Testing causal effects in observational survival data using propensity score matching design

Time‐to‐event data are very common in observational studies. Unlike randomized experiments, observational studies suffer from both observed and unobserved confounding biases. To adjust for observed confounding in survival analysis, the commonly used methods are the Cox proportional hazards (PH) model, the weighted logrank test, and the inverse probability of treatment weighted Cox PH model. These methods do not rely on fully parametric models, but their practical performances are highly influenced by the validity of the PH assumption. Also, there are few methods addressing the hidden bias in causal survival analysis. We propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the P‐values to assumptions about unmeasured confounding. Specifically, we apply the paired Prentice‐Wilcoxon (PPW) test or the modified PPW test to the propensity score matched data. Simulation studies show that the PPW‐type test has higher power in situations when the PH assumption fails. For potential hidden bias, we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding, following Rosenbaum's idea for nonsurvival data. For a real data illustration, we apply our method to an observational cohort of chronic liver disease patients from a Mayo Clinic study. The PPW test based on observed data initially shows evidence of a significant treatment effect. But this finding is not robust, as the sensitivity analysis reveals that the P‐value becomes nonsignificant if there exists an unmeasured confounder with a small impact.     

Bayesian sensitivity analysis for unmeasured confounding in observational studies

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.     

Comparing methods for estimation of heterogeneous treatment effects using observational data from health care databases

There is growing interest in using routinely collected data from health care databases to study the safety and effectiveness of therapies in “real‐world” conditions, as it can provide complementary evidence to that of randomized controlled trials. Causal inference from health care databases is challenging because the data are typically noisy, high dimensional, and most importantly, observational. It requires methods that can estimate heterogeneous treatment effects while controlling for confounding in high dimensions. Bayesian additive regression trees, causal forests, causal boosting, and causal multivariate adaptive regression splines are off‐the‐shelf methods that have shown good performance for estimation of heterogeneous treatment effects in observational studies of continuous outcomes. However, it is not clear how these methods would perform in health care database studies where outcomes are often binary and rare and data structures are complex. In this study, we evaluate these methods in simulation studies that recapitulate key characteristics of comparative effectiveness studies. We focus on the conditional average effect of a binary treatment on a binary outcome using the conditional risk difference as an estimand. To emulate health care database studies, we propose a simulation design where real covariate and treatment assignment data are used and only outcomes are simulated based on nonparametric models of the real outcomes. We apply this design to 4 published observational studies that used records from 2 major health care databases in the United States. Our results suggest that Bayesian additive regression trees and causal boosting consistently provide low bias in conditional risk difference estimates in the context of health care database studies.     

因果图模型及其在营养流行病学研究中的应用

不良饮食是慢性非传染性疾病最重要的可控危险因素之一,但通过随机对照试验定量阐明具体饮食因素与健康结局的因果关联面临很多困难。近年来,因果推断的迅速发展为充分利用和发掘观察性研究数据,产生高质量的营养流行病学研究证据提供了有力的理论和方法工具。其中,因果图模型通过整合大量先验知识将复杂的因果关系系统可视化,提供了识别混杂和确定因果效应估计策略的基础框架,基于不同的因果图,可选择调整混杂、工具变量或中介分析等不同的分析策略。本文对因果图模型的思想和各种分析策略的特点及其在营养流行病学研究中的应用进行介绍,旨在促进因果图模型在营养领域的应用,为后续研究提供参考和建议。     

有向无环图在混杂因素识别与控制中的应用及实例分析

观察性研究是流行病学病因研究常用的研究设计,但应用观察性研究进行因果推断时,常由于未经识别、校正的混杂因素的存在,歪曲暴露因素与研究结局之间的真实因果关系。传统混杂因素判断标准在实际应用中不够直观,且有一定局限性,有时甚至出现混杂因素的误判。有向无环图(DAGs)可以直观识别观察性研究中存在的混杂因素,将复杂的因果关系可视化,判断研究中需要校正的最小校正子集,并可避免传统混杂因素判断标准的局限性,结合DAGs还可以指导混杂因素校正方法的选择,在观察性研究中因果推断具有重要指导价值,DAGs在未来的流行病学研究中将有更多的应用。     

