Estimating efficacy in the presence of non-ignorable non-trial interventions in the Helsinki Psychotherapy Study.
In a randomised clinical trial with a longitudinal outcome, analyses of the efficacy of the study treatments may be complicated by both non-trial interventions, which have not been administered by the researcher, and sparsely measured outcome values. The delay between the change in outcome and the starting of the non-trial intervention may be much shorter than the time intervals between the actual measurements. We propose a model that accounts for the possible dynamic interdependence between the longitudinal outcome and time-to-event data. The model is based on discretising time into short intervals. This results in a missing data problem, which we tackle using Bayesian inference and data augmentation. The method is based on the assumption that decisions to initiate non-trial interventions are not confounded by unobservable factors. The Helsinki Psychotherapy Study data are used as an illustration. Different psychotherapies were compared, and possible episodes of psychotropic medication were viewed as non-trial interventions. Simulation studies suggest that our method provides reasonable estimates of the effects of both the study treatment and the non-trial intervention also showing some robustness against possible latent background factors. An application of marginal structural modelling, however, appeared to underestimate the differences between the treatments.