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 unmeasured confounders of the treatment-outcome relationship. We develop sensitivity analysis techniques for these settings. We describe several sensitivity analysis techniques for the infectiousness effect which, in a vaccine trial, captures the effect of the vaccine of one person on protecting a second person from infection even if the first is infected. We also develop two sensitivity analysis techniques for causal effects under interference in the presence of unmeasured confounding which generalize analogous techniques when interference is absent. These two techniques for unmeasured confounding are compared and contrasted.
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.…
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…
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…
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…
Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure and adjust for such common causes (or confounders), some confounders typically remain unmeasured, raising the prospect of biased inference in observational studies. Therefore, it is crucial that investigators can practically assess their substantive conclusions' relative (in)sensitivity to potential unmeasured confounding. In this article, we propose a sensi…
We present a method for assessing the sensitivity of the true causal effect to unmeasured confounding. The method requires the analyst to set two intuitive parameters. Otherwise, the method is assumption-free. The method returns an interval that contains the true causal effect, and whose bounds are arbitrarily sharp, i.e. practically attainable. We show experimentally that our bounds can be tighter than those obtained by the method of Ding and VanderWeele (2016a) which, moreover, requires to set one more parameter than our method. Finally, we extend our method to bound the natural direct and i…
Real Effect or Bias? Best Practices for Evaluating the Robustness of Real-World Evidence through Quantitative Sensitivity Analysis for Unmeasured Confounding
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), …
Unmeasured confounding, selection bias, and measurement error are well-known sources of bias in epidemiologic research. Methods for assessing these biases have their own limitations. Many quantitative sensitivity analysis approaches consider each type of bias individually, while more complex approaches are harder to implement or require numerous assumptions. By failing to consider multiple biases at once, researchers can underestimate -- or overestimate -- their joint impact. We show that it is possible to bound the total composite bias due to these three sources, and to use that bound to asse…
We consider the problem of constructing bounds on the average treatment effect (ATE) when unmeasured confounders exist but have bounded influence. Specifically, we assume that omitted confounders could not change the odds of treatment for any unit by more than a fixed factor. We derive the sharp partial identification bounds implied by this assumption by leveraging distributionally robust optimization, and we propose estimators of these bounds with several novel robustness properties. The first is double sharpness: our estimators consistently estimate the sharp ATE bounds when one of two nuisa…
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.…
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…
For settings with a binary treatment and a binary outcome, instrumental variables can be used to construct bounds on a causal treatment effect. With continuous outcomes, meaningful bounds are more difficult to obtain because the domain of the outcome is typically unrestricted. In this paper, we combine an instrumental variable and subjective assumptions in the context of an obser- vational cohort study of HIV-infected women to construct meaningful bounds on the initial-stage causal effect of antiretroviral therapy on CD4 count. The subjective assumptions are encoded in terms of the potential o…
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…
Methods have been developed for Mendelian randomization that can obtain consistent causal estimates while relaxing the instrumental variable assumptions. These include multivariable Mendelian randomization, in which a genetic variant may be associated with multiple risk factors so long as any association with the outcome is via the measured risk factors (measured pleiotropy), and the MR-Egger (Mendelian randomization-Egger) method, in which a genetic variant may be directly associated with the outcome not via the risk factor of interest, so long as the direct effects of the variants on the out…
MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；Microsoft Research（微软研究院）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；University College London（伦敦大学学院）
Causal approaches to fairness have seen substantial recent interest, both from the machine learning community and from wider parties interested in ethical prediction algorithms. In no small part, this has been due to the fact that causal models allow one to simultaneously leverage data and expert knowledge to remove discriminatory effects from predictions. However, one of the primary assumptions in causal modeling is that you know the causal graph. This introduces a new opportunity for bias, caused by misspecifying the causal model. One common way for misspecification to occur is via unmeasure…
Many spatial phenomena exhibit treatment interference where treatments at one location may affect the response at other locations. Because interference violates the stable unit treatment value assumption, standard methods for causal inference do not apply. We propose a new causal framework to recover direct and spill-over effects in the presence of spatial interference, taking into account that treatments at nearby locations are more influential than treatments at locations further apart. Under the no unmeasured confounding assumption, we show that a generalized propensity score is sufficient …