Causal inference in survival analysis using pseudo‐observations

Causal inference for non‐censored response variables, such as binary or quantitative outcomes, is often based on either (1) direct standardization (‘G‐formula’) or (2) inverse probability of treatment assignment weights (‘propensity score’). To do causal inference in survival analysis, one needs to address right‐censoring, and often, special techniques are required for that purpose. We will show how censoring can be dealt with ‘once and for all’ by means of so‐called pseudo‐observations when doing causal inference in survival analysis. The pseudo‐observations can be used as a replacement of the outcomes without censoring when applying ‘standard’ causal inference methods, such as (1) or (2) earlier. We study this idea for estimating the average causal effect of a binary treatment on the survival probability, the restricted mean lifetime, and the cumulative incidence in a competing risks situation. The methods will be illustrated in a small simulation study and via a study of patients with acute myeloid leukemia who received either myeloablative or non‐myeloablative conditioning before allogeneic hematopoetic cell transplantation. We will estimate the average causal effect of the conditioning regime on outcomes such as the 3‐year overall survival probability and the 3‐year risk of chronic graft‐versus‐host disease. Copyright © 2017 John Wiley & Sons, Ltd.     

Utility of inverse probability weighting in molecular pathological epidemiology

As one of causal inference methodologies, the inverse probability weighting (IPW) method has been utilized to address confounding and account for missing data when subjects with missing data cannot be included in a primary analysis. The transdisciplinary field of molecular pathological epidemiology (MPE) integrates molecular pathological and epidemiological methods, and takes advantages of improved understanding of pathogenesis to generate stronger biological evidence of causality and optimize strategies for precision medicine and prevention. Disease subtyping based on biomarker analysis of biospecimens is essential in MPE research. However, there are nearly always cases that lack subtype information due to the unavailability or insufficiency of biospecimens. To address this missing subtype data issue, we incorporated inverse probability weights into Cox proportional cause-specific hazards regression. The weight was inverse of the probability of biomarker data availability estimated based on a model for biomarker data availability status. The strategy was illustrated in two example studies; each assessed alcohol intake or family history of colorectal cancer in relation to the risk of developing colorectal carcinoma subtypes classified by tumor microsatellite instability (MSI) status, using a prospective cohort study, the Nurses’ Health Study. Logistic regression was used to estimate the probability of MSI data availability for each cancer case with covariates of clinical features and family history of colorectal cancer. This application of IPW can reduce selection bias caused by nonrandom variation in biospecimen data availability. The integration of causal inference methods into the MPE approach will likely have substantial potentials to advance the field of epidemiology.     

Systematically missing confounders in individual participant data meta‐analysis of observational cohort studies

One difficulty in performing meta‐analyses of observational cohort studies is that the availability of confounders may vary between cohorts, so that some cohorts provide fully adjusted analyses while others only provide partially adjusted analyses. Commonly, analyses of the association between an exposure and disease either are restricted to cohorts with full confounder information, or use all cohorts but do not fully adjust for confounding. We propose using a bivariate random‐effects meta‐analysis model to use information from all available cohorts while still adjusting for all the potential confounders. Our method uses both the fully adjusted and the partially adjusted estimated effects in the cohorts with full confounder information, together with an estimate of their within‐cohort correlation. The method is applied to estimate the association between fibrinogen level and coronary heart disease incidence using data from 154 012 participants in 31 cohorts.^? One hundred and ninety‐nine participants from the original 154 211 withdrew their consent and have been removed from this analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

Sensitivity analysis for unmeasured confounding in principal stratification settings with binary variables

Within causal inference, principal stratification (PS) is a popular approach for dealing with intermediate variables, that is, variables affected by treatment that also potentially affect the response. However, when there exists unmeasured confounding in the treatment arms--as can happen in observational studies--causal estimands resulting from PS analyses can be biased. We identify the various pathways of confounding present in PS contexts and their effects for PS inference. We present model-based approaches for assessing the sensitivity of complier average causal effect estimates to unmeasured confounding in the setting of binary treatments, binary intermediate variables, and binary outcomes. These same approaches can be used to assess sensitivity to unknown direct effects of treatments on outcomes because, as we show, direct effects are operationally equivalent to one of the pathways of unmeasured confounding. We illustrate the methodology using a randomized study with artificially introduced confounding and a sensitivity analysis for an observational study of the effects of physical activity and body mass index on cardiovascular disease.     

