Presence Of Unmeasured Confounders Research Articles

Unveiling challenges in Mendelian randomization for gene-environment interaction.

Gene-environment (GxE) interactions play a crucial role in understanding the complex etiology of various traits, but assessing them using observational data can be challenging due to unmeasured confounders for lifestyle and environmental risk factors. Mendelian randomization (MR) has emerged as a valuable method for assessing causal relationships based on observational data. This approach utilizes genetic variants as instrumental variables (IVs) with the aim of providing a valid statistical test and estimation of causal effects in the presence of unmeasured confounders. MR has gained substantial popularity in recent years largely due to the success of genome-wide association studies. Many methods have been developed for MR; however, limited work has been done on evaluating GxE interaction. In this paper, we focus on two primary IV approaches: the two-stage predictor substitution and the two-stage residual inclusion, and extend them to accommodate GxE interaction under both the linear and logistic regression models for continuous and binary outcomes, respectively. Comprehensive simulation study and analytical derivations reveal that resolving the linear regression model is relatively straightforward. In contrast, the logistic regression model presents a considerably more intricate challenge, which demands additional effort.

Sensitivity analysis of G-estimators to invalid instrumental variables.

Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured confounders. A valid instrumental variable is a variable that is associated with the exposure, affects the outcome only through the exposure (exclusion), and is not confounded with the outcome (exogeneity). Unlike the first assumption, the other two are generally untestable and rely on subject-matter knowledge. Therefore, a sensitivity analysis is desirable to assess the impact of assumptions' violation on the estimated parameters. In this paper, we propose and demonstrate a new method of sensitivity analysis for G-estimators in causal linear and non-linear models. We introduce two novel aspects of sensitivity analysis in instrumental variables studies. The first is a single sensitivity parameter that captures violations of exclusion and exogeneity assumptions. The second is an application of the method to non-linear models. The introduced framework is theoretically justified and is illustrated via a simulation study. Finally, we illustrate the method by application to real-world data and provide guidelines on conducting sensitivity analysis.

Group sequential testing under instrumented difference-in-differences approach.

Unmeasured confounding is a major obstacle to reliable causal inference based on observational studies. Instrumented difference-in-differences (iDiD), a novel idea connecting instrumental variable and standard DiD, ameliorates the above issue by explicitly leveraging exogenous randomness in an exposure trend. In this article, we utilize the above idea of iDiD, and propose a novel group sequential testing method that provides valid inference even in the presence of unmeasured confounders. At each time point, we estimate the average or conditional average treatment effect under iDiD setting using the data accumulated up to that time point, and test the significance of the treatment effect. We derive the joint distribution of the test statistics under the null using the asymptotic properties of M-estimation, and the group sequential boundaries are obtained using the -spending functions. The performance of our proposed approach is evaluated on both synthetic data and Clinformatics Data Mart Database (OptumInsight, Eden Prairie, MN) to examine the association between rofecoxib and acute myocardial infarction, and our method detects significant adverse effect of rofecoxib much earlier than the time when it was finally withdrawn from the market.

Estimating the average treatment effect in randomized clinical trials with all-or-none compliance

Noncompliance is a common intercurrent event in randomized clinical trials that raises important questions about analytical objectives and approaches. Motivated by the Multiple Risk Factor Intervention Trial (MRFIT), we consider how to estimate the average treatment effect (ATE) in randomized trials with all-or-none compliance. Confounding is a major challenge in estimating the ATE, and conventional methods for confounding adjustment typically require the assumption of no unmeasured confounders which may be difficult to justify. Using randomized treatment assignment as an instrumental variable, the ATE can be identified in the presence of unmeasured confounders under suitable assumptions, including an assumption that limits the effect-modifying activities of unmeasured confounders. We describe and compare several estimation methods based on different modeling assumptions. Some of these methods are able to incorporate information from auxiliary covariates for improved efficiency without introducing bias. The different methods are compared in a simulation study and applied to the MRFIT.

An instrumental variable method for point processes: generalized Wald estimation based on deconvolution

Summary Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods.

A novel penalized inverse-variance weighted estimator for Mendelian randomization with applications to COVID-19 outcomes.

