Conditional Average Treatment Effect Research Articles

The application of Bayesian method in estimating heterogeneity of treatment effect

It is well recognized that the benefit of medical interventions may not be distributed evenly in the target population due to patient heterogeneity, and conclusions based on traditional randomized clinical trials do not apply to everyone. Considering the increasing cost of randomized trials and difficulties in recruiting patients, there is an urgent need to develop analytical methods to estimate treatment effects in subgroups. In particular, due to limited sample sizes of subgroups, standard analysis tends to yield wide confidence intervals for the treatment effect, which are often uninformative. In this article, the superiority of the empirical Bayes estimate of the conditional average treatment effect is demonstrated by using a linear regression model to specifically represent treatment-covariate interactions. To obtain more accurate prior distributions and posterior estimates of treatment effects in subgroups, we utilize the covariate-dependent precision parameter across subgroups. Based on subgroup data obtained from clinical trials, the covariate-dependent precision parameter is used to assess the similarity of treatment effects across subgroups, which is an approach to obtain more reasonable prior information. To verify the validity of the empirical Bayes method, we evaluate it by a real clinical trial comparing insulin and metformin.

Model Averaging for Estimating Treatment Effects With Binary Responses

ABSTRACTIn this article, we present a novel approach for estimating the conditional average treatment effect in models with binary responses. Our proposed method involves model averaging, and we establish a weight choice criterion based on jackknife model averaging. We analyze the theoretical properties of this approach, including its asymptotic optimality in achieving the lowest possible squared error and the convergence rate of the weights assigned to correctly specified models. Additionally, we introduce a new matching method that combines partition and nearest neighbor pairing, leveraging the strengths of both techniques. To evaluate the performance of our method, we conduct comparisons with existing approaches via a Monte Carlo study and a real data analysis. Overall, our results demonstrate the effectiveness and practicality of our proposed approach for estimating the conditional average treatment effect in binary response models.

Comparison of random forest methods for conditional average treatment effect estimation with a continuous treatment.

We are addressing the problem of estimating conditional average treatment effects with a continuous treatment and a continuous response, using random forests. We explore two general approaches: building trees with a split rule that seeks to increase the heterogeneity of the treatment effect estimation and building trees to predict as a proxy target variable. We conduct a simulation study to investigate several aspects including the presence or absence of confounding and colliding effects and the merits of locally centering the treatment and/or the response. Our study incorporates both existing and new implementations of random forests. The results indicate that locally centering both the response and treatment variables is generally the best strategy, and both general approaches are viable. Additionally, we provide an illustration using data from the 1987 National Medical Expenditure Survey.

Augmented inverse probability weighted estimation for conditional treatment effect

The Augmented Inverse Probability Weighted (AIPW) estimation has been extensively studied in various scenarios across diverse research areas. This investigation explores the asymptotic properties of the AIPW estimator for the conditional average treatment effect. Under various combinations of the parametric, semiparametric, and nonparametric structure in the nuisance propensity score and outcome regression models, we discuss the asymptotic bias and compare the asymptotic variances among the corresponding estimators. The study covers the asymptotic properties with no model misspecified; with either propensity score or outcome regressions locally/globally misspecified; and with all models locally/globally misspecified. To provide a deeper insight into the nature of these estimators and out of curiosity, we reveal the phenomenon that the asymptotic variances, with model-misspecification, could sometimes be even smaller than those with all models correctly specified. We also conduct a numerical study to validate the theoretical results.

Heterogeneous effects of Medicaid coverage on cardiovascular risk factors: secondary analysis of randomized controlled trial

ObjectivesTo investigate whether health insurance generated improvements in cardiovascular risk factors (blood pressure and hemoglobin A1c (HbA1c) levels) for identifiable subpopulations, and using machine learning to identify characteristics of people...

Development of optimised causal AI and its application in retail banking

Causal artificial intelligence (AI) has emerged as a promising approach in machine learning (ML), as it considers not only correlations but also cause-and-effect relationships in data, resulting in more human-like decision making. The pivotal stages within causal AI involve causal discovery and inferencing, each playing a crucial role in extracting meaningful insights from the data. In the realm of causal discovery, various algorithms have been developed to uncover the underlying cause-and-effect structures within data sets. A notable limitation, however, surfaces when attempting to apply these algorithms to data sets characterised by binary variables. This constraint prompts a crucial examination of the current methodologies and calls for innovative solutions that can seamlessly navigate the complexities of binary variable data sets. This paper proposes an optimised causal discovery algorithm that is integrated with the causal inference method based on the estimation of conditional average treatment effects (CATE) scores. The results present the potential of causal AI in terms of incremental impact on the predictive capability of AI/ML models. And the incremental impact is elucidated by comparing conventional propensity-based modelling and causal AI-based modelling by means of a use case in the field of retail banking.