匹配在观察性研究中的作用——有向无环图视角

匹配是观察性研究中选择研究对象的一种常用方法,具有控制混杂因素、提高统计效率等作用,但其控制混杂因素的作用在不同观察性研究中并不一致,匹配在队列研究中能够消除匹配变量的混杂偏倚,但在病例对照研究中匹配本身并不能消除混杂偏倚。在匹配性病例对照研究选择匹配变量时,研究者可能并不能准确判断该变量是否为混杂变量,若误将真实情况为非混杂因素的变量进行匹配,则会形成过度匹配,造成统计效率下降或引入难以避免的偏倚或增加工作量等;若将真实情况为混杂因素的变量遗漏不予匹配,则会造成混杂偏倚。有向无环图是一种直观的展示不同流行病学研究设计、变量间复杂因果关系的可视化图形语言。本文从有向无环图视角分析匹配在不同观察性研究设计中的作用、匹配性病例对照研究中欲匹配变量的选择标准制定,为今后流行病学研究设计提供一定的参考建议。     

Addressing positivity violations in causal effect estimation using Gaussian process priors

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.     

Using Propensity Scores for Causal Inference: Pitfalls and Tips

Methods based on propensity score (PS) have become increasingly popular as a tool for causal inference. A better understanding of the relative advantages and disadvantages of the alternative analytic approaches can contribute to the optimal choice and use of a specific PS method over other methods. In this article, we provide an accessible overview of causal inference from observational data and two major PS-based methods (matching and inverse probability weighting), focusing on the underlying assumptions and decision-making processes. We then discuss common pitfalls and tips for applying the PS methods to empirical research and compare the conventional multivariable outcome regression and the two alternative PS-based methods (ie, matching and inverse probability weighting) and discuss their similarities and differences. Although we note subtle differences in causal identification assumptions, we highlight that the methods are distinct primarily in terms of the statistical modeling assumptions involved and the target population for which exposure effects are being estimated.Key words: propensity score, matching, inverse probability weighting, target population     

Interpreting epidemiological evidence: how meta-analysis and causal inference methods are related

Interpreting observational epidemiological evidence can involve both the quantitative method of meta-analysis and the qualitative criteria-based method of causal inference. The relationships between these two methods are examined in terms of the capacity of meta-analysis to contribute to causal claims, with special emphasis on the most commonly used causal criteria: consistency, strength of association, dose-response, and plausibility. Although meta-analysis alone is not sufficient for making causal claims, it can provide a reproducible weighted average of the estimate of effect that seems better than the rules-of-thumb (e.g. majority rules and all-or-none) often used to assess consistency. A finding of statistical heterogeneity, however, need not preclude a conclusion of consistency (e.g. consistently greater than 1.0). For the criteria of strength of association and dose-response, meta-analysis provides more precise estimates, but the causal relevance of these estimates remains a matter of judgement. Finally, meta-analysis may be used to summarize evidence from biological, clinical, and social levels of knowledge, but combining evidence across levels is beyond its current capacity. Meta-analysis has a real but limited role in causal inference, adding to an understanding of some causal criteria. Meta-analysis may also point to sources of confounding or bias in its assessment of heterogeneity.     

The Janus face of statistical adjustment: confounders versus colliders

It has long been established that controlling for confounders is essential to delineate the causal relationship between exposure and disease. For this purpose, statistical adjustment is widely used in observational studies. However, many researchers don’t acknowledge the potential pitfalls of statistical adjustment. The aim of the present paper was to demonstrate that statistical adjustment is a double edged sword. By using numerically identical examples, we show that adjustment for a common consequence of the exposure and the outcome can lead to as much bias as absence of necessary adjustment for a confounder.     

