Marginal structural models for analyzing causal effects of time-dependent treatments: an application in perinatal epidemiology

Marginal structural models (MSMs) are causal models designed to adjust for time-dependent confounding in observational studies of time-varying treatments. MSMs are powerful tools for assessing causality with complicated, longitudinal data sets but have not been widely used by practitioners. The objective of this paper is to illustrate the fitting of an MSM for the causal effect of iron supplement use during pregnancy (time-varying treatment) on odds of anemia at delivery in the presence of time-dependent confounding. Data from pregnant women enrolled in the Iron Supplementation Study (Raleigh, North Carolina, 1997-1999) were used. The authors highlight complexities of MSMs and key issues epidemiologists should recognize before and while undertaking an analysis with these methods and show how such methods can be readily interpreted in existing software packages, including SAS and Stata. The authors emphasize that if a data set with rich information on confounders is available, MSMs can be used straightforwardly to make robust inferences about causal effects of time-dependent treatments/exposures in epidemiologic research.     

Causation and causal inference in epidemiology

Concepts of cause and causal inference are largely self-taught from early learning experiences. A model of causation that describes causes in terms of sufficient causes and their component causes illuminates important principles such as multi-causality, the dependence of the strength of component causes on the prevalence of complementary component causes, and interaction between component causes. Philosophers agree that causal propositions cannot be proved, and find flaws or practical limitations in all philosophies of causal inference. Hence, the role of logic, belief, and observation in evaluating causal propositions is not settled. Causal inference in epidemiology is better viewed as an exercise in measurement of an effect rather than as a criterion-guided process for deciding whether an effect is present or not.     

Regression methods and causal inference: structural equations models

The estimate of correlations among observed outcomes is crucial in biomedical research, especially when the aim of the study is to infer, from the magnitude of these correlations, the causal influence of certain, sometimes latent, factors. In such situations, a typical regression approach, known as "structural equation models" (SEM), which was introduced in the 1970s, becomes significant. These models allow hypotheses to be formulated quite clearly, thanks to some explicit and rigorous graphical representations, on which the "path analysis" is based. SEM, which were initially used in economics, have in the past decade been applied in a wide variety of fields, especially in genetic epidemiology. It's in this field that SEM are extraordinarily effective, representing a simple yet powerful means of estimating the contribution of genes and the environment to the phenotypic expression of a given disease. To this end, data on twins are particularly useful, and in this case the correlation between the outcomes describes the extent of similarity of the twin phenotypes. From this standpoint, SEM undoubtedly constitute one of the most promising statistical tools for family studies and quantitative genetic research. The method can be easily extended to traditional epidemiology, and some interesting applications have already been developed in occupational and social epidemiology. In this paper, we describe in detail the SEM approach and discuss the use of these models in genetic epidemiology, using twin studies as an example. We also discuss the application of SEM in fields other than genetic research.     

Marginal structural models for skewed outcomes: identifying causal relationships in health care utilization

Evaluating the impacts of clinical or policy interventions on health care utilization requires addressing methodological challenges for causal inference while also analyzing highly skewed data. We examine the impact of registering with a Family Medicine Group, an integrated primary care model in Quebec, on hospitalization and emergency department visits using propensity scores to adjust for baseline characteristics and marginal structural models to account for time‐varying exposures. We also evaluate the performance of different marginal structural generalized linear models in the presence of highly skewed data and conduct a simulation study to determine the robustness of alternative generalized linear models to distributional model mis‐specification. Although the simulations found that the zero‐inflated Poisson likelihood performed the best overall, the negative binomial likelihood gave the best fit for both outcomes in the real dataset. Our results suggest that registration to a Family Medicine Group for all 3 years caused a small reduction in the number of emergency room visits and no significant change in the number of hospitalizations in the final year. Copyright © 2013 John Wiley & Sons, Ltd.     

Individual causal models and population system models in epidemiology.

