Estimating an individual treatment effect (ITE) is essential to personalized decision making. However, existing methods for estimating the ITE often rely on unconfoundedness, an assumption that is fundamentally untestable with observed data. To assess the robustness of individual-level causal conclusion with unconfoundedness, this paper proposes a method for sensitivity analysis of the ITE, a way to estimate a range of the ITE under unobserved confounding. The method we develop quantifies unmeasured confounding through a marginal sensitivity model [Ros2002, Tan2006], and adapts the framework of conformal inference to estimate an ITE interval at a given confounding strength. In particular, we formulate this sensitivity analysis problem as a conformal inference problem under distribution shift, and we extend existing methods of covariate-shifted conformal inference to this more general setting. The result is a predictive interval that has guaranteed nominal coverage of the ITE, a method that provides coverage with distribution-free and nonasymptotic guarantees. We evaluate the method on synthetic data and illustrate its application in an observational study.
A fundamental limitation of causal inference in observational studies is that perceived evidence for an effect might instead be explained by factors not accounted for in the primary analysis. Methods for assessing the sensitivity of a study's conclusions to unmeasured confounding have been established under the assumption that the treatment effect is constant across all individuals. In the potential presence of unmeasured confounding, it has been argued that certain patterns of effect heterogeneity may conspire with unobserved covariates to render the performed sensitivity analysis inadequate.…
In the absence of a randomized experiment, a key assumption for drawing causal inference about treatment effects is the ignorable treatment assignment. Violations of the ignorability assumption may lead to biased treatment effect estimates. Sensitivity analysis helps gauge how causal conclusions will be altered in response to the potential magnitude of departure from the ignorability assumption. However, sensitivity analysis approaches for unmeasured confounding in the context of multiple treatments and binary outcomes are scarce. We propose a flexible Monte Carlo sensitivity analysis approach…
Identifying causal treatment (or exposure) effects in observational studies requires the data to satisfy the unconfoundedness assumption which is not testable using the observed data. With sensitivity analysis, one can determine how the conclusions might change if assumptions are violated to a certain degree. In this paper, we propose a new technique for sensitivity analysis applicable to clusters observational data with a normally distributed or binary outcome. The proposed methods aim to assess the robustness of estimated treatment effects in a single study as well as in multiple studies, i.…
We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the $Γ$-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data is confounded. Under the marginal sensitivity model of Tan (2006), we characterize the shift between the distribution of the observations and that of the counterfactuals. We f…
This paper considers conducting inference about the effect of a treatment (or exposure) on an outcome of interest. In the ideal setting where treatment is assigned randomly, under certain assumptions the treatment effect is identifiable from the observable data and inference is straightforward. However, in other settings such as observational studies or randomized trials with noncompliance, the treatment effect is no longer identifiable without relying on untestable assumptions. Nonetheless, the observable data often do provide some information about the effect of treatment, that is, the param…
In the presence of treatment effect heterogeneity, the average treatment effect (ATE) in a randomized controlled trial (RCT) may differ from the average effect of the same treatment if applied to a target population of interest. If all treatment effect moderators are observed in the RCT and in a dataset representing the target population, we can obtain an estimate for the target population ATE by adjusting for the difference in the distribution of the moderators between the two samples. This paper considers sensitivity analyses for two situations: (1) where we cannot adjust for a specific mode…
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…
Background: Randomized controlled trials are often used to inform policy and practice for broad populations. The average treatment effect (ATE) for a target population, however, may be different from the ATE observed in a trial if there are effect modifiers whose distribution in the target population is different that from that in the trial. Methods exist to use trial data to estimate the target population ATE, provided the distributions of treatment effect modifiers are observed in both the trial and target population -- an assumption that may not hold in practice. Methods: The proposed sensi…
