arXiv subjects

Stefan Wager

Publications and source records attributed to Stefan Wager.

At least 37 records · Page 2Linked to original sources

arXiv2025

Admissibility of Completely Randomized Trials: A Large-Deviation Approach

When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the experimenter aims to allocate measurement efforts judiciously to confidently deploy the most effective treatment arm. We find that, whenever there are at least three treatment arms, there exist simple adaptive designs that universally and strictly dominate non-adaptive completely randomized trials. This dominance is characterized by a notion called efficiency exponent, which quantifies a design's statistical efficiency when the experimental sample is large. Our analysis focuses on the class of batched arm elimination designs, which progressively eliminate underperforming arms at pre-specified batch intervals. We characterize simple sufficient conditions under which these designs universally and strictly dominate completely randomized trials. These results resolve the second open problem posed in Qin [2022].

stat.ML↗

arXiv2025

Noise-Induced Randomization in Regression Discontinuity Designs

Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a pre-specified threshold. Here we propose a new approach to identification, estimation, and inference in regression discontinuity designs that uses knowledge about exogenous noise (e.g., measurement error) in the running variable. In our strategy, we weight treated and control units to balance a latent variable of which the running variable is a noisy measure. Our approach is driven by effective randomization provided by the noise in the running variable, and complements standard formal analyses that appeal to continuity arguments while ignoring the stochastic nature of the assignment mechanism.

stat.ME↗

arXiv2025

Policy Learning with Competing Agents

Decision makers often aim to learn a treatment assignment policy under a capacity constraint on the number of agents that they can treat. When agents can respond strategically to such policies, competition arises, complicating estimation of the optimal policy. In this paper, we study capacity-constrained treatment assignment in the presence of such interference. We consider a dynamic model where the decision maker allocates treatments at each time step and heterogeneous agents myopically best respond to the previous treatment assignment policy. When the number of agents is large but finite, we show that the threshold for receiving treatment under a given policy converges to the policy's mean-field equilibrium threshold. Based on this result, we develop a consistent estimator for the policy gradient. In a semi-synthetic experiment with data from the National Education Longitudinal Study of 1988, we demonstrate that this estimator can be used for learning capacity-constrained policies in the presence of strategic behavior.

stat.ML↗

arXiv2025

Optimal Mechanisms for Demand Response: An Indifference Set Approach

The time at which renewable (e.g., solar or wind) energy resources produce electricity cannot generally be controlled. In many settings, however, consumers have some flexibility in their energy consumption needs, and there is growing interest in demand-response programs that leverage this flexibility to shift energy consumption to better match renewable production -- thus enabling more efficient utilization of these resources. We study optimal demand response in a setting where consumers use home energy management systems (HEMS) to autonomously adjust their electricity consumption. Our core assumption is that HEMS operationalize flexibility by querying the consumer for their preferences and computing the ``indifference set'' of all energy consumption profiles that can be used to satisfy these preferences. Then, given an indifference set, HEMS can respond to grid signals while guaranteeing user-defined comfort and functionality; e.g., if a consumer sets a temperature range, a HEMS can precool and preheat to align with peak renewable production, thus improving efficiency without sacrificing comfort. We show that while price-based mechanisms are not generally optimal for demand response, they become asymptotically optimal in large markets under a mean-field limit. Furthermore, we show that optimal dynamic prices can be efficiently computed in large markets by only querying HEMS about their planned consumption under different price signals. Using an OpenDSS-powered grid simulation for Phoenix, Arizona, we demonstrate that our approach enables meaningful demand response without creating grid instability.

math.OC↗

arXiv2025

Treatment Effects in Market Equilibrium

Policy-relevant treatment effect estimation in a marketplace setting requires taking into account both the direct benefit of the treatment and any spillovers induced by changes to the market equilibrium. The standard way to address these challenges is to evaluate interventions via cluster-randomized experiments, where each cluster corresponds to an isolated market. This approach, however, cannot be used when we only have access to a single market (or a small number of markets). Here, we show how to identify and estimate policy-relevant treatment effects using a unit-level randomized trial run within a single large market. A standard Bernoulli-randomized trial allows consistent estimation of direct effects, and of treatment heterogeneity measures that can be used for welfare-improving targeting. Estimating spillovers - as well as providing confidence intervals for the direct effect - requires estimates of price elasticities, which we provide using an augmented experimental design. Our results rely on all spillovers being mediated via the (observed) prices of a finite number of traded goods, and the market power of any single unit decaying as the market gets large. We illustrate our results using a simulation calibrated to a conditional cash transfer experiment in the Philippines.