A group of individuals behaves as a population system when patterns of connections among individuals influence population health outcomes. Epidemiology usually treats populations as collections of independent individuals rather than as systems of interacting individuals. An appropriate theoretical structure, which includes the determinants of connections among individuals, is needed to develop a "population system epidemiology." Infection transmission models and sufficient-component cause models provide contrasting templates for the needed theoretical structure. Sufficient-component cause models focus on joint effects of multiple exposures in individuals. They handle time and interactions between individuals in the definition of variables and assume that populations are the sum of their individuals. Transmission models, in contrast, model interactions among individuals over time. Their nonlinear structure means that population risks are not simply the sum of individual risks. The theoretical base for "population system epidemiology" should integrate both approaches. It should model joint effects of multiple exposures in individuals as time related processes while incorporating the determinants and effects of interactions among individuals. Recent advances in G-estimation and discrete individual transmission model formulation provide opportunities for such integration.     

Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men

Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.     

On the use of discrete choice models for causal inference

Methodology for causal inference based on propensity scores has been developed and popularized in the last two decades. However, the majority of the methodology has concentrated on binary treatments. Only recently have these methods been extended to settings with multi-valued treatments. We propose a number of discrete choice models for estimating the propensity scores. The models differ in terms of flexibility with respect to potential correlation between treatments, and, in turn, the accuracy of the estimated propensity scores. We present the effects of discrete choice models used on performance of the causal estimators through a Monte Carlo study. We also illustrate the use of discrete choice models to estimate the effect of antipsychotic drug use on the risk of diabetes in a cohort of adults with schizophrenia.     

Marginal structural models as a tool for standardization

In this article, we show the general relation between standardization methods and marginal structural models. Standardization has been recognized as a method to control confounding and to estimate causal parameters of interest. Because standardization requires stratification by confounders, the sparse-data problem will occur when stratified by many confounders and one then might have an unstable estimator. A new class of causal models called marginal structural models has recently been proposed. In marginal structural models, the parameters are consistently estimated by the inverse-probability-of-treatment weighting method. Marginal structural models give a nonparametric standardization using the total group (exposed and unexposed) as the standard. In epidemiologic analysis, it is also important to know the change in the average risk of the exposed (or the unexposed) subgroup produced by exposure, which corresponds to the exposed (or the unexposed) group as the standard. We propose modifications of the weights in the marginal structural models, which give the nonparametric estimation of standardized parameters. With the proposed weights, we can use the marginal structural models as a useful tool for the nonparametric multivariate standardization.     

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.     

The (mis)estimation of neighborhood effects: causal inference for a practicable social epidemiology

The resurgence of interest in the effect of neighborhood contexts on health outcomes, motivated by advances in social epidemiology, multilevel theories and sophisticated statistical models, too often fails to confront the enormous methodological problems associated with causal inference. This paper employs the counterfactual causal framework to illuminate fundamental obstacles in the identification, explanation, and usefulness of multilevel neighborhood effect studies. We show that identifying useful independent neighborhood effect parameters, as currently conceptualized with observational data, to be impossible. Along with the development of a dependency-based methodology and theories of social interaction, randomized community trials are advocated as a superior research strategy, one that may help social epidemiology answer the causal questions necessary for remediating disparities and otherwise improving the public's health.     

分布式循证因果数据融合方法进展

为了实现大样本量和多样化的研究人群分析,整合来自多个异质来源的数据库已经变得越来越流行。本文综述了整合多个不同人群下的不同设计的数据库在因果推理方法方面的进展。尤其是随机临床试验与外部信息相结合的研究进展以及将观察性研究和历史对照相结合的方法。此外,针对单一样本缺乏相关混杂变量信息,也可以应用两样本孟德尔随机化方法控制未知的混杂因素从而推断因果关系。这种分布式数据设计具有有效性和真实世界数据研究的安全性。     

