We consider estimation of the causal treatment effects in randomised trials with non-adherence, where there is an interest in treatment effects modification by baseline covariates.
Assuming randomised treatment is a valid instrument, we describe two doubly robust (DR) estimators of the parameters of a partially linear instrumental variable model for the average treatment effect on the treated, conditionally on baseline covariate. The first method is a locally efficient g-estimator, while the second is a targeted minimum loss-based estimator (TMLE).
These two DR estimators can be viewed as a generalisation of the two-stage least squares (TSLS) method in the instrumental variable methodology to a semiparametric model with weaker assumptions. We exploit recent theoretical results to extend the use of data-adaptive machine learning to the g-estimator. A simulation study is used to compare the estimators' finite-sample performance (1) when fitted using parametric models, and (2) using Super Learner, with the TSLS.
Data-adaptive DR estimators have lower bias and improved precision, when compared to incorrectly specified parametric DR estimators. Finally, we illustrate the methods by obtaining the causal effect on the treated of receiving cognitive behavioural therapy training on pain-related disability, with heterogeneous treatment by depression at baseline, using the COPERS (COping with persistent Pain, Effectiveness Research in Self-management) trial.