Confounding and exposure measurement error can introduce bias when drawing inference about the marginal effect of an exposure on an outcome of interest. While there are broad methodologies for addressing each source of bias individually, confounding and exposure measurement error frequently co-occur, and there is a need for methods that address them simultaneously. In this paper, corrected score methods are derived under classical additive measurement error to draw inference about marginal exposure effects using only measured variables. Three estimators are proposed based on g-formula, inverse probability weighting, and doubly-robust estimation techniques. The estimators are shown to be consistent and asymptotically normal, and the doubly-robust estimator is shown to exhibit its namesake property. The methods, which are implemented in the R package mismex, perform well in finite samples under both confounding and measurement error as demonstrated by simulation studies. The proposed doubly-robust estimator is applied to study the effects of two biomarkers on HIV-1 infection using data from the HVTN 505 preventative vaccine trial.
In the presence of unmeasured spatial confounding, spatial models may actually increase (rather than decrease) bias, leading to uncertainty as to how they should be applied in practice. We evaluated spatial modeling approaches through simulation and application to a big data electronic health record study. Whereas the risk of bias was high for purely spatial exposures (e.g., built environment), we found very limited potential for increased bias for individual-level exposures that cluster spatially (e.g., smoking status). We also proposed a novel exposure-penalized spline approach that selects …
The Clean Air Act mandates that the National Ambient Air Quality Standards (NAAQS) must be routinely assessed to protect populations based on the latest science. Therefore, researchers should continue to address whether exposure to levels of air pollution below the NAAQS is harmful to human health. The contentious nature surrounding environmental regulations urges us to cast this question within a causal inference framework. Parametric and semi-parametric regression approaches have been used to estimate the exposure-response (ER) curve between ambient air pollution and health outcomes. Most of…
Joint misclassification of exposure and outcome variables can lead to considerable bias in epidemiological studies of causal exposure-outcome effects. In this paper, we present a new maximum likelihood based estimator for the marginal causal odd-ratio that simultaneously adjusts for confounding and several forms of joint misclassification of the exposure and outcome variables. The proposed method relies on validation data for the construction of weights that account for both sources of bias. The weighting estimator, which is an extension of the exposure misclassification weighting estimator pr…
The use of causal mediation analysis to evaluate the pathways by which an exposure affects an outcome is widespread in the social and biomedical sciences. Recent advances in this area have established formal conditions for identification and estimation of natural direct and indirect effects. However, these conditions typically involve stringent no unmeasured confounding assumptions and that the mediator has been measured without error. These assumptions may fail to hold in practice where mediation methods are often applied. The goal of this paper is two-fold. First, we show that the natural in…
Introduction: Methods now exist to detect residual confounding. One requires an "indicator" with two key properties: conditional independence of the outcome (given exposure and measured covariates) absent confounding and other model miss-specification; and an association with unmeasured confounders (like the exposure). We now present a new method for correcting for residual confounding in time-series and other epidemiological studies. We argue that estimators from models that include an indicator with these key properties should have less bias than those from models without the indicator. Meth…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (e.g. the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecifica…
Adjustment for Unmeasured Spatial Confounding in Settings of Continuous Exposure Conditional on the Binary Exposure Status: Conditional Generalized Propensity Score-Based Spatial Matching
In observational studies, researchers must select a method to control for confounding. Options include propensity score methods and regression. It remains unclear how dataset characteristics (size, overlap in propensity scores, exposure prevalence) influence the relative performance of the methods, making it difficult to select the best method for a particular dataset. A simulation study to evaluate the role of dataset characteristics on the performance of propensity score methods, compared to logistic regression, for estimating a marginal odds ratio in the presence of confounding was conducte…
In many scientific studies, it is of interest to determine whether an exposure has a causal effect on an outcome. In observational studies, this is a challenging task due to the presence of confounding variables that affect both the exposure and the outcome. Many methods have been developed to test for the presence of a causal effect when all such confounding variables are observed and when the exposure of interest is discrete. In this article, we propose a class of nonparametric tests of the null hypothesis that there is no average causal effect of an arbitrary univariate exposure on an outco…
It is often of interest to decompose a total effect of an exposure into the component that acts on the outcome through some mediator and the component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured…
It is often of interest in the health and social sciences to investigate the joint mediation effects of multiple post-exposure mediating variables. Identification of such joint mediation effects generally require no unmeasured confounding of the outcome with respect to the whole set of mediators. As the number of mediators under consideration grows, this key assumption is likely to be violated as it is often infeasible to intervene on any of the mediators. In this paper, we develop a simple two-step method of moments estimation procedure to assess mediation with multiple mediators simultaneous…
We propose a new approach for estimating causal effects when the exposure is measured with error and confounding adjustment is performed via a generalized propensity score (GPS). Using validation data, we propose a regression calibration (RC)-based adjustment for a continuous error-prone exposure combined with GPS to adjust for confounding (RC-GPS). The outcome analysis is conducted after transforming the corrected continuous exposure into a categorical exposure. We consider confounding adjustment in the context of GPS subclassification, inverse probability treatment weighting (IPTW) and match…
A growing area of research in epidemiology is the identification of health-related sibling spillover effects, or the effect of one individual's exposure on their sibling's outcome. The health and health care of family members may be inextricably confounded by unobserved factors, rendering identification of spillover effects within families particularly challenging. We demonstrate a gain-score regression method for identifying exposure-to-outcome spillover effects within sibling pairs in a linear fixed effects framework. The method can identify the exposure-to-outcome spillover effect if only o…
