Estimating dose-response effects in psychological treatment trials: the role of instrumental variables

We present a relatively non-technical and practically orientated review of statistical methods that can be used to estimate dose-response relationships in randomised controlled psychotherapy trials in which participants fail to attend all of the planned sessions of therapy. Here we are investigating the effects on treatment outcome of the number of sessions attended when the latter is possibly subject to hidden selection effects (hidden confounding). The aim is to estimate the parameters of a structural mean model (SMM) using randomisation, and possibly randomisation by covariate interactions, as instrumental variables. We describe, compare and illustrate the equivalence of the use of a simple G-estimation algorithm and two two-stage least squares procedures that are traditionally used in economics.