Heterogeneous treatment effect. This paper examines the issue using data from impact ev.

Heterogeneous treatment effect 1 – 3 Epidemiologists have been long interested in investigating heterogenous treatment effects (HTEs) for several reasons. It has recently been show that those regressions may produce misleading estimates, if the policy's effect is heterogeneous between groups or over time, as is often the case. We show that a linear-in Instrumental variables (IV) with heterogeneous treatment effects (HTEs) ! Unobservable heterogeneity Complicates IV methods tremendously An enormous and sometimes contentious cross-disciplinary literature Featured centrally in three Nobel prizes (Heckman, Imbens, Angrist) ! Speaks to several fundamental issues in empirical methodology Estimating heterogeneous treatment effects (HTE) has gained significant attention in healthcare research, as it captures variations in treatment efficacy across individuals or subgroups exposed to the same treatment. In particular, treatment effects may vary systematically by the propensity for treatment. Most cases of causal inference involve ordering units based on treatment effects, for example, to find units/ individuals that are more likely to positively respond to treatment. Abstract Heterogeneous treatment efects (HTEs) are commonly identified during randomized controlled trials (RCTs). However, a comprehensive review of these algorithms is lacking. Often, multiple clinical outcomes are measured during an RCT, each having a potentially heterogeneous efect. In this tutorial, we describe different meta-learners, which are flexible algorithms that can be used to estimate personalized Different combinations of treatments may have different effects Interaction among treatment variables instead of interaction between a treatment and covariates Factorial designs, e. For example, an HTE-informed understanding can critically guide physicians to individualize the medical treatment for a certain disease. Apr 21, 2017 · Many scientific and engineering challenges—ranging from personalized medicine to customized marketing recommendations—require an understanding of treatment effect heterogeneity. To enhance Feb 24, 2025 · In public health and clinical settings, it is not uncommon to observe some heterogeneity in intervention or treatment effects—which occurs when the effect of an intervention or treatment is different from one subgroup to another. This concept is crucial in fields such as statistics, data analysis, and data science, where understanding the nuances of how different segments respond to treatments can lead to more Mar 17, 2025 · Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates, even though no formal statistical methods exist for such analyses. However, the interpretation of estimated individualized effects requires caution because insights from these data-driven approaches might be misaligned with the contextual needs of a human audience. Instrumental variable analysis with binary out-effect free of bias. These varying patient characteristics can potentially modify the effect of a treatment on outcomes. This measure provides insight into effect heterogeneity and enables personalization. Dec 21, 2024 · Abstract To test scientific theories and develop individualized treatment rules, researchers often wish to learn heterogeneous treatment effects that can be consistently found across diverse populations and contexts. Our goal in this article is to promote the use of Bayesian methods for subgroup analysis and to lower the Oct 30, 2021 · Abstract Heterogeneous treatment effect (HTE) analysis focuses on examining varying treatment effects for individuals or subgroups in a population. Abstract Many scienti c and engineering challenges|ranging from personalized medicine to customized marketing recommendations|require an understanding of treatment e ect heterogeneity. harvard. Jan 1, 2013 · The chapter has four main sections. May 24, 2025 · The norepinephrine equivalence (NEE) formula balance treatment of different vasoactive drugs, with NEE captured hourly for up to 72 h to record both time of use and dosage. Feb 9, 2023 · In particular, social scientists are interested in (1) whether there exists treatment effect heterogeneity, and if so, the main drivers (moderators) of such heterogeneity; (2) how the heterogeneous treatment effects vary along with moderators. In other words, ML is incredibly useful when you want to map from a known input X (like an english We address the problem of estimating heterogeneous treatment effects in panel data, adopting the popular Difference-in-Differences (DiD) framework under the conditional parallel trends assumption. We focus on the case of a choice between 2 treatments, which for the purposes of this manuscript we label as treatment and control. While the average causal effect provides a broad measure of a treatment’s effectiveness and informs general policy decisions, uncovering covariate heterogeneity patterns is essential for evaluating substantive hypotheses and specific policy interventions. This post explains, at a high level, what heterogeneous treatment effects are, why they are essential, and how to think about them. Introduction and motivating applications. Differences in the effect of a policy or intervention for different people are known as heterogeneous treatment effects (HTEs). Identifying subgroups of patients with similar treatment efects is of high interest in clinical research to advance precision medicine. 