26 Nov 2015 11:00am

Causal modelling in randomised trials: applications and extensions of finite mixture models


Understanding treatment effect heterogeneity is an important aspect of randomised trials, and process variables describing the intervention content are crucial components of this. Frequently these variables can only be measured in intervention groups.

Principal stratification, whereby control group participants are assigned to the latent class they would have been in had they been randomised to intervention, has been proposed for analysing this problem and is often estimated using finite mixture models. This estimates an estimand known as the principal stratum direct effect. The standard principal stratification approach generally makes use of a single observation of the process and outcome variables, which more realistically have repeated measures collected.

This principal stratification approach to evaluation will be illustrated using randomised trials comparing psychotherapy with treatment as usual in patients with recent onset of psychosis where the process measure is the therapeutic alliance or therapeutic empathy between the therapist and patient.  We extend this to account for repeated measures of the process variables and outcomes using general growth mixture models. We will discuss the estimation of these models, comparing the traditional one-step approach with a recently proposed three-step procedure.