Estimation of conditional average treatment effect based on greedy model averaging method

Estimation of conditional average treatment effect based on greedy model averaging method

Individualized treatment effects of a digital alcohol intervention and their associations with participant characteristics and engagement.

Conditional average treatment effects are often reported in intervention studies, in which assumptions are made regarding how effects are similar across a heterogeneous sample. Nonetheless, differing factors, such as genetics, age, and sex, can impact an intervention's effect on outcomes. The study aimed to estimate the individualized effects of a digital alcohol intervention among individuals looking online to reduce their drinking. We used data from a randomized controlled trial (RCT), including 2129 adults from the Swedish general population. The RCT concerned a text message-based alcohol intervention that sought to engender change through increasing knowledge on how to change and instilling confidence in changing behaviour. Outcomes were total weekly alcohol consumption and monthly heavy episodic drinking. Individualized treatment effects were modelled using baseline characteristics (age, gender, alcohol consumption, and psychosocial variables) and engagement with the intervention content. We found evidence that the effects of the digital alcohol intervention were heterogeneous concerning participants' age, baseline alcohol consumption, confidence, and importance. For heavy episodic drinking, there was evidence that effects were heterogeneous concerning age, sex, and baseline alcohol consumption. Overall, women, older individuals, and heavier drinkers benefitted more from the intervention in terms of effect size. In addition, participants who engaged more with the goal-setting and screening content reported better outcomes. The results highlight how different individuals respond differently to a digital alcohol intervention. This allows insight into who benefits the most and least from the intervention and highlights the potential merit of designing interventions adapted to different individuals' needs.

Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments

Researchers are increasingly turning to machine learning (ML) algorithms to investigate causal heterogeneity in randomized experiments. Despite their promise, ML algorithms may fail to accurately ascertain heterogeneous treatment effects under practical settings with many covariates and small sample size. In addition, the quantification of estimation uncertainty remains a challenge. We develop a general approach to statistical inference for heterogeneous treatment effects discovered by a generic ML algorithm. We apply the Neyman’s repeated sampling framework to a common setting, in which researchers use an ML algorithm to estimate the conditional average treatment effect and then divide the sample into several groups based on the magnitude of the estimated effects. We show how to estimate the average treatment effect within each of these groups, and construct a valid confidence interval. In addition, we develop nonparametric tests of treatment effect homogeneity across groups, and rank-consistency of within-group average treatment effects. The validity of our methodology does not rely on the properties of ML algorithms because it is solely based on the randomization of treatment assignment and random sampling of units. Finally, we generalize our methodology to the cross-fitting procedure by accounting for the additional uncertainty induced by the random splitting of data.

Learning Optimal Dynamic Treatment Regimes from Longitudinal Data.

Studies often report estimates of the average treatment effect (ATE). While the ATE summarizes the effect of a treatment on average, it does not provide any information about the effect of treatment within any individual. A treatment strategy that uses an individual's information to tailor treatment to maximize benefit is known as an optimal dynamic treatment rule (ODTR). Treatment, however, is typically not limited to a single point in time; consequently, learning an optimal rule for a time-varying treatment may involve not just learning the extent to which the comparative treatments' benefits vary across the characteristics of individuals, but also learning the extent to which the comparative treatments' benefits vary as relevant circumstances evolve within an individual. The goal of this paper is to provide a tutorial for estimating ODTR from longitudinal observational and clinical trial data for applied researchers. We describe an approach that uses a doubly-robust unbiased transformation of the conditional average treatment effect. We then learn a time-varying ODTR for when to increase buprenorphine-naloxone (BUP-NX) dose to minimize return-to-regular-opioid-use among patients with opioid use disorder. Our analysis highlights the utility of ODTRs in the context of sequential decision making: the learned ODTR outperforms a clinically defined strategy.

Estimation of the Local Conditional Tail Average Treatment Effect

The conditional tail average treatment effect (CTATE) is defined as a difference between the conditional tail expectations of potential outcomes, which can capture heterogeneity and deliver aggregated local information on treatment effects over different quantile levels and is closely related to the notion of second-order stochastic dominance and the Lorenz curve. These properties render it a valuable tool for policy evaluation. In this article, we study estimation of the CTATE locally for a group of compliers (local CTATE or LCTATE) under the two-sided noncompliance framework. We consider a semiparametric treatment effect framework under endogeneity for the LCTATE estimation using a newly introduced class of consistent loss functions jointly for the CTE and quantile. We establish the asymptotic theory of our proposed LCTATE estimator and provide an efficient algorithm for its implementation. We then apply the method to evaluate the effects of participating in programs under the Job Training Partnership Act in the United States.

