Consider estimation of average treatment effects with multi-valued treatments using augmented inverse probability weighted (IPW) estimators, depending on outcome regression and propensity score models in high-dimensional settings. These regression models are often fitted by regularized likelihood-based estimation, while ignoring how the fitted functions are used in the subsequent inference about the treatment parameters. Such separate estimation can be associated with known difficulties in existing methods. We develop regularized calibrated estimation for fitting propensity score and outcome regression models, where sparsity-including penalties are employed to facilitate variable selection but the loss functions are carefully chosen such that valid confidence intervals can be obtained under possible model misspecification. Unlike in the case of binary treatments, the usual augmented IPW estimator is generalized by allowing different copies of coefficient estimators in outcome regression to ensure just-identification. For propensity score estimation, the new loss function and estimating functions are directly tied to achieving covariate balance between weighted treatment groups. We develop practical numerical algorithms for computing the regularized calibrated estimators with group Lasso by innovatively exploiting Fisher scoring, and provide rigorous high-dimensional analysis for the resulting augmented IPW estimators under suitable sparsity conditions, while tackling technical issues absent or overlooked in previous analyses. We present simulation studies and an empirical application to estimate the effects of maternal smoking on birth weights. The proposed methods are implemented in the R package mRCAL.
In randomized experiments, the actual treatments received by some experimental units may differ from their treatment assignments. This non-compliance issue often occurs in clinical trials, social experiments, and the applications of randomized experiments in many other fields. Under certain assumptions, the average treatment effect for the compliers is identifiable and equal to the ratio of the intention-to-treat effects of the potential outcomes to that of the potential treatment received. To improve the estimation efficiency, we propose three model-assisted estimators for the complier averag…
In paired randomized experiments individuals in a given matched pair may differ on prognostically important covariates despite the best efforts of practitioners. We examine the use of regression adjustment as a way to correct for persistent covariate imbalances after randomization, and present two regression assisted estimators for the sample average treatment effect in paired experiments. Using the potential outcomes framework, we prove that these estimators are consistent for the sample average treatment effect under mild regularity conditions even if the regression model is improperly speci…
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…
Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions, recently derived by Dorn, Guo, and Kallus. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly robust point estimators for the relaxed population bounds with respect to misspecificatio…
There is currently a dearth of appropriate methods to estimate the causal effects of multiple treatments when the outcome is binary. For such settings, we propose the use of nonparametric Bayesian modeling, Bayesian Additive Regression Trees (BART). We conduct an extensive simulation study to compare BART to several existing, propensity score-based methods and to identify its operating characteristics when estimating average treatment effects on the treated. BART consistently demonstrates low bias and mean-squared errors. We illustrate the use of BART through a comparative effectiveness analys…
Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation, which involves Lasso …
We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi-/non-parametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural functions that are non-additively separable, with flexible functional forms and heteroskedasticy in the residuals, and it also en…
Most causal inference methods consider counterfactual variables under interventions that set the treatment deterministically. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Furthermore, violations to the positivity assumption, necessary for identification, are exacerbated with continuous and multi-valued treatments and deterministic interventions. In this paper we propose longitudinal modified treatment policies (LMTPs) as a non-parametric alternat…
Policy evaluation studies, which intend to assess the effect of an intervention, face some statistical challenges: in real-world settings treatments are not randomly assigned and the analysis might be further complicated by the presence of interference between units. Researchers have started to develop novel methods that allow to manage spillover mechanisms in observational studies; recent works focus primarily on binary treatments. However, many policy evaluation studies deal with more complex interventions. For instance, in political science, evaluating the impact of policies implemented by …
We consider the problem of how to assign treatment in a randomized experiment, in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes. Then we leverage these models to develop restricted randomization strategies for allocating treatment optimally, by minimizing the mean square error of the estimated average treatment effect. Analytical decompositions of the mean square error, due both to the model and to the ran…
Cluster-randomized experiments are widely used due to their logistical convenience and policy relevance. To analyze them properly, we must address the fact that the treatment is assigned at the cluster level instead of the individual level. Standard analytic strategies are regressions based on individual data, cluster averages, and cluster totals, which differ when the cluster sizes vary. These methods are often motivated by models with strong and unverifiable assumptions, and the choice among them can be subjective. Without any outcome modeling assumption, we evaluate these regression estimat…
Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building and fitting iteratively can be difficult to implement, depending on ad hoc choices of what variables are included. In addition, uncertainty from the iterative process of model selection is complicated and often ignored in subsequent inference about treatment effects. We develop new methods and theory to obtain not only doubly robust point estimators for avera…
This paper estimates individual treatment effects in a triangular model with binary--valued endogenous treatments. Following the identification strategy established in Vuong and Xu (2014), we propose a two--stage estimation approach. First, we estimate the counterfactual outcome and hence the individual treatment effect (ITE) for every observational unit in the sample. Second, we estimate the density of individual treatment effects in the population. Our estimation method does not suffer from the ill--posed inverse problem associated with inverting a non--linear functional. Asymptotic properti…
The preponderance of large-scale healthcare databases provide abundant opportunities for comparative effectiveness research. Evidence necessary to making informed treatment decisions often relies on comparing effectiveness of multiple treatment options on outcomes of interest observed in a small number of individuals. Causal inference with multiple treatments and rare outcomes is a subject that has been treated sparingly in the literature. This paper designs three sets of simulations, representative of the structure of our healthcare database study, and propose causal analysis strategies for s…
In this paper, we present a new way of matching in observational studies that overcomes three limitations of existing matching approaches. First, it directly balances covariates with multi-valued treatments without requiring the generalized propensity score. Second, it builds self-weighted matched samples that are representative of a target population by design. Third, it can handle large data sets, with hundreds of thousands of observations, in a couple of minutes. The key insights of this new approach to matching are balancing the treatment groups relative to a target population and positing…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by subtracting a minimax linear estimate of its error. We show that our method is semiparametrically efficient under weak conditions…
Principal Stratification with Bayesian Additive Regression Trees for Count-Valued Intermediate Variables: Estimating the Effect of Fertility on Women's Employment
University of Oxford（牛津大学）；ETH Zurich（苏黎世联邦理工学院）；Technion – Israel Institute of Technology（以色列理工学院）
Estimating the effects of continuous-valued interventions from observational data is a critically important task for climate science, healthcare, and economics. Recent work focuses on designing neural network architectures and regularization functions to allow for scalable estimation of average and individual-level dose-response curves from high-dimensional, large-sample data. Such methodologies assume ignorability (observation of all confounding variables) and positivity (observation of all treatment levels for every covariate value describing a set of units), assumptions problematic in the c…
There is growing interest in developing causal inference methods for multi-valued treatments with a focus on pairwise average treatment effects. Here we focus on a clinically important, yet less-studied estimand: causal drug-drug interactions (DDIs), which quantifies the degree to which the causal effect of drug A is altered by the presence versus the absence of drug B. Confounding adjustment when studying the effects of DDIs can be accomplished via inverse probability of treatment weighting (IPTW), a standard approach originally developed for binary treatments and later generalized to multi-v…
Inference of Sample Complier Average Causal Effects under Experiments with Completely Randomized Design and Computer Assisted Balance-Improving Designs
This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep tail characteristics: the extreme quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then we define the extreme quantile treatment effect (EQTE) and the extreme average treatment effect (EATE), which can be identified through the commonly adopted unconfoundedness condition and estimated with the aid of extrem…
MEC-Cox: Machine-Learning-Assisted Generalized Entropy Calibration for ATT Marginal Hazard-Ratio Estimation
Department of Statistics, Texas A&M University（统计学系，德克萨斯A&M大学）；Department of Mathematics, Korea Military Academy（数学系，韩国军事学院）；Department of Statistics, Iowa State University（统计学系，爱荷华州立大学）
North Carolina State University（北卡罗来纳州立大学）；University of Waterloo（滑铁卢大学）
Dynamic treatment regimes operationalize the clinical decision process as a sequence of functions, one for each clinical decision, where each function takes as input up-to-date patient information and gives as output a single recommended treatment. Current methods for estimating optimal dynamic treatment regimes, for example Q-learning, require the specification of a single outcome by which the `goodness' of competing dynamic treatment regimes are measured. However, this is an over-simplification of the goal of clinical decision making, which aims to balance several potentially competing outco…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenge…
M$^3$TN: Multi-gate Mixture-of-Experts based Multi-valued Treatment Network for Uplift Modeling
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；Beijing Key Laboratory of Big Data Management and Analysis Methods（北京大数据管理与分析方法重点实验室）
We propose the use of non-parametric, graph-based tests to assess the distributional balance of covariates in observational studies with multi-valued treatments. Our tests utilize graph structures ranging from Hamiltonian paths that connect all of the data to nearest neighbor graphs that maximally separates data into pairs. We consider algorithms that form minimal distance graphs, such as optimal Hamiltonian paths or non-bipartite matching, or approximate alternatives, such as greedy Hamiltonian paths or greedy nearest neighbor graphs. Extensive simulation studies demonstrate that the proposed…