Although the exposure can be randomly assigned in studies of mediation effects, any form of direct intervention on the mediator is often infeasible. As a result, unmeasured mediator-outcome confounding can seldom be ruled out. We propose semiparametric identification of natural direct and indirect effects in the presence of unmeasured mediator-outcome confounding by leveraging heteroskedasticity restrictions on the observed data law. For inference, we develop semiparametric estimators that remain consistent under partial misspecifications of the observed data model. We illustrate the proposed …
A Spectral Confounder Adjustment for Spatial Regression with Multiple Exposures and Outcomes
North Carolina State University（北卡罗来纳州立大学）；Colorado State University（科罗拉多州立大学）；US EPA, Center for Public Health and Environmental Assessment（美国环境保护署，公共健康与环境评估中心）
Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation of causal effects. We propose a Bayesian nonparametric approach that simultaneously 1) prioritizes inclusion of adjustment variables in accordance with existing principles of confounder selection; 2) estimates causal effects in a manner that permits complex relationships among confounders, exposures, and outcomes; and 3) provides causal estimates that account…
Mediation analysis is a strategy for understanding the mechanisms by which treatments or interventions affect later outcomes. Mediation analysis is frequently applied in randomized trial settings, but typically assumes: a) that randomized assignment is the exposure of interest as opposed to actual take-up of the intervention, and b) no unobserved confounding of the mediator-outcome relationship. In contrast to the rich literature on instrumental variable (IV) methods to estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification st…
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…
Unmeasured, spatially-structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the spline degrees of freedom do not provide an easily interpretable spatial scale. We describe a method for quantifying the extent of spatial confounding adjustment in terms of the Euclidean distance at which variation is removed. We develop this approach for confounding adjustment with splines and using Fourier and wavelet filtering. We demonstrate differences …
The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmea…
Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first stage regression of the tre…
Propensity score matching is a common tool for adjusting for observed confounding in observational studies, but is known to have limitations in the presence of unmeasured confounding. In many settings, researchers are confronted with spatially-indexed data where the relative locations of the observational units may serve as a useful proxy for unmeasured confounding that varies according to a spatial pattern. We develop a new method, termed Distance Adjusted Propensity Score Matching (DAPSm) that incorporates information on units' spatial proximity into a propensity score matching procedure. We…
Path-specific effects are a broad class of mediated effects from an exposure to an outcome via one or more causal pathways with respect to some subset of intermediate variables. The majority of the literature concerning estimation of mediated effects has focused on parametric models with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of semiparametric estimators for the effect along a pathway through a mediator, but not some exposure-induced confounder o…
In this paper we propose a new template for empirical studies intended to assess causal effects: the outcome-wide longitudinal design. The approach is an extension of what is often done to assess the causal effects of a treatment or exposure using confounding control, but now, over numerous outcomes. We discuss the temporal and confounding control principles for such outcome-wide studies, metrics to evaluate robustness or sensitivity to potential unmeasured confounding for each outcome, and approaches to handle multiple testing. We argue that the outcome-wide longitudinal design has numerous a…
Addressing the Influence of Unmeasured Confounding in Observational Studies with Time-to-Event Outcomes: A Semiparametric Sensitivity Analysis Approach
Unmeasured confounding is a threat to causal inference in observational studies. In recent years, use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a longstanding tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao et al. (2018) have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to nonparametrically identify the average treatment effect (…
Scientists have been interested in estimating causal peer effects to understand how people's behaviors are affected by their network peers. However, it is well known that identification and estimation of causal peer effects are challenging in observational studies for two reasons. The first is the identification challenge due to unmeasured network confounding, for example, homophily bias and contextual confounding. The second issue is network dependence of observations, which one must take into account for valid statistical inference. Negative control variables, also known as placebo variables…
In causal mediation analysis, nonparametric identification of the pure (natural) direct effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called "cross-world-counterfactuals" independence and (ii) no exposure- induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data fro…
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 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…
Confounding by unmeasured spatial variables has received some attention in the spatial statistics and causal inference literatures, but concepts and approaches have remained largely separated. In this paper, we aim to bridge these distinct strands of statistics by considering unmeasured spatial confounding within a causal inference framework, and estimating effects using outcome regression tools popular within the spatial literature. First, we show how using spatially correlated random effects in the outcome model, an approach common among spatial statisticians, does not necessarily mitigate b…
Which Regularized Propensity-Score and Doubly Robust Methods Are Best Calibrated When Exposures or Outcomes Are Rare? A Plasmode Study of Proxy-Based Confounding Adjustment
School of Population and Public Health, University of British Columbia（英属哥伦比亚大学公共卫生与人口健康学院）
In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ($p$) is larger than the number of observations ($n$), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable $X_j$ is strongly associated with the treatment $T$ but weakly with the outcom…
We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the nuisance function, while mitigating the resulting errors-in-variables. The result is a robust and accurate inference method for spatially varying heterogeneous causal effects. The properties of the method are demonstrated on synthetic as well as real data from Germany and the US.
