Estimation Of Average Treatment Effects Research Articles

Ranking of average treatment effects with generalized random forests for time-to-event outcomes.

Linkage between drug claims data and clinical outcome allows a data-driven experimental approach to drug repurposing. We develop an estimation procedure based on generalized random forests for estimation of time-point specific average treatment effects in a time-to-event setting with competing risks. To handle right-censoring, we propose a two-step procedure for estimation, applying inverse probability weighting to construct time-point specific weighted outcomes as input for the generalized random forest. The generalized random forests adaptively handle covariate effects on the treatment assignment by applying a splitting rule that targets a causal parameter. Using simulated data we demonstrate that the method is effective for a causal search through a list of treatments to be ranked according to the magnitude of their effect on clinical outcome. We illustrate the method using the Danish national health registries where it is of interest to discover drugs with an unexpected protective effect against relapse of severe depression.

PCA Rerandomization

AbstractMahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high‐dimensional cases because it balances all orthogonalized covariates equally. We propose using principal component analysis (PCA) to identify proper subspaces in which Mahalanobis distance should be calculated. Not only can PCA effectively reduce the dimensionality for high‐dimensional covariates, but it also provides computational simplicity by focusing on the top orthogonal components. The PCA rerandomization scheme has desirable theoretical properties for balancing covariates and thereby improving the estimation of average treatment effects. This conclusion is supported by numerical studies using both simulated and real examples.

Adaptive normalization for IPW estimation

Abstract Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used in both Horvitz–Thompson estimators, which normalize by the sample size, and Hájek/self-normalized estimators, which normalize by the sum of the inverse probability weights. In this work, we study a family of IPW estimators, first proposed by Trotter and Tukey in the context of Monte Carlo problems, that are normalized by an affine combination of the sample size and a sum of inverse weights. We show how selecting an estimator from this family in a data-dependent way to minimize asymptotic variance leads to an iterative procedure that converges to an estimator with connections to regression control methods. We refer to such estimators as adaptively normalized estimators. For mean estimation in survey sampling, the adaptively normalized estimator has asymptotic variance that is never worse than the Horvitz–Thompson and Hájek estimators. Going further, we show that adaptive normalization can be used to propose improvements of the augmented IPW (AIPW) estimator, average treatment effect (ATE) estimators, and policy learning objectives. Appealingly, these proposals preserve both the asymptotic efficiency of AIPW and the regret bounds for policy learning with IPW objectives, and deliver consistent finite sample improvements in simulations for all three of mean estimation, ATE estimation, and policy learning.

Robust estimation of average treatment effects from panel data

In order to evaluate the impact of a policy intervention on a group of units over time, it is important to correctly estimate the average treatment effect (ATE) measure. Due to lack of robustness of the existing procedures of estimating ATE from panel data, in this paper, we introduce a robust estimator of the ATE and the subsequent inference procedures using the popular approach of minimum density power divergence inference. Asymptotic properties of the proposed ATE estimator are derived and used to construct robust test statistics for testing parametric hypotheses related to the ATE. Besides asymptotic analyses of efficiency and power, extensive simulation studies are conducted to study the finite-sample performances of our proposed estimation and testing procedures under both pure and contaminated data. The robustness of the ATE estimator is further investigated theoretically through the influence function analyses. Finally our proposal is applied to study the long-term economic effects of the 2004 Indian Ocean earthquake and tsunami on the (per-capita) gross domestic products (GDP) of five mostly affected countries, namely Indonesia, Sri Lanka, Thailand, India and Maldives.

Preoperative anxiolytic and antidepressant medications as risk factors for increased opioid use after total knee arthroplasty: a matched retrospective cohort analysis.

Previous literature has suggested that the presence of anxiety or depression may be linked to increased postoperative pain. The objective of this retrospective analysis was to assess whether patients who use anxiolytics or antidepressants preoperatively were associated with worse acute pain outcomes after elective total knee arthroplasty (TKA). A chart review of patients who underwent TKA at our institution was conducted. The primary outcome was mean opioid use in oral morphine equivalents (OME) on the day of surgery (POD 0) through postoperative day 1 (POD1). Secondary outcomes included median pain scores during hospitalization, the need for an acute pain service (APS) consultation, and mean length of stay. Patients were matched (1 : 1) according to multiple factors including age, surgical anaesthesia type, preoperative pain scores, and placement of a single-injection adductor canal block. 83 patients were successfully matched in each group. During POD0-1, patients with anxiolytic or antidepressant prescriptions required a mean of 101.36 mg OME (SD = 66.89), compared to 86.78 mg (SD = 62.66) among patients without use of these medications ( P = 0.011) (estimate of average treatment effect of +22.86). Similarly, these patients were more likely to report a slightly higher median pain score than patients not taking anxiolytics or antidepressants (4.00 [SD 1.95] vs. 3.77 [SD 2.01], P = 0.031) (estimate of average treatment effect of +0.55). However, there were no differences in hospital length of stay, acute pain service consultation, visit to an Emergency Department within one week of discharge, and readmission within one week of discharge. There were also no differences in outcomes when comparing patients with a history of anxiety or depression to those without this history. The use of chronic anxiolytics or antidepressants was associated with increased opioid use and slightly higher pain scores in patients undergoing TKA. These associations were independent of a medical diagnosis of anxiety or depression. The mode-rate increase in perioperative opioid consumption and pain scores was not associated with an increase in APS consultations or length of stay.

Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

Trimmed Mean Group Estimation of Average Treatment Effects in Ultra Short T Panels Under Correlated Heterogeneity

Trimmed Mean Group Estimation of Average Treatment Effects in Ultra Short T Panels Under Correlated Heterogeneity

Doubly Robust Estimation of Average Treatment Effects on the Treated through Marginal Structural Models

Doubly Robust Estimation of Average Treatment Effects on the Treated through Marginal Structural Models

Robust nonparametric estimation of average treatment effects: A propensity score‐based varying coefficient approach

AbstractWe present a novel nonparametric approach for estimating average treatment effects (ATEs), addressing a fundamental challenge in causal inference research, both in theory and empirical studies. Our method offers an effective solution to mitigate the instability problem caused by propensity scores close to zero or one, which are commonly encountered in (augmented) inverse probability weighting approaches. Notably, our method is straightforward to implement and does not depend on outcome model specification. We introduce an estimator for ATE and establish its consistency and asymptotic normality through rigorous analysis. To demonstrate the robustness of our method against extreme propensity scores, we conduct an extensive simulation study. Additionally, we apply our proposed methods to estimate the impact of social activity disengagement on cognitive ability using a nationally representative cohort study. Furthermore, we extend our proposed method to estimate the ATE on the treated population.

Network A/B Testing: Nonparametric Statistical Significance Test Based on Cluster-Level Permutation

A/B testing is widely used for comparing two versions of a product and evaluating new proposed product features. It is of great importance for decision-making and has been applied as a golden standard in the IT industry. It is essentially a form of two-sample statistical hypothesis testing. Average treatment effect (ATE) and the corresponding p-value can be obtained under certain assumptions. One key assumption in traditional A/B testing is the stable-unit-treatment-value assumption (SUTVA): there is no interference among different units. It means that the observation on one unit is unaffected by the particular assignment of treatments to the other units. Nonetheless, interference is very common in social network settings where people communicate and spread information to their neighbors. Therefore, the SUTVA assumption is violated. Analysis ignoring this network effect will lead to biased estimation of ATE. Most existing works focus mainly on the design of experiment and data analysis in order to produce estimators with good performance in regards to bias and variance. Little attention has been paid to the calculation of p-value. We work on the calculation of p-value for the ATE estimator in network A/B tests. After a brief review of existing research methods on design of experiment based on graph cluster randomization and different ATE estimation methods, we propose a permutation method for calculating p-value based on permutation test at the cluster level. The effectiveness of the method against that based on individual-level permutation is validated in a simulation study mimicking realistic settings.

Large Sample Properties of Matching for Balance

Matching methods are widely used for causal inference in observational studies. Among them, nearest neighbor matching is arguably the most popular. However, nearest neighbor matching does not generally yield an average treatment effect estimator that is $\sqrt{n}$-consistent (Abadie and Imbens, 2006). Are matching methods not $\sqrt{n}$-consistent in general? In this paper, we study a recent class of matching methods that use integer programming to directly target aggregate covariate balance as opposed to finding close neighbor matches. We show that under suitable conditions these methods can yield simple estimators that are $\sqrt{n}$-consistent and asymptotically optimal.

A SuperLearner-enforced approach for the estimation of treatment effect in pediatric trials.

Randomized Clinical Trials (RCT) represent the gold standard among scientific evidence. RCTs are tailored to control selection bias and the confounding effect of baseline characteristics on the effect of treatment. However, trial conduction and enrolment procedures could be challenging, especially for rare diseases and paediatric research. In these research frameworks, the treatment effect estimation could be compromised. A potential countermeasure is to develop predictive models on the probability of the baseline disease based on previously collected observational data. Machine learning (ML) algorithms have recently become attractive in clinical research because of their flexibility and improved performance compared to standard statistical methods in developing predictive models. This manuscript proposes an ML-enforced treatment effect estimation procedure based on an ensemble SuperLearner (SL) approach, trained on historical observational data, to control the confounding effect. The REnal SCarring Urinary infEction trial served as a motivating example. Historical observational study data have been simulated through 10,000 Monte Carlo (MC) runs. Hypothetical RCTs have been also simulated, for each MC run, assuming different treatment effects of antibiotics combined with steroids. For each MC simulation, the SL tool has been applied to the simulated observational data. Furthermore, the average treatment effect (ATE), has been estimated on the trial data and adjusted for the SL predicted probability of renal scar. The simulation results revealed an increased power in ATE estimation for the SL-enforced estimation compared to the unadjusted estimates for all the algorithms composing the ensemble SL.

