We propose a sensitivity analysis for Synthetic Control (SC) treatment effect estimates to interrogate the assumption that the SC method is well-specified, namely that choosing weights to minimize pre-treatment prediction error yields accurate predictions of counterfactual post-treatment outcomes. Our data-driven procedure recovers the set of treatment effects consistent with the assumption that the misspecification error incurred by the SC method is at most the observable misspecification error incurred when using the SC estimator to predict the outcomes of some control unit. We show that under one definition of misspecification error, our procedure provides a simple, geometric motivation for comparing the estimated treatment effect to the distribution of placebo residuals to assess estimate credibility. When we apply our procedure to several canonical studies that report SC estimates, we broadly confirm the conclusions drawn by the source papers.
The synthetic control (SC) method is a popular approach for estimating treatment effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear combination of the untreated units. This linearity assumption, however, can be unlikely to hold in practice and, when violated, the resulting SC estimates are incorrect. In this paper we examine two questions: (1) How large can the misspecification error be? (2) How can we limit it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspe…
Sibling fixed effects (FE) models are useful for estimating causal treatment effects while offsetting unobserved sibling-invariant confounding. However, treatment estimates are biased if an individual's outcome affects their sibling's outcome. We propose a robustness test for assessing the presence of outcome-to-outcome interference in linear two-sibling FE models. We regress a gain-score--the difference between siblings' continuous outcomes--on both siblings' treatments and on a pre-treatment observed FE. Under certain restrictions, the observed FE's partial regression coefficient signals the…
The presence of confounding by high-dimensional variables complicates estimation of the average effect of a point treatment. On the one hand, it necessitates the use of variable selection strategies or more general data-adaptive high-dimensional statistical methods. On the other hand, the use of such techniques tends to result in biased estimators with a non-standard asymptotic behaviour. Double-robust estimators are vital for offering a resolution because they possess a so-called small bias property (Newey et al., 2004). This means that their bias vanishes faster than the bias in the nuisance…
Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment-free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estima…
Propensity score (PS) weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting (IPW), assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for IPW estimation is the positivity assumption, i.e., the PS must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the PS distributions betw…
Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability weighted estimators or extensions to estimate treatment effects. However, a challenging issue is that such inverse probability weighting methods including doubly robust methods can perform poorly even when the logistic model appears adequate as examined by conventional techniques. In addition, there is increasing difficulty to appropriately estimate propens…
Identifying heterogeneous treatment effects (HTEs) in randomized controlled trials is an important step toward understanding and acting on trial results. However, HTEs are often small and difficult to identify, and HTE modeling methods which are very general can suffer from low power. We present a method that exploits any existing relationship between illness severity and treatment effect, and identifies the "sweet spot", the contiguous range of illness severity where the estimated treatment benefit is maximized. We further compute a bias-corrected estimate of the conditional average treatment…
Inferring the heterogeneous treatment effect is a fundamental problem in the sciences and commercial applications. In this paper, we focus on estimating Conditional Average Treatment Effect (CATE), that is, the difference in the conditional mean outcome between treatments given covariates. Traditionally, Q-Learning based approaches rely on the estimation of conditional mean outcome given treatment and covariates. However, they are subject to misspecification of the main effect model. Recently, simple and flexible one-step methods to directly learn (D-Learning) the CATE without model specificat…
The average treatment effect (ATE) is popularly used to assess the treatment effect. However, the ATE implicitly assumes a homogenous treatment effect even amongst individuals with different characteristics. In this paper, we mainly focus on assessing the treatment effect heterogeneity, which has important implications in designing the optimal individual treatment regimens and in policy making. The treatment benefit rate (TBR) and treatment harm rate (THR) have been defined to characterize the magnitude of heterogeneity for binary outcomes. When the outcomes are continuous, we extend the defin…
The micro-randomized trial (MRT) is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health (mHealth) intervention components that may be delivered at hundreds or thousands of decision points. MRTs have motivated a new class of causal estimands, termed "causal excursion effects", for which semiparametric inference can be conducted via a weighted, centered least squares criterion (Boruvka et al., 2018). Existing methods assume between-subject independence and non-interference. Deviations from these assumptions often occur. In this paper, causal exc…
