Conditional effects are commonly used measures for understanding how treatment effects vary across different groups, and are often used to target treatments/interventions to groups who benefit most. In this work we review existing methods and propose novel ones, focusing on the odds ratio (OR) and the risk ratio (RR). While estimation of the conditional average treatment effect (ATE) has been widely studied, estimators for the OR and RR lag behind, and cutting edge estimators such as those based on doubly robust transformations or orthogonal risk functions have not been generalized to these parameters. We propose such a generalization here, focusing on the DR-learner and the R-learner. We derive orthogonal risk functions for the OR and RR and show that the associated pseudo-outcomes satisfy second-order conditional-mean remainder properties analogous to the ATE case. We also evaluate estimators for the conditional ATE, OR, and RR in a comprehensive nonparametric Monte Carlo simulation study to compare them with common alternatives under hundreds of different data-generating distributions. Our numerical studies provide empirical guidance for choosing an estimator. For instance, they show that while parametric models are useful in very simple settings, the proposed nonparametric estimators significantly reduce bias and mean squared error in the more complex settings expected in the real world. We illustrate the methods in the analysis of physical activity and sleep trouble in U.S. adults using data from the National Health and Nutrition Examination Survey (NHANES). The results demonstrate that our estimators uncover substantial treatment effect heterogeneity that is obscured by traditional regression approaches and lead to improved treatment decision rules, highlighting the importance of data-adaptive methods for advancing precision health research.
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Figure 5: NHANES application for the effect of physical activity on sleep trouble. The left panel shows the validation-sample distribution of estimated conditional log odds ratios. The right panel compares the estimated mean outcome under OR-based treatment rules induced by each estimator, using TMLE. Because sleep trouble is the undesirable outcome, lower values in the right panel are better.
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Estimator
iMSE (IQR)
iBias 2 (IQR)
iVar (IQR)
LR
10 (6–21)
6 (2–15)
4 (3–5)
LR-T
29 (22–37)
1 (1–5)
27 (22–32)
SL
9 (5–17)
4 (2–12)
4 (3–5)
SL-T
26 (21–29)
3 (2–5)
21 (19–24)
R-CATE
67 (57–77)
3 (2–5)
63 (54–73)
DR-P
45 (32–56)
1 (1–3)
43 (30–52)
Table 1: CATE estimation: Interaction Order 1, Sample Size 200, HTE High
When treatment effects are naturally expressed as ratios -- as in medicine, pricing, and marketing -- the ratio-based CATE τ(x)=E[Y∣W=1,X=x]/E[Y∣W=0,X=x] is the appropriate estimand. Yet existing estimators either impose a log-linear parametric structure or apply generic regression without robustness guarantees for this functional. We introduce the Q-Learner, which decomposes τ(x) into a product of two odds ratios, reducing ratio-CATE estimation for binary outcomes to two propensity classification tasks. We further derive doubly robust augmentations for both S/T- and Q-style ratio learners and characterize their distinct robustness properties. In benchmarks on seven RCT datasets, the Q-Learner is the most consistently competitive method in low-conversion regimes, where its propensity-only construction sidesteps the imbalanced regression that hurts outcome-based estimators. On four observational datasets, where propensity must be estimated and confounding cannot be ruled out, the DR learners introduced here decisively come out on top, making them practitioners' natural default for confounded observational data.
Michael Fuchs, Dominik Kreiss
Actuarial Department Allianz Versicherungs-AG Munich, Germany
Conditional average treatment effects (CATEs) are central to treatment decision-making in personalized medicine. In competing risks settings, estimating CATEs from survival data allows for patient-specific assessments of treatment effectiveness for a specific event of interest while properly accounting for alternative event types. This distinction is essential in the presence of comorbidities, where competing causes of death may otherwise confound the therapeutic benefit. Focusing on right-censored survival times with binary treatment, we examine CATEs defined as covariate-conditional differences in the absolute risk for the event of interest at a fixed time. To this end, we study meta-learners which adapt machine learning algorithms for CATE estimation in competing risks scenarios. We systematically compare six meta-learners, combining Cox regression or random survival forests for risk modeling with elastic net regression or random forests for direct CATE modeling. To provide practical guidance on model selection, we evaluate their performance in multiple simulation settings, that differ in hazard complexity, treatment heterogeneity, treatment assignment, event type distribution and censoring. To facilitate applied use, we provide the R package, crsurvlearners, which implements all considered approaches.
Daniel Klippert, Sarah Friedrich, Markus Pauly
Department of Statistics, TU Dortmund University · Research Center Trustworthy Data Science and Security, University Alliance Ruhr (UA Ruhr) · Institute for Mathematics, University of Augsburg
Estimating conditional distributional potential outcomes (CDPOs) over time is important in medicine (e.g., to estimate patient-specific risks under different treatment sequences). However, this task is challenging because of time-varying confounding, yet existing adjustment strategies for this task are limited. In this paper, we aim to learn CDPOs under time-varying treatments using flexible generative models. Our contributions are two-fold. (1) We introduce a tailored adjustment strategy for our setting, namely, generative recursive g-computation. Our adjustment strategy recursively propagates full conditional outcome distributions rather than conditional means, modeling the variables of interest directly rather than full trajectories. Building on our adjustment strategy, we formulate simple generative learners for CDPO estimation. However, these learners can be sensitive to nuisance estimation errors, which motivates an orthogonal learner. (2) We thus introduce OrthoGen, a Neyman-orthogonal and doubly robust generative learner. Importantly, we show that OrthoGen further achieves rate double robustness and quasi-oracle efficiency under suitable conditions. Our learners are flexible and can be instantiated with different generative backbones (e.g., normalizing flows and diffusion models). Across experiments with synthetic, semi-synthetic and real-world datasets, we find that OrthoGen is highly effective. To the best of our knowledge, we are the first to propose a generative orthogonal learner for estimating CDPOs under time-varying treatments.
Tomàs Garriga, Valentyn Melnychuk, Konstantin Hess +4
Novartis · Barcelona Supercomputing Center · Universitat Polit`ecnica de Catalunya +2