In causal mediation studies that decompose an average treatment effect into a natural indirect effect (NIE) and a natural direct effect (NDE), examples of post-treatment confounding are abundant. Past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due to incomplete information: it is observed under the actual treatment condition while missing under the counterfactual treatment condition. This study proposes a new sensitivity analysis strategy for handling post-treatment confounding and incorporates it into weightin…
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 und…
Analysis of longitudinal randomised controlled trials is frequently complicated because patients deviate from the protocol. Where such deviations are relevant for the estimand, we are typically required to make an untestable assumption about post-deviation behaviour in order to perform our primary analysis and estimate the treatment effect. In such settings, it is now widely recognised that we should follow this with sensitivity analyses to explore the robustness of our inferences to alternative assumptions about post-deviation behaviour. Although there has been a lot of work on how to conduct…
Causal inference with interference is a rapidly growing area. The literature has begun to relax the "no-interference" assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper we briefly review the literature on causal inference in the presence of interference when treatments have been randomized. We then consider settings in which causal effects in the presence of interference are not identified, either because randomization alone does not suffice for identification or because treatment is not randomized and there may be unmeasur…
A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible models for the observed data and (2) clean separation of the identified and unidentified parts of the sensitivity model. …
Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these methods enjoy some theoretical appeal in terms of consistency and convergence rates, they generally perform poorly in terms of uncertainty quantification. This is troubling since assessing risk is crucial for reliable decision-making in sensitive and uncertain environments. In this work, we propose a conformal inference-based approach that can produce reliabl…
In observational studies, it is typically unrealistic to assume that treatments are randomly assigned, even conditional on adjusting for all observed covariates. Therefore, a sensitivity analysis is often needed to examine how hidden biases due to unobserved covariates would affect inferences on treatment effects. In matched observational studies where each treated unit is matched to one or multiple untreated controls for observed covariates, the Rosenbaum bounds sensitivity analysis is one of the most popular sensitivity analysis models. In this paper, we show that in the presence of interact…
We develop sensitivity analyses for weak nulls in matched observational studies while allowing unit-level treatment effects to vary. The methods may be applied to studies using any optimal without-replacement matching algorithm. In contrast to randomized experiments and to paired observational studies, we show for general matched designs that over a large class of test statistics, any valid sensitivity analysis for the entirety of the weak null must be unnecessarily conservative if Fisher's sharp null of no treatment effect for any individual also holds. We present a sensitivity analysis valid…
Two problems that arise in making causal inferences for non-mortality outcomes such as bronchopulmonary dysplasia (BPD) are unmeasured confounding and censoring by death, i.e., the outcome is only observed when subjects survive. In randomized experiments with noncompliance, instrumental variable methods can be used to control for the unmeasured confounding without censoring by death. But when there is censoring by death, the average causal treatment effect cannot be identified under usual assumptions, but can be studied for a specific subpopulation by using sensitivity analysis with additional…
For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our…
Denoised Conformal Alignment for Reliable Selection of Conditional Average Treatment Effect Predictions
Shanghai Jiao Tong University（上海交通大学）；Shanghai University of Finance and Economics（上海财经大学）；National University of Defense Technology（国防科学技术大学）；School of Statistics and Data Science（统计与数据科学学院）；Institute of Big Data Research（大数据研究院）
In randomized experiments, interactions between units might generate a treatment diffusion process. This is common when the treatment of interest is an actual object or product that can be shared among peers (e.g., flyers, booklets, videos). For instance, if the intervention of interest is an information campaign realized through the distribution of a video to targeted individuals, some of these treated individuals might share the video they received with their friends. Such a phenomenon is usually unobserved, causing a misallocation of individuals in the two treatment arms: some of the initia…
Sensitivity Analysis of the Consistency Assumption
Department of Computer Science, Utah Valley University（乌得拉山谷大学计算机科学系）；School of Public Health and Community Medicine, University of Gothenburg（哥德堡大学公共卫生与社区医学学院）；Institute for Health Informatics, University of Minnesota（明尼苏达大学健康信息研究所）；Department of Counseling, Educational Psychology, and Special Education, Michigan State University（密歇根州立大学咨询、教育心理学与特殊教育系）