econ.EM↗

arXiv2024

Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests

Flexible machine learning tools are increasingly used to estimate heterogeneous treatment effects. This paper gives an accessible tutorial demonstrating the use of the causal forest algorithm, available in the R package grf. We start with a brief non-technical overview of treatment effect estimation methods, focusing on estimation in observational studies; the same techniques can also be applied in experimental studies. We then discuss the logic of estimating heterogeneous effects using the extension of the random forest algorithm implemented in grf. Finally, we illustrate causal forest by conducting a secondary analysis on the extent to which individual differences in resilience to high combat stress can be measured among US Army soldiers deploying to Afghanistan based on information about these soldiers available prior to deployment. We illustrate simple and interpretable exercises for model selection and evaluation, including targeting operator characteristics curves, Qini curves, area-under-the-curve summaries, and best linear projections. A replication script with simulated data is available at https://github.com/grf-labs/grf/tree/master/experiments/ijmpr

stat.AP↗

arXiv2024

Qini Curves for Multi-Armed Treatment Rules

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms, that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout.

stat.ME↗

arXiv2024

Minimax-Regret Sample Selection in Randomized Experiments

Randomized controlled trials are often run in settings with many subpopulations that may have differential benefits from the treatment being evaluated. We consider the problem of sample selection, i.e., whom to enroll in a randomized trial, such as to optimize welfare in a heterogeneous population. We formalize this problem within the minimax-regret framework, and derive optimal sample-selection schemes under a variety of conditions. Using data from a COVID-19 vaccine trial, we also highlight how different objectives and decision rules can lead to meaningfully different guidance regarding optimal sample allocation.

stat.ME↗

arXiv2024

Sequential Validation of Treatment Heterogeneity

We use the martingale construction of Luedtke and van der Laan (2016) to develop tests for the presence of treatment heterogeneity. The resulting sequential validation approach can be instantiated using various validation metrics, such as BLPs, GATES, QINI curves, etc., and provides an alternative to cross-validation-like cross-fold application of these metrics.

econ.EM↗

arXiv2024

Treatment heterogeneity with right-censored outcomes using grf

This article walks through how to estimate conditional average treatment effects (CATEs) with right-censored time-to-event outcomes using the function causal_survival_forest (Cui et al., 2023) in the R package grf (Athey et al., 2019, Tibshirani et al., 2024) using data from the National Job Training Partnership Act.

stat.CO↗

arXiv2023

What Makes Forest-Based Heterogeneous Treatment Effect Estimators Work?

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 L2 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.

stat.ME↗

arXiv2023

Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects

There are a number of available methods for selecting whom to prioritize for treatment, including ones based on treatment effect estimation, risk scoring, and hand-crafted rules. We propose rank-weighted average treatment effect (RATE) metrics as a simple and general family of metrics for comparing and testing the quality of treatment prioritization rules. RATE metrics are agnostic as to how the prioritization rules were derived, and only assess how well they identify individuals that benefit the most from treatment. We define a family of RATE estimators and prove a central limit theorem that enables asymptotically exact inference in a wide variety of randomized and observational study settings. RATE metrics subsume a number of existing metrics, including the Qini coefficient, and our analysis directly yields inference methods for these metrics. We showcase RATE in the context of a number of applications, including optimal targeting of aspirin to stroke patients.

stat.ME↗

arXiv2023

Weak Signal Asymptotics for Sequentially Randomized Experiments

We use the lens of weak signal asymptotics to study a class of sequentially randomized experiments, including those that arise in solving multi-armed bandit problems. In an experiment with $n$ time steps, we let the mean reward gaps between actions scale to the order $1/\sqrt{n}$ so as to preserve the difficulty of the learning task as $n$ grows. In this regime, we show that the sample paths of a class of sequentially randomized experiments -- adapted to this scaling regime and with arm selection probabilities that vary continuously with state -- converge weakly to a diffusion limit, given as the solution to a stochastic differential equation. The diffusion limit enables us to derive refined, instance-specific characterization of stochastic dynamics, and to obtain several insights on the regret and belief evolution of a number of sequential experiments including Thompson sampling (but not UCB, which does not satisfy our continuity assumption). We show that all sequential experiments whose randomization probabilities have a Lipschitz-continuous dependence on the observed data suffer from sub-optimal regret performance when the reward gaps are relatively large. Conversely, we find that a version of Thompson sampling with an asymptotically uninformative prior variance achieves near-optimal instance-specific regret scaling, including with large reward gaps, but these good regret properties come at the cost of highly unstable posterior beliefs.