Mendelian randomization utilizes genetic variants as instrumental variables (IVs) to estimate the causal effect of an exposure variable on an outcome of interest even in the presence of unmeasured confounders. However, the popular inverse‐variance weighted (IVW) estimator could be biased in the presence of weak IVs, a common challenge in MR studies. In this article, we develop a novel penalized inverse‐variance weighted (pIVW) estimator, which adjusts the original IVW estimator to account for the weak IV issue by using a penalization approach to prevent the denominator of the pIVW estimator from being close to zero. Moreover, we adjust the variance estimation of the pIVW estimator to account for the presence of balanced horizontal pleiotropy. We show that the recently proposed debiased IVW (dIVW) estimator is a special case of our proposed pIVW estimator. We further prove that the pIVW estimator has smaller bias and variance than the dIVW estimator under some regularity conditions. We also conduct extensive simulation studies to demonstrate the performance of the proposed pIVW estimator. Furthermore, we apply the pIVW estimator to estimate the causal effects of five obesity‐related exposures on three coronavirus disease 2019 (COVID‐19) outcomes. Notably, we find that hypertensive disease is associated with an increased risk of hospitalized COVID‐19; and peripheral vascular disease and higher body mass index are associated with increased risks of COVID‐19 infection, hospitalized COVID‐19, and critically ill COVID‐19.

Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction

Recently, Wang and Tchetgen Tchetgen (2018) showed that the global average treatment effect is identifiable even in the presence of unmeasured confounders so long as they do not modify the instrument’s additive effect on the treatment. We use a simple and direct method to show that this no-interaction assumption allows identification of the entire outcome distribution, which leads to multiply robust estimation procedures for nonlinear functionals like the quantile and Mann–Whitney treatment effects. Similarly, we can bound these causal estimands through the outcome distribution in sensitivity analysis against confounder–instrument interaction.

Causal inference for observational longitudinal studies using deep survival models

ObjectiveCausal inference for observational longitudinal studies often requires the accurate estimation of treatment effects on time-to-event outcomes in the presence of time-dependent patient history and time-dependent covariates. Materials and MethodsTo tackle this longitudinal treatment effect estimation problem, we have developed a time-variant causal survival (TCS) model that uses the potential outcomes framework with an ensemble of recurrent subnetworks to estimate the difference in survival probabilities and its confidence interval over time as a function of time-dependent covariates and treatments. ResultsUsing simulated survival datasets, the TCS model showed good causal effect estimation performance across scenarios of varying sample dimensions, event rates, confounding and overlapping. However, increasing the sample size was not effective in alleviating the adverse impact of a high level of confounding. In a large clinical cohort study, TCS identified the expected conditional average treatment effect and detected individual treatment effect heterogeneity over time. TCS provides an efficient way to estimate and update individualized treatment effects over time, in order to improve clinical decisions. DiscussionThe use of a propensity score layer and potential outcome subnetworks helps correcting for selection bias. However, the proposed model is limited in its ability to correct the bias from unmeasured confounding, and more extensive testing of TCS under extreme scenarios such as low overlapping and the presence of unmeasured confounders is desired and left for future work. ConclusionTCS fills the gap in causal inference using deep learning techniques in survival analysis. It considers time-varying confounders and treatment options. Its treatment effect estimation can be easily compared with the conventional literature, which uses relative measures of treatment effect. We expect TCS will be particularly useful for identifying and quantifying treatment effect heterogeneity over time under the ever complex observational health care environment.

Testability of Instrumental Variables in Linear Non-Gaussian Acyclic Causal Models.

This paper investigates the problem of selecting instrumental variables relative to a target causal influence from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method.

How Do Tumor Cytogenetics Inform Cancer Treatments? Dynamic Risk Stratification and Precision Medicine Using Multi-armed Bandits

Multiple myeloma is an incurable cancer of bone marrow plasma cells with a median overall survival of 5 years. With newly approved drugs to treat this disease over the last decade, physicians are afforded more opportunities to tailor treatment to individual patients and thereby improve survival outcomes and quality of life. However, since the optimal sequence of therapy is unknown, selecting a treatment that will result in the most effective outcome for each individual patient is challenging. This paper addresses this challenge, considering the problem of designing personalized treatment recommendations for patients with multiple myeloma using a data-driven analytics method. We formulate the treatment recommendation problem as a Bayesian contextual bandit, which sequentially selects treatments based on contextual information about patients and therapies, with the goal of maximizing overall survival outcomes. We developed a multilevel Bayesian linear Thompson sampling to learn patients’ heterogeneous response on treatment decisions, which allows us to flexibly account for patient and line-of-therapy level heterogeneity even in the absence of a large number of observations. Facing the difficulty of evaluating the performance of the policy with only observational data, we propose a causal offline evaluation approach to measure the effect of the treatment in the presence of unmeasured confounders. We evaluate the performance of our policy on clinical data collected from 803 patients treated at Seattle Cancer Care Alliance. Our policy achieved an 19.75\% predicted improvement compared to the current clinical practice, and outperforms other benchmark strategies. Moreover, our policy achieves higher improvement for aging or high-risk patients with more complications by keeping the disease controlled at a relatively stable condition.

Instrumental variable estimation in semi-parametric additive hazards models.

SummaryInstrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two‐stage least‐squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi‐parametric additive hazard model which can include time‐independent and time‐dependent covariate effects is particularly suited for the two‐stage residual inclusion method, since it allows direct estimation of time‐independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two‐stage residual inclusion estimators of regression coefficients in a semi‐parametric additive hazard model with time‐independent and time‐dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure‐dependent censoring.

SENSITIVITY ANALYSIS FOR UNMEASURED CONFOUNDING IN COARSE STRUCTURAL NESTED MEAN MODELS.

Coarse Structural Nested Mean Models (SNMMs, Robins (2000)) and G-estimation can be used to estimate the causal effect of a time-varying treatment from longitudinal observational studies. However, they rely on an untestable assumption of no unmeasured confounding. In the presence of unmeasured confounders, the unobserved potential outcomes are not missing at random, and standard G-estimation leads to biased effect estimates. To remedy this, we investigate the sensitivity of G-estimators of coarse SNMMs to unmeasured confounding, assuming a nonidentifiable bias function which quantifies the impact of unmeasured confounding on the average potential outcome. We present adjusted G-estimators of coarse SNMM parameters and prove their consistency, under the bias modeling for unmeasured confounding. We apply this to a sensitivity analysis for the effect of the ART initiation time on the mean CD4 count at year 2 after infection in HIV-positive patients, based on the prospective Acute and Early Disease Research Program.

Adjusting for bias introduced by instrumental variable estimation in the Cox proportional hazards model.

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) algorithm recommended for use in non-linear 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 procedure that augments 2SRI with an individual frailty and prove that it is consistent under certain conditions. The finite sample-size behavior is studied across a broad set of conditions via Monte Carlo simulations. Finally, the proposed methodology is used to estimate the average effect of carotid endarterectomy versus carotid stenting on the mortality of patients suffering from carotid artery disease. Results suggest that the 2SRI-frailty estimator generally reduces the bias of both point and interval estimators compared to traditional 2SRI.

Mortgage Pricing and Race: Evidence from the Northeast

The putative existence of race-based discrimination in mortgage pricing is both a scholarly and societal concern. Efforts to assess discrimination empirically, however, are typically plagued by omitted variables, which leave any evidence of discrimination open to interpretation. We take a two-pronged approach to the problem. First, we analyze a dataset comprising discretionary mortgage fees collected by brokers working for a brokerage company. Mortgage brokers are intermediaries between lenders and borrowers; they neither approve loans nor share in the risk of default. Variables that measure risk should therefore have no effect on these discretionary fees, and indeed, we show that default risk as measured by credit scores have no effect on discretionary pricing. Second, we perform a formal sensitivity analysis that quantifies the impact of potentially omitted variables. Our results suggest that minority borrowers pay more on average for mortgages than non-minorities, and that this effect persists even in the presence of unmeasured confounders.

Applying Nonparametric Methods to Analyses of Short-Term Fine Particulate Matter Exposure and Hospital Admissions for Cardiovascular Diseases among Older Adults.

Short-term exposure to fine particulate matter (PM2.5) has been associated with increased risks of cardiovascular diseases (CVDs), but whether such associations are supportive of a causal relationship is unclear, and few studies have employed formal causal analysis methods to address this. We employed nonparametric methods to examine the associations between daily concentrations of PM2.5 and hospital admissions (HAs) for CVD among adults aged 75 years and older in Texas, USA. We first quantified the associations in partial dependence plots generated using the random forest approach. We next used a Bayesian network learning algorithm to identify conditional dependencies between CVD HAs of older men and women and several predictor variables. We found that geographic location (county), time (e.g., month and year), and temperature satisfied necessary information conditions for being causes of CVD HAs among older men and women, but daily PM2.5 concentrations did not. We also found that CVD HAs of disjoint subpopulations were strongly predictive of CVD HAs among older men and women, indicating the presence of unmeasured confounders. Our findings from nonparametric analyses do not support PM2.5 as a direct cause of CVD HAs among older adults.

The Selective Labels Problem: Evaluating Algorithmic Predictions in the Presence of Unobservables.

Evaluating whether machines improve on human performance is one of the central questions of machine learning. However, there are many domains where the data is selectively labeled in the sense that the observed outcomes are themselves a consequence of the existing choices of the human decision-makers. For instance, in the context of judicial bail decisions, we observe the outcome of whether a defendant fails to return for their court appearance only if the human judge decides to release the defendant on bail. This selective labeling makes it harder to evaluate predictive models as the instances for which outcomes are observed do not represent a random sample of the population. Here we propose a novel framework for evaluating the performance of predictive models on selectively labeled data. We develop an approach called contraction which allows us to compare the performance of predictive models and human decision-makers without resorting to counterfactual inference. Our methodology harnesses the heterogeneity of human decision-makers and facilitates effective evaluation of predictive models even in the presence of unmeasured confounders (unobservables) which influence both human decisions and the resulting outcomes. Experimental results on real world datasets spanning diverse domains such as health care, insurance, and criminal justice demonstrate the utility of our evaluation metric in comparing human decisions and machine predictions.

