatment change in adolescent reports of adolescent marijuana use and delinquent behavior was specified. The SEM was implemented using EB estimation with data-derived maximum likelihood (ML) prior parameters and Markov Chain Monte Carlo (MCMC) estimation of the joint posterior distribution. The EB SEM results indicated that a relatively high proportion of individually focused general interventions (i.e., seek information, acknowledge) as well as relationally focused meaning change interventions by therapists during sessions of FFT were predictive of pre- to posttreatment increases in levels of family functioning as reported by mothers in families of substance-abusing adolescents. In turn, increases in mother-reported family functioning were predictive of reductions in levels of adolescent-reported delinquent behavior. EB MCMC methods produced more stable results than did ML, especially regarding the variances on the change factors in the SEM. EB MCMC estimation is a viable alternative to ML estimation of SEMs in clinical research with prohibitively small samples.