Marginal structural models are a popular tool for investigating the effects of time-varying treatments, but they require an assumption of no unobserved confounders between the treatment and outcome. With observational data, this assumption may be difficult to maintain, and in studies with panel data, many researchers use fixed effects models to purge the data of time-constant unmeasured confounding. Unfortunately, traditional linear fixed effects models are not suitable for estimating the effects of time-varying treatments, since they can only estimate lagged effects under implausible assumptions. To resolve this tension, we a propose a novel inverse probability of treatment weighting estimator with propensity-score fixed effects to adjust for time-constant unmeasured confounding in marginal structural models of fixed-length treatment histories. We show that these estimators are consistent and asymptotically normal when the number of units and time periods grow at a similar rate. Unlike traditional fixed effect models, this approach works even when the outcome is only measured at a single point in time as is common in marginal structural models. We apply these methods to estimating the effect of negative advertising on the electoral success of candidates for statewide offices in the United States.
Instrumental variable methods are popular choices in combating unmeasured confounding to obtain less biased effect estimates. However, we demonstrate that alternative methods may give less biased estimates depending on the nature of unmeasured confounding. Treatment preferences of clusters (e.g., physician practices) are the most f6requently used instruments in instrumental variable analyses (IVA). These preference-based IVAs are usually conducted on data clustered by region, hospital/facility, or physician, where unmeasured confounding often occurs within or between clusters. We aim to quanti…
An important concern in an observational study is whether or not there is unmeasured confounding, i.e., unmeasured ways in which the treatment and control groups differ before treatment that affect the outcome. We develop a test of whether there is unmeasured confounding when an instrumental variable (IV) is available. An IV is a variable that is independent of the unmeasured confounding and encourages a subject to take one treatment level vs. another, while having no effect on the outcome beyond its encouragement of a certain treatment level. We show what types of unmeasured confounding can b…
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…
Adjustment for Unmeasured Spatial Confounding in Settings of Continuous Exposure Conditional on the Binary Exposure Status: Conditional Generalized Propensity Score-Based Spatial Matching
Bayesian Sensitivity Analysis for Causal Estimation with Time-varying Unmeasured Confounding
Dalla Lana School of Public Health, University of Toronto（多伦多大学达拉·兰纳公共卫生学院）；Public Health Ontario（安大略省公共卫生局）；Rutgers School of Public Health, Rutgers University（罗格斯大学罗格斯公共卫生学院）；Division of Gastroenterology, Hepatology Nutrition, The Hospital for Sick Children（儿童医院胃肠病学、肝病营养科）；University of Utah and Intermountain Healthcare Primary Children’s Hospital（犹他大学和山脊医疗初级儿童医院）；Institute of Health Policy, Management and Evaluation, University of Toronto（多伦多大学卫生政策、管理与评估研究所）
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 …
Real Effect or Bias? Best Practices for Evaluating the Robustness of Real-World Evidence through Quantitative Sensitivity Analysis for Unmeasured Confounding
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…
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…
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 (…
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), …
Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be…
Mediation analysis with unmeasured confounding between parallel mediators and outcome
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；The Beijing Institute of Brain Disorders, Chinese Institutes for Medical Research, Capital Medical University（首都医科大学中国医学研究院北京脑 disorder 研究所）
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…
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…
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…
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…
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…
Proximal Mediation Analysis with Unmeasured Treatment-Induced Confounding
Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学统计学院与应用统计中心）；Department of Biostatistics & Medical Informatics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物统计与医学信息学系）
Partial identification and unmeasured confounding with multiple treatments and multiple outcomes
Harvard T.H. Chan School of Public Health（哈佛陈曾熙公共卫生学院）；Dana-Farber Cancer Institute（达纳法伯癌症研究所）；University of Florida（佛罗里达大学）；University of Central Florida（中佛罗里达大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
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.…
The George Washington University（乔治华盛顿大学）；University of California, Irvine（加州大学欧文分校）
Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in observational studies. Motivated by the recent proposed proximal causal inference, we develop several proximal learning approaches to estimating optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. In particular, we establish several identification results for different classes of ITRs, exhibiting the trade-off between the ri…
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…
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…
Clinical studies sometimes encounter truncation by death, rendering outcomes undefined. Statistical analysis based solely on observed survivors may give biased results because the characteristics of survivors differ between treatment groups. By principal stratification, the survivor average causal effect was proposed as a causal estimand defined in always-survivors. However, this estimand is not identifiable when there is unmeasured confounding between the treatment assignment and survival or outcome process. In this paper, we consider the comparison between an aggressive treatment and a conse…
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 this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured co- variates. Instrumental variable (IV) methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. Based on a semi-parametric additive hazard model for the subdistribution hazard, we pro- pose an instrumental variab…
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…
Estimating causal effects of continuous-time dynamic treatments with unmeasured confounders
Key Laboratory of Advanced Theory and Application in Statistics and Data Science -MOE, School of Statistics, East China Normal University（华东师范大学统计学院统计学与数据科学前沿理论及应用教育部重点实验室）
A Doubly Robust Instrumental Variable Approach for Estimating Average Treatment Effects in Time-to-Event Data with Unmeasured Confounding: Application to Real-World Data on ICU Patients with Septic Shock
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…
Estimating the average treatment causal effect in clustered data often involves dealing with unmeasured cluster-specific confounding variables. Such variables may be correlated with the measured unit covariates and outcome. When the correlations are ignored, the causal effect estimation can be biased. By utilizing sufficient statistics, we propose an inverse conditional probability weighting (ICPW) method, which is robust to both (i) the correlation between the unmeasured cluster-specific confounding variable and the covariates and (ii) the correlation between the unmeasured cluster-specific c…
Semiparametric Mediation Analysis with Separately Observed Mediator and Outcome under Unmeasured Confounding
Department of Biostatistics, University of California, Los Angeles（加州大学洛杉矶分校生物统计系）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院生物统计系）