00 Sep 4, 2017 · But political scientists are often interested in how effects vary across subpopulations—heterogeneous treatment effects—and how differences in the content of the treatment affects responses—the response to heterogeneous treatments. , conjoint analysis Nov 8, 2022 · Methods for inferring Causality Heterogeneous Treatment Effect using Meta learners Double machine learning (DML) is the method for estimating heterogeneous treatment effects especially when we have a large number of confounders. Two foundations of the framework are conditional average treatment effects (CATEs) and off-policy evaluation using data with randomized targeting. Despite the presence of this heterogeneity 18 hours ago · In this article, we provide a rigorous general framework for developing and evaluating effect models to characterize heterogeneous treatment effects from a single randomized control trial. We thus aimed to catalog and outline Heterogeneity of treatment effects (HTE) refers to the non-random variation in the magnitude or direction of a treatment effect across levels of a covariate, as measured on a selected scale, against a clinical outcome. The second section discusses recent research that attends to causal effect heterogeneity, what we gain from such attention, and how we reconcile discrepant findings across methods. In this paper, we discuss a practical approach to studying heterogeneous treatment effects as a function of the treatment propensity, under the 1. Understanding this heterogeneity of treatment effect is critical for evaluating how well a treatment can be expected to work for an individual or a subgroup of individuals. Analyzing heterogeneous treatment effects based on pretreatment covariates is crucial in modern causal inference. We consider the problem of generalizing heterogeneous treatment effects (HTE) based on data from multiple sites. We propose a random forest Background: Recent evidence suggests that there is often substantial variation in the benefits and harms across a trial population. Most existing methods are not sufficiently robust against data irregularities. Methods We performed a literature review using a broad search strategy, complemented by suggestions of a technical expert panel Feb 22, 2025 · Background Classical approaches to subgroup analysis in randomised controlled trials (RCTs) to identify heterogeneous treatment effects (HTEs) involve testing the interaction between each pre-specified possible treatment effect modifier and the treatment effect. Abstract Accurately estimating heterogeneous treatment effects (HTE) is various domains such as personalized medicine, marketing campaigns, public policy and educa-tional interventions. edu This Guide to Statistics and Methods discusses the various approaches to estimating variability in treatment effects, including heterogeneity of treatment effect, which was used to assess the association between surgery to close patent foramen ovale and risk of recurrent stroke in patients who Sep 23, 2024 · On the other hand, in a large superiority trial with well-established treatment effects risk-based stratification may be more relevant to facilitate the clinical interpretability of the heterogeneity. This paper proposes, under the RD setup, formal tests for treatment effect heterogeneity among individuals with different observed pre-treatment characteristics. This paper reviews state The estimation of heterogeneous treatment effects has attracted considerable interest in many disciplines, most prominently in medicine and economics. May 15, 2021 · Estimating the individualized treatment effect has become one of the most popular topics in statistics and machine learning communities in recent years. Sep 19, 2024 · Background and Objectives: Estimating heterogeneous treatment effects (HTEs) in randomized controlled trials (RCTs) has received substantial attention recently. Our method seeks to reduce the bias in treatment effect estimates Dec 1, 2021 · The first main contribution of our paper is to interpret estimates from two-way fixed effects specifications when researchers include “dynamic” indicators for time relative to treatment and when treatment effects are heterogeneous across adoption cohorts. This treatment effect heterogeneity is of interest in patient-centered outcomes Mar 8, 2019 · Identification of heterogeneous treatment effects typically involves 2 separate but associated goals: (1) identification of subgroups with different treatment effects and (2) estimation of individual treatment effects, ie, individual risk prediction. In this tutorial, we describe different meta-learners, which are flexible algorithms that can be used to estimate personalized treatment Linear regressions with period and group fixed effects are widely used to estimate treatment effects. That is, they embody characteristics that vary between individuals, such as age, sex, disease etiology and severity, presence of comorbidities, concomitant exposures, and genetic variants. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. The quantile treatment effect (QTE) characterizes the heterogeneous treatment effect on individuals and groups across various positions in the distributions of different outcomes of interest. Contemporary research has so far primarily focused on continuous and binary responses where heterogeneous treatment effects are traditionally estimated by a linear model, which allows the estima-tion of constant or heterogeneous This paper proposes a method to estimate treatment effects in difference-in-differences designs in which the treatment start is staggered over time and treatment effects are heterogeneous by group, time, and covariates, and when the data are repeated cross-sections. We show that the multi-study R-learner treatment effect estimator is asymptotically normal within the series estimation framework. In randomized controlled Mar 6, 2025 · Characterizing heterogeneity of treatment effects (HTE) is a fundamental goal of pharmacoepidemiology, addressing why medications work differently across patient populations. Thus, a practical framework that integrates advanced machine learning methods and Oct 23, 2020 · Background Recent evidence suggests that there is often substantial variation in the benefits and harms across a trial population. However, tests based on the quantile process often suffer from estimated nuisance parameters that je Abstract Although often conflated, determining the best treatment for an individual (the task of a doctor) is fundamentally different from determining the average effect of treatment in a population (the purpose of a trial). In this paper, we review concepts of heterogeneity of treatment effects (HTE) essential in providing the evidence base for precision medicine and patient-centred care, and Oct 15, 2015 · Heterogeneous Treatment Effects in Impact Evaluation by Eva Vivalt. Differences in the effectiveness of treatments across participants in a clinical trial are important to Jan 10, 2023 · Most work on extending (generalizing or transporting) inferences from a randomized trial to a target population has focused on estimating average treatment effects (i. This policy evaluation approach allows us to evaluate an The basis for extrapolation is a set of assumptions about the cross-sectional homogeneity or temporal stability of causal effects. In the potential outcomes framework with The view that treatment effects can be heterogeneous led to new methods for causal inference and also to new uses and interpretations of existing methods (e. 3, 4 Broadly, machine The key quantity for such analyses is the conditional average treatment effect (CATE), which captures how treatment effects vary according to baseline covariates (features). Abstract The estimation of heterogeneous treatment effects has attracted considerable interest in many disciplines, most promi-nently in medicine and economics. It also discusses and demonstrates methods for estimating how effects vary and interpreting results: from testing for heterogeneity, to estimating subgroup treatment effects and their differences, to addressing the pitfalls of multiple comparisons and See full list on imai. Causal inference, a cornerstone of modern econometrics, acknowledges that treatment effects often vary significantly across different subgroups within a population. However, individual significant interactions may not always yield clinically actionable subgroups, particularly for continuous This JAMA Guide to Statistics and Methods discusses instrumental variable analysis, a method designed to reduce or eliminate unobserved confounding in observational studies, with the goal of achieving unbiased estimation of treatment effects. We aimed to identify regression modeling approaches that assess heterogeneity of treatment effect within a randomized clinical trial. We propose another To study heterogeneous treat-ment effects in the presence of self-selection, Heckman and Vytlacil (1999, 2001a, 2005, 2007b) have developed a structural approach that builds on the marginal treatment effect (MTE). The multi-study R-learner is flexible in its ability to incorporate many machine learning techniques for estimating heterogeneous treatment effects, nuisance functions, and membership probabilities. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in survival and observational setting where outcomes may be right-censored. For instance, we can estimate the average treatment effect for highly connected units (high-degree nodes) and compare it to less connected units, providing novel insights into how network characteristics influence treatment effects. The proposed tests study whether a policy treatment (1) is beneficial for at least some subpopulations defined by pre-treatment Mar 22, 2022 · The overall goal ment effect because it applies only “locally” to the subgroup of of an instrumental variable analysis is to measure the treatment marginal patients. Feb 1, 2019 · Treatment effect heterogeneity is frequently studied in regression discontinuity (RD) applications. We define treatment effect heterogeneity as the degree to which different treatments have differential causal effects on each Oct 30, 2021 · Abstract Heterogeneous treatment effect (HTE) analysis focuses on examining varying treatment effects for individuals or subgroups in a population. We thus Tree-based