Data-adaptive doubly robust instrumental variable methods for treatment effect heterogeneity.

We consider the estimation of the average treatment effect in the treated asa function of baseline covariates, where there is a valid (conditional)instrument.

We describe two doubly robust (DR) estimators: a locally efficientg-estimator, and a targeted minimum loss-based estimator (TMLE). These two DRestimators can be viewed as generalisations of the two-stage least squares(TSLS) method to semi-parametric models that make weaker assumptions. Weexploit recent theoretical results that extend to the g-estimator the use ofdata-adaptive fits for the nuisance parameters.

A simulation study is used to compare standard TSLS with the two DRestimators' finite-sample performance, (1) when fitted using parametricnuisance models, and (2) using data-adaptive nuisance fits, obtained from theSuper Learner, an ensemble machine learning method.

Data-adaptive DR estimators have lower bias and improved coverage, whencompared to incorrectly specified parametric DR estimators and TSLS. When theparametric model for the treatment effect curve is correctly specified, theg-estimator outperforms all others, but when this model is misspecified, TMLEperforms best, while TSLS can result in large biases and zero coverage.

Finally, we illustrate the methods by reanalysing the COPERS (COping withpersistent Pain, Effectiveness Research in Self-management) trial to makeinference about the causal effect of treatment actually received, and theextent to which this is modified by depression at baseline.