Yes, health is important, but as much for its importance via social life: The direct and indirect effects of health on subjective well-being in chronically ill individuals.

There is an increasing evidence that health-related quality of life, income, and social relationships are important to our subjective well-being (SWB). Little is known, however, about the specific indirect pathways that link health to SWB via social relationships and income. On the basis of a unique data set of 7 disease groups from 6 OECD-countries (N=6,173), we investigate the direct and indirect effects of health on SWB by using structural equation modeling. Three alternative measures of health are used: For generic instruments (EQ-5D-5L; SF-6D), the total indirect effect was stronger (0.226; 0.249) than its direct effect (0.157; 0.205). For the visual analogue scale, the direct effect was stronger (0.322) than its total indirect effect (0.179). Most of the indirect effect of improved health on SWB transmitted through social relationships. The effect via income was small. Nevertheless, the presence of unmeasured confounders may bias the estimates. An important lesson for researchers is to include meaningful items on social relationships when measuring the benefits from improved health. An important lesson for policy makers is that social isolation appears to be more detrimental to overall well-being than ill health. Hence, the Health and Care Services should facilitate social arenas for people with chronic conditions.

Instrumental Variable Analyses and Selection Bias.

Instrumental variables (IV) are used to draw causal conclusions about the effect of exposure E on outcome Y in the presence of unmeasured confounders. IV assumptions have been well described: (1) IV affects E; (2) IV affects Y only through E; (3) IV shares no common cause with Y. Even when these assumptions are met, biased effect estimates can result if selection bias allows a noncausal path from E to Y. We demonstrate the presence of bias in IV analyses on a sample from a simulated dataset, where selection into the sample was a collider on a noncausal path from E to Y. By applying inverse probability of selection weights, we were able to eliminate the selection bias. IV approaches may protect against unmeasured confounding but are not immune from selection bias. Inverse probability of selection weights used with IV approaches can minimize bias.

Instrumental Variable Methods for Continuous Outcomes That Accommodate Nonignorable Missing Baseline Values.

Instrumental variable (IV) methods provide unbiased treatment effect estimation in the presence of unmeasured confounders under certain assumptions. To provide valid estimates of treatment effect, treatment effect confounders that are associated with the IV (IV-confounders) must be included in the analysis, and not including observations with missing values may lead to bias. Missing covariate data are particularly problematic when the probability that a value is missing is related to the value itself, which is known as nonignorable missingness. In such cases, imputation-based methods are biased. Using health-care provider preference as an IV method, we propose a 2-step procedure with which to estimate a valid treatment effect in the presence of baseline variables with nonignorable missing values. First, the provider preference IV value is estimated by performing a complete-case analysis using a random-effects model that includes IV-confounders. Second, the treatment effect is estimated using a 2-stage least squares IV approach that excludes IV-confounders with missing values. Simulation results are presented, and the method is applied to an analysis comparing the effects of sulfonylureas versus metformin on body mass index, where the variables baseline body mass index and glycosylated hemoglobin have missing values. Our result supports the association of sulfonylureas with weight gain.

A tutorial on the use of instrumental variables in pharmacoepidemiology.

Instrumental variable (IV) methods are used increasingly in pharmacoepidemiology to address unmeasured confounding. In this tutorial, we review the steps used in IV analyses and the underlying assumptions. We also present methods to assess the validity of those assumptions and describe sensitivity analysis to examine the effects of possible violations of those assumptions. Observational studies based on regression or propensity score analyses rely on the untestable assumption that there are no unmeasured confounders. IV analysis is a tool that removes the bias caused by unmeasured confounding provided that key assumptions (some of which are also untestable) are met. When instruments are valid, IV methods provided unbiased treatment effect estimation in the presence of unmeasured confounders. However, the standard error of the IV estimate is higher than the standard error of non-IV estimates, e.g., regression and propensity score methods. Sensitivity analyses provided insight about the robustness of the IV results to the plausible degrees of violation of assumptions. IV analysis should be used cautiously because the validity of IV estimates relies on assumptions that are, in general, untestable and difficult to be certain about. Thus, assessing the sensitivity of the estimate to violations of these assumptions is important and can better inform the causal inferences that can be drawn from the study. Copyright © 2017 John Wiley & Sons, Ltd.