Orthogonal prediction of counterfactual outcomes

Orthogonal meta-learners, such as DR-learner (Kennedy EH. Towards optimal doubly robust estimation of heterogeneous causal effects. arXiv preprint arXiv:2004.14497 2020), R-learner (Nie X, Wager S. Quasi-oracle estimation of heterogeneous treatment effects. Biometrika 2021;108:299–319) and IF-learner (Curth A, Alaa AM, van der Schaar M. Estimating structural target functions using machine learning and influence functions. arXiv preprint arXiv:2008.06461 2020), are increasingly used to estimate conditional average treatment effects. They are hoped to improve convergence rates relative to naïve meta-learners (e.g., T-, S- and X-learner (Künzel SR, Sekhon JS, Bickel PJ, Yu B. Metalearners for estimating heterogeneous treatment effects using machine learning. Proc Natl Acad Sci 2019;116:4156–65)) through de-biasing procedures that involve applying standard learners to specifically transformed outcome data. This leads them to disregard the possibly constrained outcome space, which can be particularly problematic for dichotomous outcomes: these typically get transformed to values that are no longer constrained to the unit interval, which may cause instability and makes it difficult for standard learners to guarantee predictions within the unit interval. To address this, we construct a non-orthogonal imputation-learner and an orthogonal ‘i-learner’ for the prediction of counterfactual outcomes, which respect the outcome space. These are more generally expected to outperform existing learners, even when the outcome is unconstrained, as we confirm empirically in simulation studies and an analysis of critical care data. Our development also sheds broader light onto the construction of orthogonal learners for other estimands.