The nexus of intellectual property rights and firm productivity in China: A nonlinear approach

This paper explores the way that intellectual property rights (IPRs) protection as a moderator variable affects firm-level productivity gains through innovation (filing patents) and diffusion (importing goods). Applying the estimation method of conditional average treatment effect by Lee, Okui, and Whang (2017) to Chinese firm data, I show the graphic representation of the non-linearity that characterizes the heterogeneous average treatment effects of patenting and importing activities on firm productivity. The graphic results suggest that the productivity effect of patenting is positively influenced by local IPRs protection, while that of importing is initially negatively and subsequently positively affected by IPRs protection. I also find that overstrict protection of IPRs may diminish the productivity impact of both channels, and private-owned firms rely more on IPRs protection to enhance productivity through filing patents.

Quantifying water effluent violations and enforcement impacts using causal AI

AbstractIn the landscape of environmental governance, controlling water pollution through the regulation of point sources is vital as it preserves ecosystems, protects human health, ensures legal compliance, and fulfills global environmental responsibilities. Under the Clean Water Act, the integrated compliance information system monitors the compliance and enforcement status of facilities regulated by the National Pollutant Discharge Elimination System (NPDES) permit program. This study assesses temporal and geographic trends for effluent violations within the United States and introduces a novel metric for quantifying violation trends at the facility level. Furthermore, we utilize a linear parametric approach for Conditional Average Treatment Effect (CATE) causal analysis to quantify the heterogeneous effects of EPA and state enforcement actions on effluent violation trends at facilities with NPDES permits. Our research reveals insights into national pollutant discharge trends, regional clustering of all pollutant violation types in Ohio ( Z‐score of 2.15), and priority pollutants in West Virginia ( Z‐score of 3.07). The trend metric identifies regulated facilities that struggle with severe and recurring violations. The causal model highlights variations in state compliance and enforcement effectiveness, underscoring the successful moderation of violation trends by states such as Montana and Maryland, among others.

Assessing external validity in practice

We review, from a practical standpoint, the evolving literature on assessing external validity (EV) of estimated treatment effects. We review existing EV measures, and focus on methods that permit multiple datasets (Hotz et al., 2005). We outline criteria for practical usage, evaluate the existing approaches, and identify a gap in potential methods. Our practical considerations motivate a novel method utilizing the Group Lasso (Yuan and Lin, 2006) to estimate a tractable regression-based model of the conditional average treatment effect (CATE). This approach can perform better when settings have differing covariate distributions and allows for easily extrapolating the average treatment effect to new settings. We apply these measures to a set of identical field experiments upgrading slum dwellings in three different countries (Galiani et al., 2017).

Learning optimal biomarker-guided treatment policy for chronic disorders.

Electroencephalogram (EEG) provides noninvasive measures of brain activity and is found to be valuable for the diagnosis of some chronic disorders. Specifically, pre-treatment EEG signals in the alpha and theta frequency bands have demonstrated some association with antidepressant response, which is well-known to have a low response rate. We aim to design an integrated pipeline that improves the response rate of patients with major depressive disorder by developing a treatment policy guided by the resting state pre-treatment EEG recordings and other treatment effects modifiers. First, we design an innovative automatic site-specific EEG preprocessing pipeline to extract features with stronger signals than raw data. We then estimate the conditional average treatment effect (CATE) using causal forests and use a doubly robust technique to improve efficiency in the estimation of the average treatment effect. We present evidence of heterogeneity in the treatment effect and the modifying power of the EEG features, as well as a significant average treatment effect, a result that cannot be obtained with conventional methods. Finally, we employ an efficient policy learning algorithm to learn an optimal depth-2 treatment assignment decision tree and compare its performance with Q-Learning and outcome-weighted learning via simulation studies and an application to a large multi-site, double-blind, randomized controlled clinical trial, EMBARC.

Quantifying uncertainty of uplift: Trees and T-learners

Uplift modeling refers to the task of estimating the causal effect of a treatment on an individual, also known as the conditional average treatment effect. However, uplift models do not usually provide uncertainty estimates of the predictions. We explain why estimating uncertainty of the treatment effect is particularly important in many common use cases and we show how epistemic uncertainty of the uplift estimates can be quantified for T-learners and trees. We tested the methods on three empirical datasets and evaluated them on a simulated dataset. We found that high uncertainty might be the result of both modeling choices and properties of the data. Sometimes there is not enough data or the data is simply not rich enough to identify the treatment effect well resulting in high uncertainty. In addition, our results suggest that one commonly used dataset might not be suitable for benchmarking.