methods are very popular in regression and clas-sification tasks and demonstrate an additional superiority in heterogeneous treatment effects estimation, since the splitting procedure of trees can be understood as implicit matching/stratification. e. 00 We develop a new method, the Panel Clustering Estimator (PaCE), for estimating heterogeneous treatment effects in panel data under general treatment patterns. Applied micro Jan 25, 2021 · Instead, it is often more informative to study how the effect of an intervention varies across different population subgroups. , averaged over the target population’s covariate distribution). This article Heterogeneous treatment effect (HTE) analysis focuses on examining varying treatment effects for individuals or subgroups in a population. g. Surprisingly, however, not much attention is usually paid to the explicit analysis of the heterogeneity of treatment effects in applied Outline A causal framework for heterogeneous treatment effects (HTE) Four general approaches for estimating HTEs What to look at in papers on HTE evaluation? Post-selection inference on HTE Mar 21, 2023 · This exploratory study of a multiplatform randomized trial investigating the effects of therapeutic-dose heparin in early-pandemic hospitalized COVID-19 patients describes findings from 3 statistical approaches to detecting differences of treatment effect in clinically relevant patient subgroups. We thus Treatment Effect Heterogeneity* Knowledge of treatment effect heterogeneity or “essential heterogeneity” plays an important role in our understanding of how programs work and in the design of systems to allocate them among the eligible. To estimate heterogeneous effects, PaCE splits the observations into disjoint clusters using a regression tree and Abstract—Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or subgroups. This guide discusses the theoretical and policy relevance of heterogeneous treatment effects, which is when effects vary by individual or group. Feb 27, 2023 · Abstract Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Understanding which characteristics are associated with treatment effect heterogeneity can help to customize therapy to the individual patient. Jul 22, 2025 · This scoping review describes and evaluates findings from reports that cited the Predictive Approaches to Treatment Effect Heterogeneity (PATH) Statement and presented predictive modeling of heterogeneity in treatment effects in randomized clinical trials (RCTs). Researchers at institutions like the National Bureau of Economic Research (NBER May 5, 2018 · We propose and study methods for estimation and inference of heterogeneous treatment effects, for both randomized experiments and observational studies. Social policies are important determinants of population health but may have varying effects on subgroups of people. Our approach relies on orthogonal estimating equations to robustly adjust The credibility revolution advances the use of research designs that permit identification and estimation of causal effects. However, standard regression approaches for estimating Abstract Individuals differ not only in their background characteristics, but also in how they respond to a particular treatment, intervention, or stimulation. In this paper, we introduce an approach motivated by the concept of ‘multi-calibration’ from the recent advancements in machine learning. Published in volume 110, issue 9, pages 2964-96 of American Economic Review, September 2020, Abstract: Linear regressions with period and group fixed effects are widely used Abstract Psychotherapy has been proven to be effective on average, though patients respond very differently to treatment. 1, 2, 4 First, it is well-known that Nov 6, 2022 · The heterogeneous treatment effect is then the process of estimating the causal relationship between Tᵢ on Yᵢ, under the context of Xᵢ. Patient populations within a research study are heterogeneous. A dominant current approach to the quantitative evaluation of mechanisms relies on the detection of heterogeneous treatment effects with re-spect to pre-treatment covariates Mar 4, 2025 · Effect heterogeneity analyses using causal machine learning algorithms have gained popularity in recent years. Most existing methods focus on modeling the heterogeneous treatment effects for univariate outcomes. It also works with continuous treatment, unlike the meta-learners we discussed in the previous article. Apr 5, 2024 · We present a general framework to target customers using optimal targeting policies, and we document the profit differences from alternative estimates of the optimal targeting policies. Most existing methods consider the setting with a single treatment arm and a single outcome metric. Most existing HTE estimation meth-ods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units, but ignore distribution shifts across populations. Univariate subgroups analyses remain relevant in several contexts, especially in terms of hypothesis generation, and should not be disregarded. In particular, there is increasing interest in estimating HTE for survival outcomes, which provides a deeper understanding of treatment heterogeneity in disease progression and When baseline risk of an outcome varies within a population, the effect of a treatment on that outcome will vary on at least one scale (e. 00 USD $58. For example, an HTE‐informed understanding can critically guide physicians to individualize the medical Oct 1, 2023 · The widespread availability of rich, real-world data (RWD) generated from patient care provides increased opportunities to generate evidence to inform clinical decisions for subpopulations of patients, and perhaps even for individuals (1, 2). 