A growing number of methods aim to assess the challenging question of treatment effect variation in observational studies. This special section of "Observational Studies" reports the results of a workshop conducted at the 2018 Atlantic Causal Inference Conference designed to understand the similarities and differences across these methods. We invited eight groups of researchers to analyze a synthetic observational data set that was generated using a recent large-scale randomized trial in education. Overall, participants employed a diverse set of methods, ranging from matching and flexible outc…
This paper constructs a doubly robust estimator for continuous dose-response estimation. An outcome regression model is augmented with a set of inverse generalized propensity score covariates to correct for potential misspecification bias. From the augmented model we can obtain consistent estimates of mean average potential outcomes for distinct strata of the treatment. A polynomial regression is then fitted to these point estimates to derive a Taylor approximation to the continuous dose-response function. The bootstrap is used for variance estimation. Analytical results and simulations show t…
In this paper, we apply doubly robust approach to estimate, when some covariates are given, the conditional average treatment effect under parametric, semiparametric and nonparametric structure of the nuisance propensity score and outcome regression models. We then conduct a systematic study on the asymptotic distributions of nine estimators with different combinations of estimated propensity score and outcome regressions. The study covers the asymptotic properties with all models correctly specified; with either propensity score or outcome regressions locally / globally misspecified; and with…
In this commentary, we highlight the importance of: (1) carefully considering and clarifying whether a marginal or conditional treatment effect is of interest in a population-adjusted indirect treatment comparison; and (2) developing distinct methodologies for estimating the different measures of effect. The appropriateness of each methodology depends on the preferred target of inference.
Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve, and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via simulation and in a study of the effect …
Causal mediation analysis aims at disentangling a treatment effect into an indirect mechanism operating through an intermediate outcome or mediator, as well as the direct effect of the treatment on the outcome of interest. However, the evaluation of direct and indirect effects is frequently complicated by non-ignorable selection into the treatment and/or mediator, even after controlling for observables, as well as sample selection/outcome attrition. We propose a method for bounding direct and indirect effects in the presence of such complications using a method that is based on a sequence of l…
Treatment effect heterogeneity occurs when individual characteristics influence the effect of a treatment. We propose a novel approach that combines prognostic score matching and conditional inference trees to characterize effect heterogeneity of a randomized binary treatment. One key feature that distinguishes our method from alternative approaches is that it controls the Type I error rate, i.e., the probability of identifying effect heterogeneity if none exists and retains the underlying subgroups. This feature makes our technique particularly appealing in the context of clinical trials, whe…
Propensity score matching has been a long-standing tradition for handling confounding in causal inference, however requiring stringent model assumptions. In this article, we propose double score matching(DSM) for general causal estimands utilizing two balancing scores including the propensity score and prognostic score. To gain the protection of possible model misspecification, we posit multiple candidate models for each score. We show that the de-biasing DSM estimator achieves the multiple robustness property in that it is consistent for the true causal estimand if any model of the propensity…
In mobile health interventions aimed at behavior change and maintenance, treatments are provided in real time to manage current or impending high risk situations or promote healthy behaviors in near real time. Currently there is great scientific interest in developing data analysis approaches to guide the development of mobile interventions. In particular data from mobile health studies might be used to examine effect moderators-i.e., individual characteristics, time-varying context or past treatment response that moderate the effect of current treatment on a subsequent response. This paper in…
A Framework for Parametric Time-Varying Treatment Effects in Multiple Intervention Stepped Wedge Design Clinical Trials in the Presence of Non-Uniform Cluster-Period Correlation Structures
The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；UTHealth Houston School of Public Health, The University of Texas Health Science Center at Houston（休斯顿德克萨斯大学健康科学中心休斯顿公共卫生学院）
There is a large literature on semiparametric estimation of average treatment effects under unconfounded treatment assignment in settings with a fixed number of covariates. More recently attention has focused on settings with a large number of covariates. In this paper we extend lessons from the earlier literature to this new setting. We propose that in addition to reporting point estimates and standard errors, researchers report results from a number of supplementary analyses to assist in assessing the credibility of their estimates.
