What Makes Forest-Based Heterogeneous Treatment Effect Estimators Work?

Abstract

Estimation of heterogeneous treatment effects (HTE) is of prime importance in many disciplines, ranging from personalized medicine to economics among many others. Random forests have been shown to be a flexible and powerful approach to HTE estimation in both randomized trials and observational studies. In particular "causal forests", introduced by Athey, Tibshirani, and Wager (2019), along with the R implementation in package grf were rapidly adopted. A related approach, called "model-based forests", that is geared towards randomized trials and simultaneously captures effects of both prognostic and predictive variables, was introduced by Seibold, Zeileis, and Hothorn (2018) along with a modular implementation in the R package model4you.Here, we present a unifying view that goes beyond the theoretical motivations and investigates which computational elements make causal forests so successful and how these can be blended with the strengths of model-based forests. To do so, we show that both methods can be understood in terms of the same parameters and model assumptions for an additive model under L 2 loss. This theoretical insight allows us to implement several flavors of "model-based causal forests" and dissect their different elements in silico.The original causal forests and model-based forests are compared with the new blended versions in a benchmark study exploring both randomized trials and observational settings. In the randomized setting, both approaches performed akin. If confounding was present in the data generating process, we found local centering of the treatment indicator with the corresponding propensities to be the main driver for good performance. Local centering of the outcome was less important, and might be replaced or enhanced by simultaneous split selection with respect to both prognostic and predictive effects. This lays the foundation for future research combining random forests for HTE estimation with other types of models.We demonstrate the practical aspects of such a model-agnostic approach to HTE estimation analyzing the effect of cesarean section on postpartum blood loss in comparison to vaginal delivery. Clearly, randomization is hardly possible in this setup, and we present a tailored model-based forest for skewed and interval-censored data to infer possible predictive variables and their impact on the treatment effect.

Comparison of methods that combine multiple randomized trials to estimate heterogeneous treatment effects

“…Dandl and colleagues compared honesty vs adaptive (not honest) forests in their simulations including causal forests and found that in their setting that was meant to represent an RCT, the adaptive forests performed better. 9 Additionally, honesty requires large sample sizes. Thus, we do not include honesty in the causal forests in the primary simulations but do investigate it in a second round of method comparisons.…”

Harnessing heterogeneity in behavioural research using computational social science

“…These advancements have expanded the potential applications of Causal Trees and their variants in academia and fields like healthcare, marketing and public policy, where personalising interventions can lead to better outcomes. In summary, Causal Trees provide a promising method for identifying and understanding heterogeneous causal effects (Dandl et al, 2022). This works particularly well for experiments and unconfoundedness because, in these cases, the effect estimates are based on treated and controls with similar values of the covariates.…”