Functional data analysis is an important area in modern statistics and has been successfully applied in many fields. Although many scientific studies aim to find causations, a predominant majority of functional data analysis approaches can only reveal correlations. In this paper, average treatment effect estimation is studied for observational data with functional covariates. This paper generalizes various state-of-art propensity score estimation methods for multivariate data to functional data. The resulting average treatment effect estimators via propensity score weighting are numerically evaluated by a simulation study and applied to a real-world dataset to study the causal effect of duloxitine on the pain relief of chronic knee osteoarthritis patients.
We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually or cluster randomized trials. In this manuscript, we study the properties of this estimator and develop a new estimator that utilizes both covariate adjustment and inverse probability weighting We support our theoretical results with a simulation study and an application in an infectious disease setting. The covariate-adjusted residuals estimator is an effic…
To improve precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes, researchers and regulatory agencies recommend using g-computation as a reliable method of covariate adjustment. However, the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest. To fill this gap, we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that t…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The effect of a functional variable on an outcome is an essential theme in functional data analysis, but a majority of related studies are restricted to correlational effects rather than causal effects. This paper makes the first attempt to study the causal effect of a functional variable as a treatment in observational studies. Despite the lack of a probability dens…
To maximize clinical benefit, clinicians routinely tailor treatment to the individual characteristics of each patient, where individualized treatment rules are needed and are of significant research interest to statisticians. In the covariate-adjusted randomization clinical trial with many covariates, we model the treatment effect with an unspecified function of a single index of the covariates and leave the baseline response completely arbitrary. We devise a class of estimators to consistently estimate the treatment effect function and its associated index while bypassing the estimation of th…
With a large number of baseline covariates, we propose a new semi-parametric modeling strategy for heterogeneous treatment effect estimation and individualized treatment selection, which are two major goals in personalized medicine. We achieve the first goal through estimating a covariate-specific treatment effect (CSTE) curve modeled as an unknown function of a weighted linear combination of all baseline covariates. The weight or the coefficient for each covariate is estimated by fitting a sparse semi-parametric logistic single-index coefficient model. The CSTE curve is estimated by a spline-…
Individual participant data (IPD) meta-analyses of randomised trials are considered a reliable way to assess participant-level treatment effect modifiers but may not make the best use of the available data. Traditionally, effect modifiers are explored one covariate at a time, which gives rise to the possibility that evidence of treatment-covariate interaction may be due to confounding from a different, related covariate. We aimed to evaluate current practice when estimating treatment-covariate interactions in IPD meta-analysis, specifically focusing on involvement of additional covariates in t…
Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morga…
Covariate-adaptive randomization schemes such as the minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theoretical developments on inference after covariate-adaptive randomization are mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate levels utilized in randomization and a further adjusting for covariates not used in randomization, in this ar…
Bias Mitigation in Matched Observational Studies with Continuous Treatments: Calipered Non-Bipartite Matching and Bias-Corrected Estimation and Inference
Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of…
A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the data prior to analysis. Existing design methods, developed for traditional observational studies with single designers, can yield unsatisfactory designs with suboptimum covariate balance for Big Observational Data due to their inability to accommodate the massive dimensionality, heterogeneity, and volume of the Big Data. We propose a new framework for the distributed design of Big Observational Data amongst collaborative …
Selection of covariates is crucial in the estimation of average treatment effects given observational data with high or even ultra-high dimensional pretreatment variables. Existing methods for this problem typically assume sparse linear models for both outcome and univariate treatment, and cannot handle situations with ultra-high dimensional covariates. In this paper, we propose a new covariate selection strategy called double screening prior adaptive lasso (DSPAL) to select confounders and predictors of the outcome for multivariate treatments, which combines the adaptive lasso method with the…