Randomized controlled trials (RCT's) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population, researchers must adjust for a set of treatment effect moderators. In practice, it is impossible to know whether the set of moderators has been properly accounted for. In the following paper, I propose a three parameter sensitivity analysis for generalizing or transporting experimental results using weighted estimators, with several advantages over existing methods…
Omitted variable bias can affect treatment effect estimates obtained from observational data due to the lack of random assignment to treatment groups. Sensitivity analyses adjust these estimates to quantify the impact of potential omitted variables. This paper presents methods of sensitivity analysis to adjust interval estimates of treatment effect---both the point estimate and standard error---obtained using multiple linear regression. Central to our approach is what we term benchmarking, the use of data to establish reference points for speculation about omitted confounders. The method adapt…
In observational studies, identification of ATEs is generally achieved by assuming that the correct set of confounders has been measured and properly included in the relevant models. Because this assumption is both strong and untestable, a sensitivity analysis should be performed. Common approaches include modeling the bias directly or varying the propensity scores to probe the effects of a potential unmeasured confounder. In this paper, we take a novel approach whereby the sensitivity parameter is the "proportion of unmeasured confounding:" the proportion of units for whom the treatment is no…
Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Mul…
The Hazard Ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect (SACE), is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of thei…
No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the databases, collected confounders are not exhaustive, and it is crucial to examine the extent to which the resulting estimate is sensitive to the unmeasured confounders. We consider this problem for survival and competing risks data. Due to the complexity of models for such data, we adapt the simulated potential confounders approach of Carnegie et al. (2016), …
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；Harvard Business School（哈佛商学院）
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed met…
A sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of a na\"ıve analysis that presumes all biases were removed by matching or by other analytic adjustments. The power of a sensitivity analysis and the design sensitivity anticipate the outcome of a sensitivity analysis under an assumed model for the generation of the data. It is known that the power of a sensitivity analysis is affected by the choice of test statistic, and, in particular, that a statistic with go…
The ability to generalize experimental results from randomized control trials (RCTs) across locations is crucial for informing policy decisions in targeted regions. Such generalization is often hindered by the lack of identifiability due to unmeasured effect modifiers that compromise direct transport of treatment effect estimates from one location to another. We build upon sensitivity analysis in observational studies and propose an optimization procedure that allows us to get bounds on the treatment effects in targeted regions. Furthermore, we construct more informative bounds by balancing on…
Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects
IDLab Department of Electronics and Information Systems Ghent University, Belgium（IDLab电子与信息系统系根特大学，比利时）；IDLab Department of Electronics and Information Systems Ghent University - imec, Belgium（IDLab电子与信息系统系根特大学-imec，比利时）；Biometrics Research Group Department of Morphology, Imaging, Orthopedics, Rehabilitation and Nutrition Ghent University, Belgium（生物医学研究组形态学、成像、骨科、康复与营养系根特大学，比利时）
To make informed policy recommendations from observational data, we must be able to discern true treatment effects from random noise and effects due to confounding. Difference-in-Difference techniques which match treated units to control units based on pre-treatment outcomes, such as the synthetic control approach have been presented as principled methods to account for confounding. However, we show that use of synthetic controls or other matching procedures can introduce regression to the mean (RTM) bias into estimates of the average treatment effect on the treated. Through simulations, we sh…
Estimates of the effects of treatment on cost from observational studies are subject to bias if there are unmeasured confounders. It is therefore advisable in practice to assess the potential magnitude of such biases. We derive a general adjustment formula for loglinear models of mean cost and explore special cases under plausible assumptions about the distribution of the unmeasured confounder. We assess the performance of the adjustment by simulation, in particular, examining robustness to a key assumption of conditional independence between the unmeasured and measured covariates given the tr…