00 GBP £44. fas. 18 - Heterogeneous Treatment Effects and Personalization From Predictions to Causal Inference In the last chapter, we briefly covered Machine Learning models. Machine learning methods have recently been developed and applied to health data to address each of these approaches. This has led to the widespread use of ad hoc approaches in applications. Although there is considerable literature on HTE among Mar 26, 2024 · Heterogeneity of treatment effect is intuitive to the clinician at the bedside. In biomedical science, analyzing treatment effect heterogeneity plays an essential role in assisting personalized medicine. Jan 1, 2023 · Social scientists have long been interested in the varying responses to a specific intervention, motivating the enterprise of heterogeneous treatment effects (HTE) analysis. Our approach offers some additional advantages beyond our choice of estimand. An overemphasis on Jun 8, 2022 · Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey - 24 Hours access EUR €53. This article Jan 1, 2023 · Heterogeneous treatment effect estimation is to quantify individual or subgroups' treatment effect by accounting for the heterogeneity of patient’s conditions to outcome while reducing selection bias. May 25, 2025 · The exploration of treatment efficacy often extends beyond simple averages, leading us to the critical concept of the heterogeneous treatment effect. Evaluating heterogeneous treatment effects (HTEs) of social policies is critical to determine how social policies will affect health Jul 22, 2025 · Selby et al1 provide a detailed scoping review of the application of the Prediction Approaches to Treatment Heterogeneity (PATH) statement2,3 that provides 2 frameworks for conducting heterogeneity of treatment (HTE) analyses (ie, subgroup or effect modification) in randomized clinical trials Heterogeneous Treatment Effect Estimation using machine learning for Healthcare application: tutorial and benchmark Yaobin Ling, Pulakesh Upadhyaya, Luyao Chen, Xiaoqian Jiang, Yejin Kim Dec 1, 2024 · Estimating heterogeneous treatment effects (HTEs) in randomized controlled trials (RCTs) has received substantial attention recently. May 19, 2023 · Abstract There has been much interest in the evaluation of heterogeneous treatment effects (HTE) and multiple statistical methods have emerged under the heading of personalized/precision medicine combining ideas from hypothesis testing, causal inference, and machine learning over the past 10-15 years. This has led to the development of several statistical and machine learning (ML) algorithms to assess HTEs through identifying individualized treatment effects. The main goals of analyzing treatment effect heterogeneity include estimating treatment effects in clinically relevant subgroups and predicting whether a patient subpopulation … Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects by Clément de Chaisemartin and Xavier D'Haultfœuille. In this paper, we develop a non-parametric causal forest for estimat- ing heterogeneous treatment e ects that extends Breiman’s widely used random for- est algorithm. , CATEs) that vary across population subgroups. However, understanding which mechanisms produce mea-sured causal effects remains a challenge. Evaluation of heterogeneity of treatment effect (HTE) is an essential aspect of personalized medicine and patient-centered outcomes research. Published in volume 105, issue 5, pages 467-70 of American Economic Review, May 2015, Abstract: It is very important to know how much we can extrapolate from a study's results. As a graduate student, I learned about parameter stability as ‘the Lucas critique’, while my own teaching and research focuses on the identification possibilities for average causal effects in models with heterogeneous potential outcomes. This survey reviews a fast-growing literature that documents this issue, and that proposes alternative estimators robust to heterogeneous effects. When we recommend the best treatment for patients on the basis of their individual characteristics, we are applying t Feb 24, 2023 · Abstract “Heterogeneous treatment effects” is a term which refers to conditional average treatment effects (i. The first section describes key estimation strategies for the study of heterogeneous treatment effects. While the average treatment effect can be easily estimated without bias in randomized experiments, treatment effect heterogeneity plays an essential role in evaluating the efficacy of social pro-grams and medical treatments. In this article, we develop a nonparametric causal forest for estimating heterogeneous treatment effects that extends Breiman’s widely used random forest algorithm. Over the past five decades, the rapid development of HTE methods, from conventional multiplicative interactions in linear models to explorations based on machine learning