Targeted Learning for Tilted Average Treatment Effects

This paper studies a class of causal estimands obtained by tilting the average treatment effect (ATE). We distinguish between internally tilted ATEs, defined within the study population, and externally tilted ATEs, which target a distinct external population. Internally tilted ATEs have been extensively investigated, particularly in the context of overlap-based estimands. In contrast, externally tilted ATEs are increasingly applied in settings such as randomized controlled trials augmented with external covariate information, prediction of phase III treatment effects using phase II data, and arbitrated indirect treatment comparison. We develop targeted learning approaches for both settings. In the internal case, the tilting function may depend on the treatment propensity score, while in the external case, it may depend on the selection propensity score. For each case, we derive the corresponding efficient influence functions and construct targeted maximum likelihood estimators that accommodate flexible, data-adaptive nuisance estimation. The resulting unified semiparametric framework enables efficient statistical inference for modern clinical trial and real-world evidence applications.