Randomized controlled trials are the gold standard for measuring causal effects. However, they are often not always feasible, and causal treatment effects must be estimated from observational data. Observational studies do not allow robust conclusions about causal relationships unless statistical techniques account for the imbalance of pretreatment confounders across groups while key assumptions hold. Propensity score and balance weighting (PSBW) are useful techniques that aim to reduce the imbalances between treatment groups by weighting the groups to look alike on the observed confounders. T…
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity sampling weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment an…
Covariate-specific treatment effects (CSTEs) represent heterogeneous treatment effects across subpopulations defined by certain selected covariates. In this article, we consider marginal structural models where CSTEs are linearly represented using a set of basis functions of the selected covariates. We develop a new approach in high-dimensional settings to obtain not only doubly robust point estimators of CSTEs, but also model-assisted confidence intervals, which are valid when a propensity score model is correctly specified but an outcome regression model may be misspecified. With a linear ou…
Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying lin…
A common concern in observational studies focuses on properly evaluating the causal effect, which usually refers to the average treatment effect or the average treatment effect on the treated. In this paper, we propose a data preprocessing method, the Kernel-distance-based covariate balancing, for observational studies with binary treatments. This proposed method yields a set of unit weights for the treatment and control groups, respectively, such that the reweighted covariate distributions can satisfy a set of pre-specified balance conditions. This preprocessing methodology can effectively re…
In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, a variety of methods based on the potential outcomes framework are used to estimate average treatment effects. One of the key assumptions is treatment positivity, which states that the probability of treatment is bounded away from zero and one for any possible combi…
We consider the problem of identifying sub-groups of participants in a clinical trial that have enhanced treatment effect. Recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such sub-group identification. The most commonly used recursive partitioning method, the classification and regression tree algorithm, first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all subtrees of the large tree. In the…
In sequential experiments, subjects become available for the study over a period of time, and covariates are often measured at the time of arrival. We consider the setting where the sample size is fixed but covariate values are unknown until subjects enrol. Given a model for the outcome, a sequential optimal design approach can be used to allocate treatments to minimize the variance of the treatment effect. We extend existing optimal design methodology so it can be used within a nonmyopic framework, where treatment allocation for the current subject depends not only on the treatments and covar…
The statistical tests that are commonly used for detecting mean or median treatment effects suffer from low power when the two distribution functions differ only in the upper (or lower) tail, as in the assessment of the Total Sharp Score (TSS) under different treatments for rheumatoid arthritis. In this article, we propose a more powerful test that detects treatment effects through the expected shortfalls. We show how the expected shortfall can be adjusted for covariates, and demonstrate that the proposed test can achieve a substantial sample size reduction over the conventional tests on the m…
In this paper, we study the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the in…
The first step towards investigating the effectiveness of a treatment via a randomized trial is to split the population into control and treatment groups then compare the average response of the treatment group receiving the treatment to the control group receiving the placebo. In order to ensure that the difference between the two groups is caused only by the treatment, it is crucial that the control and the treatment groups have similar statistics. Indeed, the validity and reliability of a trial are determined by the similarity of two groups' statistics. Covariate balancing methods increase …
Inferring the causal effect of a treatment on an outcome in an observational study requires adjusting for observed baseline confounders to avoid bias. However, adjusting for all observed baseline covariates, when only a subset are confounders of the effect of interest, is known to yield potentially inefficient and unstable estimators of the treatment effect. Furthermore, it raises the risk of finite-sample bias and bias due to model misspecification. For these stated reasons, confounder (or covariate) selection is commonly used to determine a subset of the available covariates that is sufficie…
In studies based on electronic health records (EHR), the frequency of covariate monitoring can vary by covariate type, across patients, and over time. This can lead to major challenges: first, the difference in monitoring protocols may invalidate the extrapolation of study results obtained in one population to the other, and second, monitoring can act as a time-varying confounder of the causal effect of a time-varying treatment on the outcomes of interest. This paper demonstrates how to account for non-systematic covariate monitoring when evaluating dynamic treatment interventions, and how to …
