In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage residual inclusion and limited information maximum likelihood are typically employed. However, these methods are known to entail difficulty in terms of potential bias of HR estimates and parameter identification. This study introduces a novel nonparametric Bayesian method designed to estimate an unbiased HR, addressing concerns that previous research methods have had. Our proposed method consists of two phases: 1) detecting clusters based on the likelihood of the exposure and outcome variables, and 2) estimating the hazard ratio within each cluster. Although it is implicitly assumed that unmeasured confounders affect outcomes through cluster effects, our algorithm is well-suited for such data structures. The proposed Bayesian estimator has good performance compared with some competitors.
Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with time-varying confounding, such as exposure-induced mediator-outcome confounders. We further extend this approach to propose two Bayesian data fusion (BDF) methods for unmeasured confounding. Using informative priors on quantities relating to the confounding bias parameters, our methods incorporate data from an external source where the confounder is measured in order t…
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 consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is avai…
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.…
Graphical models have been used extensively for modeling brain connectivity networks. However, unmeasured confounders and correlations among measurements are often overlooked during model fitting, which may lead to spurious scientific discoveries. Motivated by functional magnetic resonance imaging (fMRI) studies, we propose a novel method for constructing brain connectivity networks with correlated replicates and latent effects. In a typical fMRI study, each participant is scanned and fMRI measurements are collected across a period of time. In many cases, subjects may have different states of …
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）
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…
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）
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…
Automating the Selection of Proxy Variables of Unmeasured Confounders
Beijing Technology and Business University（北京工商大学）；Guangdong University of Technology（广东工业大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Peking University（北京大学）
The case-cohort study design bypasses resource constraints by collecting certain expensive covariates for only a small subset of the full cohort. Weighted Cox regression is the most widely used approach for analysing case-cohort data within the Cox model, but is inefficient. Alternative approaches based on multiple imputation and nonparametric maximum likelihood suffer from incompatibility and computational issues respectively. We introduce a novel Bayesian framework for case-cohort Cox regression that avoids the aforementioned problems. Users can include auxiliary variables to help predict th…
Shrinkage priors for Bayesian Substitute Confounders
School of Mathematical Sciences, University of Nottingham, Nottingham, UK（诺丁汉大学数学科学学院）；Department of Statistics, Rice University, USA（里士满大学统计学系；伯克利国家实验室）；Lawrence Berkeley National Laboratory, USA（洛斯阿拉莫斯国家实验室统计科学组）；Statistical Sciences Group, Los Alamos National Laboratory, USA
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…
The era of big data has witnessed an increasing availability of multiple data sources for statistical analyses. We consider estimation of causal effects combining big main data with unmeasured confounders and smaller validation data with supplementary information on these confounders. Under the unconfoundedness assumption with completely observed confounders, the smaller validation data allow for constructing consistent estimators for causal effects, but the big main data can only give error-prone estimators in general. However, by leveraging the information in the big main data in a principle…
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…
A Bayesian Reinterpretation of Cornfield-Type Sensitivity Analysis: From Thresholds to Probabilities
GCS-fMRI, Koelliker Hospital and Department of Psychology, University of Turin（都灵大学心理系 GCS-fMRI 科埃利凯尔医院）；FOCUS Laboratory, Department of Psychology, University of Turin（都灵大学心理系 FOCUS 实验室）；Neuroscience Institute of Turin (NIT)（都灵神经科学研究所）
Instrumental variable (IV) methods are widely used for estimating average treatment effects in the presence of unmeasured confounders. However, the capability of existing IV procedures, and most notably the two-stage residual inclusion (2SRI) procedure recommended for use in nonlinear contexts, to account for unmeasured confounders in the Cox proportional hazard model is unclear. We show that instrumenting an endogenous treatment induces an unmeasured covariate, referred to as an individual frailty in survival analysis parlance, which if not accounted for leads to bias. We propose a new proced…
Propensity score weighting is a tool for causal inference to adjust for measured confounders. Survey data are often collected under complex sampling designs such as multistage cluster sampling, which presents challenges for propensity score modeling and estimation. In addition, for clustered data, there may also be unobserved cluster effects related to both the treatment and the outcome. When such unmeasured confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment will be biased. We propose a calibrated propensity score weighting adjustment fo…
Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. In this paper, we derive necessary conditions on the coherence between the treatment variable of interest and the unmeasured confounder that ensure the causal effect of the treatment is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. The key assumption that ensures identifiability is that confounding present at global scales dissipates at local sc…
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）
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…
This paper studies the confounding effects from the unmeasured confounders and the imbalance of observed confounders in IV regression and aims at unbiased causal effect estimation. Recently, nonlinear IV estimators were proposed to allow for nonlinear model in both stages. However, the observed confounders may be imbalanced in stage 2, which could still lead to biased treatment effect estimation in certain cases. To this end, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and the imbalance of observed confounders. The…
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…
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; …
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more genera…
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）
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…
It is emphasised that for epidemiological studies where disease incidence is rare, results from conventional proportional hazards models can often correctly estimate causal associations. The well-known "backdoor criteria" from causal-inference is applied to the common epidemiological study of rare diseases with a proportional hazards model, providing an example of when and how estimates from conventional proportional hazards studies can be used. A similar study with the "frontdoor criteria", that allows studies with unmeasured confounders, finds similar results to conventional mediation analys…
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…
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…
In biometrics and related fields, the Cox proportional hazards model are widely used to analyze with covariate adjustment. However, when some covariates are not observed, an unbiased estimator usually cannot be obtained. Even if there are some unmeasured covariates, instrumental variable methods can be applied under some assumptions. In this paper, we propose the new instrumental variable estimator for the Cox proportional hazards model. The estimator is the similar feature as Martinez-Camblor et al., 2019, but not the same exactly; we use an idea of limited-information maximum likelihood. We …
Real Effect or Bias? Best Practices for Evaluating the Robustness of Real-World Evidence through Quantitative Sensitivity Analysis for Unmeasured Confounding
The Cox regression model and its associated hazard ratio (HR) are frequently used for summarizing the effect of treatments on time to event outcomes. However, the HR's interpretation strongly depends on the assumed underlying survival model. The challenge of interpreting the HR has been the focus of a number of recent works. Besides, several alternative measures have been proposed in order to deal with these concerns. The marginal Cox regression models include an identifiable hazard ratio without individual but populational causal interpretation. In this work, we study the properties of one pa…
Interventional effects have been proposed as a solution to the unidentifiability of natural (in)direct effects under mediator-outcome confounders affected by the exposure. Such confounders are an intrinsic characteristic of studies with time-varying exposures and mediators, yet the generalization of the interventional effect framework to the time-varying case has received little attention in the literature. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator…
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…