math.ST↗

arXiv2023

Off-Policy Evaluation in Partially Observed Markov Decision Processes under Sequential Ignorability

We consider off-policy evaluation of dynamic treatment rules under sequential ignorability, given an assumption that the underlying system can be modeled as a partially observed Markov decision process (POMDP). We propose an estimator, partial history importance weighting, and show that it can consistently estimate the stationary mean rewards of a target policy given long enough draws from the behavior policy. We provide an upper bound on its error that decays polynomially in the number of observations (i.e., the number of trajectories times their length), with an exponent that depends on the overlap of the target and behavior policies, and on the mixing time of the underlying system. Furthermore, we show that this rate of convergence is minimax given only our assumptions on mixing and overlap. Our results establish that off-policy evaluation in POMDPs is strictly harder than off-policy evaluation in (fully observed) Markov decision processes, but strictly easier than model-free off-policy evaluation.

cs.LG↗

arXiv2023

Policy Learning under Biased Sample Selection

Practitioners often use data from a randomized controlled trial to learn a treatment assignment policy that can be deployed on a target population. A recurring concern in doing so is that, even if the randomized trial was well-executed (i.e., internal validity holds), the study participants may not represent a random sample of the target population (i.e., external validity fails)--and this may lead to policies that perform suboptimally on the target population. We consider a model where observable attributes can impact sample selection probabilities arbitrarily but the effect of unobservable attributes is bounded by a constant, and we aim to learn policies with the best possible performance guarantees that hold under any sampling bias of this type. In particular, we derive the partial identification result for the worst-case welfare in the presence of sampling bias and show that the optimal max-min, max-min gain, and minimax regret policies depend on both the conditional average treatment effect (CATE) and the conditional value-at-risk (CVaR) of potential outcomes given covariates. To avoid finite-sample inefficiencies of plug-in estimates, we further provide an end-to-end procedure for learning the optimal max-min and max-min gain policies that does not require the separate estimation of nuisance parameters.

econ.EM↗

arXiv2023

Estimating heterogeneous treatment effects with right-censored data via causal survival forests

Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find our approach to perform well relative to a number of baselines.

stat.ME↗

arXiv2022

Treatment Heterogeneity for Survival Outcomes

Estimation of conditional average treatment effects (CATEs) plays an essential role in modern medicine by informing treatment decision-making at a patient level. Several metalearners have been proposed recently to estimate CATEs in an effective and flexible way by re-purposing predictive machine learning models for causal estimation. In this chapter, we summarize the literature on metalearners and provide concrete guidance for their application for treatment heterogeneity estimation from randomized controlled trials' data with survival outcomes. The guidance we provide is supported by a comprehensive simulation study in which we vary the complexity of the underlying baseline risk and CATE functions, the magnitude of the heterogeneity in the treatment effect, the censoring mechanism, and the balance in treatment assignment. To demonstrate the applicability of our findings, we reanalyze the data from the Systolic Blood Pressure Intervention Trial (SPRINT) and the Action to Control Cardiovascular Risk in Diabetes (ACCORD) study. While recent literature reports the existence of heterogeneous effects of intensive blood pressure treatment with multiple treatment effect modifiers, our results suggest that many of these modifiers may be spurious discoveries. This chapter is accompanied by survlearners, an R package that provides well-documented implementations of the CATE estimation strategies described in this work, to allow easy use of our recommendations as well as the reproduction of our numerical study.

stat.AP↗

arXiv2022

Partial Likelihood Thompson Sampling

We consider the problem of deciding how best to target and prioritize existing vaccines that may offer protection against new variants of an infectious disease. Sequential experiments are a promising approach; however, challenges due to delayed feedback and the overall ebb and flow of disease prevalence make available methods inapplicable for this task. We present a method, partial likelihood Thompson sampling, that can handle these challenges. Our method involves running Thompson sampling with belief updates determined by partial likelihood each time we observe an event. To test our approach, we ran a semi-synthetic experiment based on 200 days of COVID-19 infection data in the US.

stat.ME↗