We address estimation of intervention effects in experimental designs in which (a) interventions are assigned at the cluster level; (b) clusters are selected to form pairs, matched on observed characteristics; and (c) intervention is assigned to one cluster at random within each pair. One goal of policy interest is to estimate the average outcome if all clusters in all pairs are assigned control versus if all clusters in all pairs are assigned to intervention. In such designs, inference that ignores individual level covariates can be imprecise because cluster-level assignment can leave substan…
Randomized clinical trials (RCTs) are ideal for estimating causal effects, because the distributions of background covariates are similar in expectation across treatment groups. When estimating causal effects using observational data, matching is a commonly used method to replicate the covariate balance achieved in a RCT. Matching algorithms have a rich history dating back to the mid-1900s, but have been used mostly to estimate causal effects between two treatment groups. When there are more than two treatments, estimating causal effects requires additional assumptions and techniques. We propo…
A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only a…
In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome not through the mediator. The standard regression approach to mediation analysis assumes sequential ignorability of the mediator, that is that the mediator is effectively randomly assigned given baseline covariates and the randomized treatment. Since the experiment does not randomize the mediator, sequential ignorability is often not plausi…
Statistical power is often a concern for clustered 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 is the preferred approach for improving power to estimate 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 a Lasso-OLS hybrid procedure for the post-hoc selection of covariates and AT…
Fisher's randomization test (FRT) delivers exact $p$-values under the strong null hypothesis of no treatment effect on any units whatsoever and allows for flexible covariate adjustment to improve the power. Of interest is whether the procedure could also be valid for testing the weak null hypothesis of zero average treatment effect. Towards this end, we evaluate two general strategies for FRT with covariate-adjusted test statistics: that based on the residuals from an outcome model with only the covariates, and that based on the output from an outcome model with both the treatment and the cova…
Covariate adjustment has the potential to increase power in the analysis of randomised trials, but mis-specification of the adjustment model could cause error. We explore what error is possible when the adjustment model omits a covariate by randomised treatment interaction, in a setting where the covariate is perfectly balanced between randomised treatments. We use mathematical arguments and analyses of single hypothetical data sets. We show that analysis by a generalised linear model with the canonical link function leads to no error under the null -- that is, if treatment effect is truly zer…
Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The unadjusted difference in means is always unbiased. The complete-covariate analysis adjusts for all completely observed covariate…
The primary goal of randomized trials is to compare the effects of different interventions on some outcome of interest. In addition to the treatment assignment and outcome, data on baseline covariates, such as demographic characteristics or biomarker measurements, are typically collected. Incorporating such auxiliary covariates in the analysis of randomized trials can increase power, but questions remain about how to preserve type I error when incorporating such covariates in a flexible way, particularly when the number of randomized units is small. Using the Young Citizens study, a cluster-ra…
Difference-in-Differences for Heterogeneous Effects of General Treatment Strategies Accounting for Time-Varying Covariates
Ghent University（根特大学）；Harvard T. H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；University of Washington（华盛顿大学）；CUNY Graduate School of Public Health and Health Policy（纽约市立大学研究生公共健康与卫生政策学院）
Semi-parametric methods are often used for the estimation of intervention effects on correlated outcomes in cluster-randomized trials (CRTs). When outcomes are missing at random (MAR), Inverse Probability Weighted (IPW) methods incorporating baseline covariates can be used to deal with informative missingness. Also, augmented generalized estimating equations (AUG) correct for imbalance in baseline covariates but need to be extended for MAR outcomes. However, in the presence of interactions between treatment and baseline covariates, neither method alone produces consistent estimates for the mar…
Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustme…
Bias in causal comparisons has a direct correspondence with distributional imbalance of covariates between treatment groups. Weighting strategies such as inverse propensity score weighting attempt to mitigate bias by either modeling the treatment assignment mechanism or balancing specified covariate moments. This paper introduces a new weighting method, called energy balancing, which instead aims to balance weighted covariate distributions. By directly targeting distributional imbalance, the proposed weighting strategy can be flexibly utilized in a wide variety of causal analyses, including th…
This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by making the underlying covariate distribution of different treatment groups as close to each other as possible. Our estimators are data-driven, do not rely on tuning parameters such as bandwidths, admit an asymptotic linear representation, and can be used to estimate different treatment effect parameters under different identifying assumptions, including unconfo…
