We consider the estimation of the average treatment effect in the treated as a function of baseline covariates,
where there is a valid (conditional) instrument.
We describe two doubly-robust (DR) estimators: a g-estimator and a targeted minimum loss-based estimator
(TMLE). These estimators can be viewed as generalisations of the two-stage least squares (TSLS) method to semiparametric
models that make weaker assumptions. We exploit recent theoretical results and use data-adaptive estimation
of the nuisance parameters for the g-estimator.
A simulation study is used to compare standard TSLS with the two DR estimators’ finite-sample performance
when using (1) parametric or (2) data-adaptive estimation of the nuisance parameters.
Data-adaptive DR estimators have lower bias and improved coverage, when compared to incorrectly specified
parametric DR estimators and TSLS. When the parametric model for the treatment effect curve is correctly specified,
the g-estimator outperforms all others, but when this model is misspecified, TMLE performs best, while TSLS can
result in large biases and zero coverage.
The methods are also applied to the COPERS (COping with persistent Pain, Effectiveness Research in Selfmanagement)
trial to make inferences about the causal effect of treatment actually received, and the extent to which
this is modified by depression at baseline.We consider the estimation of the average treatment effect in the treated as a function of baseline covariates,
where there is a valid (conditional) instrument.
We describe two doubly-robust (DR) estimators: a g-estimator and a targeted minimum loss-based estimator
(TMLE). These estimators can be viewed as generalisations of the two-stage least squares (TSLS) method to semiparametric
models that make weaker assumptions. We exploit recent theoretical results and use data-adaptive estimation
of the nuisance parameters for the g-estimator.
A simulation study is used to compare standard TSLS with the two DR estimators’ finite-sample performance
when using (1) parametric or (2) data-adaptive estimation of the nuisance parameters.
Data-adaptive DR estimators have lower bias and improved coverage, when compared to incorrectly specified
parametric DR estimators and TSLS. When the parametric model for the treatment effect curve is correctly specified,
the g-estimator outperforms all others, but when this model is misspecified, TMLE performs best, while TSLS can
result in large biases and zero coverage.
The methods are also applied to the COPERS (COping with persistent Pain, Effectiveness Research in Selfmanagement)
trial to make inferences about the causal effect of treatment actually received, and the extent to which
this is modified by depression at baseline