Nonparametric estimation of conditional incremental effects

Abstract Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment effect (CATE). However, identification of the CATE requires that all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. Instead, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions where the odds of treatment are multiplied by some factor. These effects do not require positivity for identification and can be better suited for modeling scenarios in which people cannot be forced into treatment. We develop a projection approach and a flexible nonparametric estimator that can each estimate all the conditional effects we propose and derive model-agnostic error guarantees showing that both estimators satisfy a form of double robustness. Further, we propose a summary of treatment effect heterogeneity and a test for any effect heterogeneity based on the variance of a conditional derivative effect and derive a nonparametric estimator that also satisfies a form of double robustness. Finally, we demonstrate our estimators by analyzing the effect of intensive care unit admission on mortality using a dataset from the (SPOT)light study.

Finding the best subgroup with differential treatment effect with multiple outcomes.

Precision medicine aims to identify specific patient subgroups that may benefit the most from a particular treatment than the whole population. Existing definitions for the best subgroup in subgroup analysis are based on a single outcome and do not consider multiple outcomes; specifically, outcomes of different types. In this article, we introduce a definition for the best subgroup under a multiple-outcome setting with continuous, binary, and censored time-to-event outcomes. Our definition provides a trade-off between the subgroup size and the conditional average treatment effects (CATE) in the subgroup with respect to each of the outcomes while taking the relative contribution of the outcomes into account. We conduct simulations to illustrate the proposed definition. By examining the outcomes of urinary tract infection and renal scarring in the RIVUR clinical trial, we identify a subgroup of children that would benefit the most from long-term antimicrobial prophylaxis.

Estimating conditional average treatment effects with heteroscedasticity by model averaging and matching

We propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effects under heteroskedastic error settings. The proposed approach has asymptotic optimality and consistency of weights and estimator. Numerical studies show that our method has good finite-sample performances.

Heterogeneity of the effect of the COVID-19 pandemic on the incidence of Metabolic Syndrome onset at a Japanese campus.

The coronavirus disease 2019 (COVID-19) outbreak began in China in December 2019, with the World Health Organization declaring a state of emergency in January 2020. Worldwide implementation of lockdown measures to slow the spread of the virus led to reduced physical activity, disrupted eating habits, mental health issues, and sleep disturbances, which increased the risk of lifestyle-related diseases such as metabolic syndrome (MetS). During the COVID-19 pandemic, healthcare workers, especially intensive care workers, experienced longer working hours and burnout, which further increased the risk of lifestyle-related diseases. Accordingly, it is important to identify individuals at a risk of new-onset MetS during a pandemic, which could direct preventive interventions. This study aimed to assess the heterogeneous impact of the COVID-19 pandemic on the incidence of new-onset MetS based on the conditional average treatment effect (CATE) and to identify at-risk populations. This study analyzed health checkup data obtained from Okayama University Shikata Campus workers using paired baseline and follow-up years. Baseline data encompassed 2017 to 2019, with respective follow-up data from 2018 to 2020. Furthermore, as the COVID-19 pandemic in Japan began in January 2020, workers who underwent follow-up health checkups in 2018 to 2019 and 2020 were considered as "unexposed" and "exposed," respectively. As the Shikata campus has several departments, comparisons among departments were made. The primary outcome was new-onset MetS at follow-up. Predictor variables included baseline health checkup results, sex, age, and department (administrative, research, medical, or intensive care department). X-learner was used to calculate the CATE. This study included 3,572 eligible individuals (unexposed, n=2,181; exposed, n=1,391). Among them, 1,544 (70.8%) and 866 (62.3%) participants in the unexposed and exposed groups, respectively, were females. The mean age (±standard deviation) of the unexposed and exposed groups was 48.2 ± 8.2 and 47.8 ± 8.3 years, respectively. The COVID-19 pandemic increased the average probability of new-onset MetS by 4.4% in the overall population. According to the department, the intensive care department showed the highest CATE, with a 15.4% increase. Moreover, there was large heterogeneity according to the department. The high-CATE group was characterized by older age, urinary protein, elevated liver enzymes, higher triglyceride levels, and a history of hyperlipidemia treatment. This study demonstrated that the COVID-19 pandemic increased the incidence of new-onset MetS, with this effect showing heterogeneity at a single Japanese campus. Regarding specific populations, workers in the intensive care department showed an increased risk of new-onset MetS. At-risk populations require specific preventive interventions in case the current COVID-19 pandemic persists or a new pandemic occurs.