techniques, has been witnessed. This paper examines the issue using data from impact ev Mar 30, 2023 · Treatment effects are often anticipated to vary across groups of patients with different baseline risk. We aimed to identify regression modeling approaches that assess heterogeneity of treatment effect within a randomized clinical Nov 3, 2023 · Psychotherapy has been proven to be effective on average, though patients respond very differently to treatment. Jul 25, 2024 · In this paper, we review recent advances in statistical methods for the evaluation of the heterogeneity of treatment effects (HTE), including subgroup identification and estimation of individualized treatment regimens, from randomized clinical trials and observational studies. The Predictive Approaches to Treatment Effect Heterogeneity (PATH) statement focused on Jun 1, 2022 · However, policies may have larger health effects for some groups and smaller effects for others. Further, the effects of each of these pol-lutants might be heterogeneous with respect to characteristics of the individuals exposed, and it is important to account for and understand this treatment effect heterogeneity. Due to the negative weights, the linear regression coefficient may for instance be nega-tive while all the ATEs are positive. In this paper, we extend the MTE-based approach through a redefinition of MTE. Recently there has been high Jun 13, 2022 · Abstract Learning heterogeneous treatment e ects (HTEs) is an important problem across many elds. Covariate-based May 16, 2023 · This paper provides estimation and inference methods for conditional average treatment effects (CATE) characterized by a high-dimensional parameter in both homogeneous cross-sectional and unit-hetero Background and objectives: Estimating heterogeneous treatment effects (HTEs) in randomized controlled trials (RCTs) has received substantial attention recently. The causal effects are modeled as a non-parametric function of the covariates of the units, which may vary over time. We propose a novel doubly robust meta-learner for the Conditional Average Treatment Effect on the Treated (CATT), reducing the estimation to a convex risk minimization problem involving a set of Individuals vary in their response to a treatment. The credibility revolution advances the use of research designs that permit identification and estimation of causal effects. Understanding Heterogeneous Treatment Effects Heterogeneous Treatment Effects (HTE) refer to the varying impacts that a treatment or intervention can have on different individuals or groups within a population. Contemporary research has so far primarily focused on continuous and binary responses where Recent evidence suggests that there is often substantial variation in the benefits and harms across a trial population. We show that they estimate weighted sums of the average treatment effects (ATE ) in each group and period, with weights that may be negative. LATE interpretation of IV estimators, revival of matching and regression discontinuity designs). However, many biomedical studies are interested in studying multiple highly correlated endpoints at the same time. , additive, multiplicative). The logistic regression model, including phenotype–dosage–time interactions, examined heterogeneous treatment effects on hospital mortality. ML models are tools for what I called predictions or, more technically, estimating the conditional expectation function E [Y | X]. Some policies may even have qualitatively different effects across subgroups, benefitting some while harming others [1, 2]. Epidemiologists are often interested in estimating such effects because they can help detect populations that may particularly benefit from or be harmed by a treatment. Motivated by common empirical practice, we develop a unified, theoretically grounded framework for RD Jun 8, 2022 · Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey - 24 Hours access EUR €53. Yet, in the presence of strong effect modification by baseline covariates, the average treatment effect in the target population may be less relevant for . Heterogeneity of treatment effects (HTE) describes how treatment effect varies across patients. However, in many real world domains, experiments are run consistently - for example, in internet companies, A/B tests are run every day to measure the impacts of potential changes across many dif Aug 1, 2024 · We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. We introduce a permutation test for heterogeneous treatment effects based on the quantile process. Jan 1, 2024 · Heterogeneous treatment effect estimation is an essential element in the practice of tailoring treatment to suit the characteristics of individual patients. A dominant current approach to the quantitative evaluation of mechanisms relies on the detection of heterogeneous treatment effects with re-spect to pre-treatment covariates This Stats, STAT! animated video explores the concept of treatment effect heterogeneity. Thereby, their applicability has Jan 1, 2023 · Social scientists have long been interested in the varying responses to a specific intervention, motivating the enterprise of heterogeneous treatment effects (HTE) analysis. fmtgdp qsicsow tycd ftgy qciurz zjdte pvg ohc qyuyfa rgao oqsdm fsqg xevocs xgwk nwvdm