A Lasso approach to covariate selection and average treatment effect estimation for clustered RCTs using design-based methods

Abstract Statistical power is often a concern for clustered randomized control trials (RCTs) due to variance inflation from design effects and the high cost of adding study clusters (such as hospitals, schools, or communities). While covariate pre-specification can improve power for estimating regression-adjusted average treatment effects (ATEs), further precision gains can be achieved through covariate selection once primary outcomes have been collected. This article uses design-based methods underlying clustered RCTs to develop Lasso methods for the post-hoc selection of covariates for ATE estimation that avoids a lack of transparency and model overfitting. Our focus is on two-stage estimators: in the first stage, Lasso estimation is conducted using data on cluster-level averages or sums, and in the second stage, standard ATE estimators are adjusted for covariates using the first-stage Lasso results. We discuss l 1 {l}_{1} consistency of the estimated Lasso coefficients, asymptotic normality of the ATE estimators, and design-based variance estimation. The nonparametric approach applies to continuous, binary, and discrete outcomes. We present simulation results and demonstrate the method using data from a federally funded clustered RCT testing the effects of school-based programs promoting behavioral health.

Hierarchical Bayesian bootstrap for heterogeneous treatment effect estimation.

A major focus of causal inference is the estimation of heterogeneous average treatment effects (HTE) - average treatment effects within strata of another variable of interest such as levels of a biomarker, education, or age strata. Inference involves estimating a stratum-specific regression and integrating it over the distribution of confounders in that stratum - which itself must be estimated. Standard practice involves estimating these stratum-specific confounder distributions independently (e.g. via the empirical distribution or Rubin's Bayesian bootstrap), which becomes problematic for sparsely populated strata with few observed confounder vectors. In this paper, we develop a nonparametric hierarchical Bayesian bootstrap (HBB) prior over the stratum-specific confounder distributions for HTE estimation. The HBB partially pools the stratum-specific distributions, thereby allowing principled borrowing of confounder information across strata when sparsity is a concern. We show that posterior inference under the HBB can yield efficiency gains over standard marginalization approaches while avoiding strong parametric assumptions about the confounder distribution. We use our approach to estimate the adverse event risk of proton versus photon chemoradiotherapy across various cancer types.

Estimation of average treatment effect based on a multi-index propensity score

BackgroundEstimating the average effect of a treatment, exposure, or intervention on health outcomes is a primary aim of many medical studies. However, unbalanced covariates between groups can lead to confounding bias when using observational data to estimate the average treatment effect (ATE). In this study, we proposed an estimator to correct confounding bias and provide multiple protection for estimation consistency.MethodsWith reference to the kernel function-based double-index propensity score (Ker.DiPS) estimator, we proposed the artificial neural network-based multi-index propensity score (ANN.MiPS) estimator. The ANN.MiPS estimator employed the artificial neural network to estimate the MiPS that combines the information from multiple candidate models for propensity score and outcome regression. A Monte Carlo simulation study was designed to evaluate the performance of the proposed ANN.MiPS estimator. Furthermore, we applied our estimator to real data to discuss its practicability.ResultsThe simulation study showed the bias of the ANN.MiPS estimators is very small and the standard error is similar if any one of the candidate models is correctly specified under all evaluated sample sizes, treatment rates, and covariate types. Compared to the kernel function-based estimator, the ANN.MiPS estimator usually yields smaller standard error when the correct model is incorporated in the estimator. The empirical study indicated the point estimation for ATE and its bootstrap standard error of the ANN.MiPS estimator is stable under different model specifications.ConclusionsThe proposed estimator extended the combination of information from two models to multiple models and achieved multiply robust estimation for ATE. Extra efficiency was gained by our estimator compared to the kernel-based estimator. The proposed estimator provided a novel approach for estimating the causal effects in observational studies.

Appropriately estimating the standardized average treatment effect with missing data: A simulation and primer.

