Combining T-learning and DR-learning: a framework for oracle-efficient
  estimation of causal contrasts
Lars van der Laan Marco Carone Alex Luedtke
We introduce efficient plug-in (EP) learning, a novel framework for the
estimation of heterogeneous causal contrasts, such as the conditional average
treatment effect and conditional relative risk. The EP-learning framework
enjoys the same oracle-efficiency as Neyman-orthogonal learning strategies,
such as DR-learning and R-learning, while addressing some of their primary
drawbacks, including that (i) their practical applicability can be hindered by
loss function non-convexity; and (ii) they may suffer from poor performance and
instability due to inverse probability weighting and pseudo-outcomes that
violate bounds. To avoid these drawbacks, EP-learner constructs an efficient
plug-in estimator of the population risk function for the causal contrast,
thereby inheriting the stability and robustness properties of plug-in
estimation strategies like T-learning. Under reasonable conditions, EP-learners
based on empirical risk minimization are oracle-efficient, exhibiting
asymptotic equivalence to the minimizer of an oracle-efficient one-step
debiased estimator of the population risk function. In simulation experiments,
we illustrate that EP-learners of the conditional average treatment effect and
conditional relative risk outperform state-of-the-art competitors, including
T-learner, R-learner, and DR-learner. Open-source implementations of the
proposed methods are available in our R package hte3.