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

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.