One size fits all approaches to medicine have become a thing of the past as the understanding of individual differences grows. The paper introduces a test for the presence of heterogeneity in treatment effects in a clinical trial. Heterogeneity is assessed on the basis of the predicted individual treatment effects (PITE) framework and a permutation test is utilized to establish if significant heterogeneity is present. We first use the novel test to show that heterogeneity in the effects of interventions exists in the Amyotrophic Lateral Sclerosis Clinical Trials. We then show, using two differ…
Exposure mappings are widely used to model potential outcomes in the presence of interference, where each unit's outcome may depend not only on its own treatment, but also on the treatment of other units as well. However, in practice these models may be only a crude proxy for social dynamics. In this work, we give estimands and estimators that are robust to the misspecification of an exposure model. In the first part, we require the treatment effect to be nonnegative (or "monotone") in both direct effects and spillovers. In the second part, we consider a weaker estimand ("contrasts attributabl…
Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel O…
When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. To avoid such bias, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of treatment and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, s…
We consider evaluating the causal effects of dynamic treatments, i.e. of multiple treatment sequences in various periods, based on double machine learning to control for observed, time-varying covariates in a data-driven way under a selection-on-observables assumption. To this end, we make use of so-called Neyman-orthogonal score functions, which imply the robustness of treatment effect estimation to moderate (local) misspecifications of the dynamic outcome and treatment models. This robustness property permits approximating outcome and treatment models by double machine learning even under hi…
The treatment effects of medications play a key role in guiding medical prescriptions. They are usually assessed with randomized controlled trials (RCTs), which are expensive. Recently, large-scale electronic health records (EHRs) have become available, opening up new opportunities for more cost-effective assessments. However, assessing a treatment effect from EHRs is challenging: it is biased by unobserved confounders, unmeasured variables that affect both patients' medical prescription and their outcome, e.g. the patients' social economic status. To adjust for unobserved confounders, we deve…
Suppose one is interested in estimating causal effects in the presence of potentially unmeasured confounding with the aid of a valid instrumental variable. This paper investigates the problem of making inferences about the average treatment effect when data are fused from two separate sources, one of which contains information on the treatment and the other contains information on the outcome, while values for the instrument and a vector of baseline covariates are recorded in both. We provide a general set of sufficient conditions under which the average treatment effect is nonparametrically i…
We propose the instrumental variable regime (IVR) method to estimate the causal effects of multiple sequential treatments. This method serves to address the problem of endogenous selections of sequential treatments. An IVR is a sequence of instrumental variables in which each IV instruments for an endogenous treatment variable. Our proposed method generalizes the LATE model in Imbens and Angrist (1994) from a single treatment to many treatments applied sequentially. More precisely, with the IVR this model allows for estimating the local average treatment regime effects (LATRE), possibly condit…
Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatme…
Inverse probability of treatment weighting (IPTW), which has been used to estimate sample average treatment effects (SATE) using observational data, tenuously relies on the positivity assumption and the correct specification of the treatment assignment model, both of which are problematic assumptions in many observational studies. Various methods have been proposed to overcome these challenges, including truncation, covariate-balancing propensity scores, and stable balancing weights. Motivated by an observational study in spine surgery, in which positivity is violated and the true treatment as…
We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome regression models to provide valid inference on the conditional average treatment effect even when high-dimensional or nonparametric models are used. We show that our approach leads to conservative inference in finite samples or under model misspecification, and provides a consistent variance estimator when both models are correctly specified. In simulations, …
The inverse probability weighting (IPW) is broadly utilized to address missing data problems including causal inference but may suffer from large variances and biases due to propensity score model misspecification. To solve these problems, I propose an estimation method called the navigated weighting (NAWT), which utilizes estimating equations suitable for a specific pre-specified parameter of interest (e.g., the average treatment effects on the treated). Since these pre-specified parameters determine the relative importance of each unit as a function of propensity scores, the NAWT prioritizes…
In clinical trials, it is often of interest to understand the principal causal effect (PCE), the average treatment effect for a principal stratum (a subset of patients defined by the potential outcomes of one or more post-baseline variables). Commonly used assumptions include monotonicity, principal ignorability, and cross-world assumptions of principal ignorability and principal strata independence. In this article, we evaluate these assumptions through a 2$\times$2 cross-over study in which the potential outcomes under both treatments can be observed, provided there are no carry-over and stu…
We show how entropy balancing can be used for transporting experimental treatment effects from a trial population onto a target population. This method is doubly-robust in the sense that if either the outcome model or the probability of trial participation is correctly specified, then the estimate of the target population average treatment effect is consistent. Furthermore, we only require the sample moments of the effect modifiers drawn from the target population to consistently estimate the target population average treatment effect. We compared the finite-sample performance of entropy balan…