Reporting standardized effects in randomized treatment studies aids interpretation and facilitates future meta-analyses and policy considerations. However, when outcome data are missing, achieving an unbiased, accurate estimate of the standardized average treatment effect, sATE, can pose challenges even for those with general knowledge of missing data handling, given that the sATE is a ratio of a mean difference to a (within-group) standard deviation. Under both homogeneity and heterogeneity of variance, a Monte Carlo simulation study was conducted to compare missing data handling strategies in terms of bias and accuracy in the sATE, under specific missingness patterns plausible for randomized pretest posttest studies. Within two broad missing data handling approaches, maximum likelihood and multiple imputation, modeling choices were thoroughly investigated including the analysis model, variance estimator, imputation algorithm, and method of pooling results across imputed datasets. Results demonstrated that although the sATE can be estimated with little bias using either maximum likelihood or multiple imputation, particular attention should be paid to the model and variance estimator, especially at smaller sample sizes (i.e., N = 50). Differences in accuracy were driven by differences in bias. To improve estimation of the sATE in practice, recommendations and a software demonstration are provided. Moreover, a pedagogical explanation of the causes of bias, described separately for the numerator and denominator of the sATE is provided, demonstrating visually how and why bias occurs with certain methods.

High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates

Regression adjustment is often used to estimate average treatment effect (ATE) in randomized experiments. Recently, some penalty-based regression adjustment methods have been proposed to handle the high-dimensional problem. However, these existing high-dimensional regression adjustment methods may fail to achieve satisfactory performance when the covariates are highly correlated. In this paper, we propose a novel adjustment estimation method for ATE by combining the semi-standard partial covariance (SPAC) and regression adjustment methods. Under some regularity conditions, the asymptotic normality of our proposed SPAC adjustment ATE estimator is shown. Some simulation studies and an analysis of HER2 breast cancer data are carried out to illustrate the advantage of our proposed SPAC adjustment method in addressing the highly correlated problem of the Rubin causal model.

Joint Deep Learning for Covariate Decomposition and Treatment Effect Estimation

This study proposes a joint deep learning method, namely, confounding factor joint decomposition under counterfactual regression (CFJD-CFR), to identify a minimum adjustment covariate set and estimate the average treatment effect (ATE). CFJD-CFR includes two levels: feature learning and prediction model. Feature learning constructs the objective function based on clear variable attribute recognition criteria to identify and decompose a covariate set of different attributes into four disjoint sets of factors: instrumental, confounding, predicting, and noise variables. The output of feature learning is then introduced into the prediction model as its input to build a joint deep learning model and reduce the systematic errors caused by step-by-step learning. The proposed method combines deep representation learning, feature selection, and prediction under the structural equation modeling framework. Simulation studies show that CFJD-CFR can effectively identify the minimum adjustment covariate set and consistently outperform other methods for ATE estimation. The proposed method is applied to the Chinese General Social Survey study. New insights into the difference in social welfare policy preference between urban and rural residents in China are obtained.

EE147 Estimating the Causal Effect of Early Use of Erythropoietic Stimulating Agents in Intermediate-1 to Low-Risk MDS Patients: An Application of the Longitudinal Targeted Maximum Likelihood Estimation

To demonstrate the use of Longitudinal Targeted Maximum Likelihood Estimation (LTMLE) methods to derive causal average treatment effect estimates for survival and health-related quality of life (measured by the EQ5D) outcomes from longitudinal real-world data with risk of bias from immortal-time and time-varying confounding.

The effect of Vitamins C and E on clinical outcomes of patients with severe traumatic brain injury: A propensity score matching study.

The aim of this study was to assess the effect of Vitamins C and E on mortality, intensive care unit (ICU) length of stay, and Glasgow Outcome Scale-Extended (GOS-E) score of traumatic brain injury (TBI) patients. Using data from records of patients in a retrospective cohort study, we included 1321 TBI patients, 269 treated and 1052 untreated, aged over 18 years with information on exposure (i.e., Vitamins C and E) and confounders. Age, Glasgow Coma Scale, pupil status, Rotterdam classification, blood sugar, blood pressure, international normalized ratio, and comorbidity of patients were considered as the confounding factors. Endpoints were GOS-E on follow-up, mortality, and ICU length of stay. Propensity score matching was performed to adjust the confounders. Based on the average treatment effect estimates, the use of Vitamins C and E reduced the risk of mortality (risk difference [RD]: -0.07; 95% confidence interval [CI]: -0.14--0.003) and reduced the length of ICU stay (RD -1.77 95% CI:-3.71-0.16). Furthermore, our results showed that GOS-E was improved significantly (RD: 0.09, 95% CI : 0.03-0.16). Our study suggests that using Vitamins C and E could decrease mortality and length of ICU stay and improve the GOS-E score and functions of the patients with severe TBI. As they are safe and inexpensive medications, they can be used in routine practice in ICUs to improve the outcomes of TBI patients.