Bias due to participant overlap in two‐sample Mendelian randomization

Mendelian randomization analyses are often performed using summarized data. The causal estimate from a one‐sample analysis (in which data are taken from a single data source) with weak instrumental variables is biased in the direction of the observational association between the risk factor and outcome, whereas the estimate from a two‐sample analysis (in which data on the risk factor and outcome are taken from non‐overlapping datasets) is less biased and any bias is in the direction of the null. When using genetic consortia that have partially overlapping sets of participants, the direction and extent of bias are uncertain. In this paper, we perform simulation studies to investigate the magnitude of bias and Type 1 error rate inflation arising from sample overlap. We consider both a continuous outcome and a case‐control setting with a binary outcome. For a continuous outcome, bias due to sample overlap is a linear function of the proportion of overlap between the samples. So, in the case of a null causal effect, if the relative bias of the one‐sample instrumental variable estimate is 10% (corresponding to an F parameter of 10), then the relative bias with 50% sample overlap is 5%, and with 30% sample overlap is 3%. In a case‐control setting, if risk factor measurements are only included for the control participants, unbiased estimates are obtained even in a one‐sample setting. However, if risk factor data on both control and case participants are used, then bias is similar with a binary outcome as with a continuous outcome. Consortia releasing publicly available data on the associations of genetic variants with continuous risk factors should provide estimates that exclude case participants from case‐control samples.     

Joint mixed‐effects models for causal inference with longitudinal data

Causal inference with observational longitudinal data and time‐varying exposures is complicated due to the potential for time‐dependent confounding and unmeasured confounding. Most causal inference methods that handle time‐dependent confounding rely on either the assumption of no unmeasured confounders or the availability of an unconfounded variable that is associated with the exposure (eg, an instrumental variable). Furthermore, when data are incomplete, validity of many methods often depends on the assumption of missing at random. We propose an approach that combines a parametric joint mixed‐effects model for the study outcome and the exposure with g‐computation to identify and estimate causal effects in the presence of time‐dependent confounding and unmeasured confounding. G‐computation can estimate participant‐specific or population‐average causal effects using parameters of the joint model. The joint model is a type of shared parameter model where the outcome and exposure‐selection models share common random effect(s). We also extend the joint model to handle missing data and truncation by death when missingness is possibly not at random. We evaluate the performance of the proposed method using simulation studies and compare the method to both linear mixed‐ and fixed‐effects models combined with g‐computation as well as to targeted maximum likelihood estimation. We apply the method to an epidemiologic study of vitamin D and depressive symptoms in older adults and include code using SAS PROC NLMIXED software to enhance the accessibility of the method to applied researchers.     

A Bayesian approach to estimating causal vaccine effects on binary post‐infection outcomes

To estimate causal effects of vaccine on post‐infection outcomes, Hudgens and Halloran (2006) defined a post‐infection causal vaccine efficacy estimand VE_I based on the principal stratification framework. They also derived closed forms for the maximum likelihood estimators of the causal estimand under some assumptions. Extending their research, we propose a Bayesian approach to estimating the causal vaccine effects on binary post‐infection outcomes. The identifiability of the causal vaccine effect VE_I is discussed under different assumptions on selection bias. The performance of the proposed Bayesian method is compared with the maximum likelihood method through simulation studies and two case studies — a clinical trial of a rotavirus vaccine candidate and a field study of pertussis vaccination. For both case studies, the Bayesian approach provided similar inference as the frequentist analysis. However, simulation studies with small sample sizes suggest that the Bayesian approach provides smaller bias and shorter confidence interval length. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of logistic regression versus propensity score when the number of events is low and there are multiple confounders

The aim of this study was to use Monte Carlo simulations to compare logistic regression with propensity scores in terms of bias, precision, empirical coverage probability, empirical power, and robustness when the number of events is low relative to the number of confounders. The authors simulated a cohort study and performed 252,480 trials. In the logistic regression, the bias decreased as the number of events per confounder increased. In the propensity score, the bias decreased as the strength of the association of the exposure with the outcome increased. Propensity scores produced estimates that were less biased, more robust, and more precise than the logistic regression estimates when there were seven or fewer events per confounder. The logistic regression empirical coverage probability increased as the number of events per confounder increased. The propensity score empirical coverage probability decreased after eight or more events per confounder. Overall, the propensity score exhibited more empirical power than logistic regression. Propensity scores are a good alternative to control for imbalances when there are seven or fewer events per confounder; however, empirical power could range from 35% to 60%. Logistic regression is the technique of choice when there are at least eight events per confounder.