Matched observational studies are commonly used to study treatment effects in non-randomized data. After matching for observed confounders, there could remain bias from unobserved confounders. A standard way to address this problem is to do a sensitivity analysis. A sensitivity analysis asks how sensitive the result is to a hypothesized unmeasured confounder U. One method, known as simultaneous sensitivity analysis, has two sensitivity parameters: one relating U to treatment assignment and the other to response. This method assumes that in each matched set, U is distributed to make the bias wo…
Bidirectional causal inference for binary outcomes in the presence of unmeasured confounding
School of Mathematics and Statistics, Beijing Technology and Business University（北京工商大学数学与统计学院）；The Dartmouth Institute for Health Policy and Clinical Practice, Geisel School of Medicine at Dartmouth（达特茅斯学院盖泽尔医学院达特茅斯健康政策与临床实践研究所）
In this paper, we consider the extent of the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and we propose sensitivity analysis techniques to correct for such biases. We give an analysis of which effects in an SEM are, and are not, biased by an unmeasured confounder. It is shown that a single unmeasured confounder will bias not just one, but numerous, effects in an SEM. We present sensitivity analysis techniques to correct for biases in total, direct, and indirect effects when using SEM analyses, and illustrate these techniques with a stud…
We present a method to analyze sensitivity of frequentist inferences to potential nonignorability of the missingness mechanism. Rather than starting from the selection model, as is typical in such analyses, we assume that the missingness arises through unmeasured confounding. Our model permits the development of measures of sensitivity that are analogous to those for unmeasured confounding in observational studies. We define an index of sensitivity, denoted MinNI, to be the minimum degree of nonignorability needed to change the mean value of the estimate of interest by a designated amount. We …
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; …
Unmeasured confounding may undermine the validity of causal inference with observational studies. Sensitivity analysis provides an attractive way to partially circumvent this issue by assessing the potential influence of unmeasured confounding on the causal conclusions. However, previous sensitivity analysis approaches often make strong and untestable assumptions such as having a confounder that is binary, or having no interaction between the effects of the exposure and the confounder on the outcome, or having only one confounder. Without imposing any assumptions on the confounder or confounde…
On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often difficult to anticipate the effects of algorithmic policies prior to deployment, making the decision to adopt them risky. In particular, one generally cannot use historical data to directly observe what would have happened had the actions recommended by the algorithm been taken. One standard strategy is to model potential outcomes for alternative decisions assumi…
Data-driven methods for personalizing treatment assignment have garnered much attention from clinicians and researchers. Dynamic treatment regimes formalize this through a sequence of decision rules that map individual patient characteristics to a recommended treatment. Observational studies are commonly used for estimating dynamic treatment regimes due to the potentially prohibitive costs of conducting sequential multiple assignment randomized trials. However, estimating a dynamic treatment regime from observational data can lead to bias in the estimated regime due to unmeasured confounding. …
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 o…
An observational study may be biased for estimating causal effects by failing to control for unmeasured confounders. This paper proposes a new quantity called the "sensitivity value", which is defined as the minimum strength of unmeasured confounders needed to change the qualitative conclusions of a naive analysis assuming no unmeasured confounder. We establish the asymptotic normality of the sensitivity value in pair-matched observational studies. The theoretical results are then used to approximate the power of a sensitivity analysis and select the design of a study. We explore the potential…
Leveraging external controls -- relevant individual patient data under control from external trials or real-world data -- has the potential to reduce the cost of randomized controlled trials (RCTs) while increasing the proportion of trial patients given access to novel treatments. However, due to lack of randomization, RCT patients and external controls may differ with respect to covariates that may or may not have been measured. Hence, after controlling for measured covariates, for instance by matching, testing for treatment effect using external controls may still be subject to unmeasured bi…
Investigating the causal relationship between exposure and the time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using the hazard ratio as a marginal causal effect measure due to its noncollapsibility property. In this paper, we advocate using the restricted mean survival time (RMST) difference as the marginal causal effect measure, which is collapsible and has a simple interpretation as the difference of area under survival curves over a certain time horizon. To address both measured and unmeasured confounding, a matc…