Compound treatments and transportability of causal inference

Ill-defined causal questions present serious problems for observational studies-problems that are largely unappreciated. This paper extends the usual counterfactual framework to consider causal questions about compound treatments for which there are many possible implementations (for example, "prevention of obesity"). We describe the causal effect of compound treatments and their identifiability conditions, with a special emphasis on the consistency condition. We then discuss the challenges of using the estimated effect of a compound treatment in one study population to inform decisions in the same population and in other populations. These challenges arise because the causal effect of compound treatments depends on the distribution of the versions of treatment in the population. Such causal effects can be unpredictable when the versions of treatment are unknown. We discuss how such issues of "transportability" are related to the consistency condition in causal inference. With more carefully framed questions, the results of epidemiologic studies can be of greater value to decision-makers.     

Instrumental variable methods for causal inference

A goal of many health studies is to determine the causal effect of a treatment or intervention on health outcomes. Often, it is not ethically or practically possible to conduct a perfectly randomized experiment, and instead, an observational study must be used. A major challenge to the validity of observational studies is the possibility of unmeasured confounding (i.e., unmeasured ways in which the treatment and control groups differ before treatment administration, which also affect the outcome). Instrumental variables analysis is a method for controlling for unmeasured confounding. This type of analysis requires the measurement of a valid instrumental variable, which is a variable that (i) is independent of the unmeasured confounding; (ii) affects the treatment; and (iii) affects the outcome only indirectly through its effect on the treatment. This tutorial discusses the types of causal effects that can be estimated by instrumental variables analysis; the assumptions needed for instrumental variables analysis to provide valid estimates of causal effects and sensitivity analysis for those assumptions; methods of estimation of causal effects using instrumental variables; and sources of instrumental variables in health studies. Copyright © 2014 John Wiley & Sons, Ltd.     

因果推断中研究人群的形成

流行病学是对一定数量的人群进行特征描述和比较,并在此基础上进行因果推断。研究人群的形成是其第一步。本研究以观察性研究为例,首先定义个体截面和人群截面,并阐明其测量需满足的3个假设：属性真实值随时间保持不变,属性变量间互不干扰,个体间互不干扰;接着指出因果推断研究应以待定因（或暴露）的发生或状态开始的时间为标准进行统一;...     

Marginal structural models might overcome confounding when analyzing multiple treatment effects in observational studies

OBJECTIVE: We review marginal structural models (MSMs) and show how they are useful when comparing the effects of multiple treatments on outcomes in observational studies. Until now, MSMs have not been used to compare the effects of more than two treatments. STUDY DESIGN AND SETTING: To illustrate the application of MSMs when patients may receive several treatments, we have reanalyzed the effects of antipsychotic medication on achieving remission in schizophrenia using data from the SOHO study, a 3-year observational study of health outcomes associated with the treatment of schizophrenia. RESULTS: The MSM results were, in general, consistent with but less statistically significant than those obtained using conventional methods. The MSM also showed qualitative differences in some comparisons in which the conventional analysis obtained results that were not consistent with previous knowledge. CONCLUSION: MSMs can be used to analyze multiple treatment effects. MSMs, by using inverse-probability of treatment weights, might provide a better control for confounding than conventional methods by improving the adjustment for treatment group differences in observational studies, which may approximate their results to those of randomized controlled trials.     

基于分层四格表资料的边际结构模型分析方法及其SAS实现

目的：结合病例对照研究中的分层四格表资料,介绍边际结构模型的思想,探索边际结构模型的分析方法。方法利用“处理倒数概率加权”的方法,使“原初人群”经过“补实”后,获得“虚拟人群”,经过Mantel-Haenszel 估计,计算ORMH值,并计算未经分层的cOR,比较ORMH与cOR的差异。结果边际结构模型的分析结果与Mantel-Haenszel估计的分析结果基本一致。结论边际结构模型为我们解决上述问题提供了一种全新的思路。     

Heuristic thinking and inference from observational epidemiology

Epidemiologic research is an exercise in measurement. Observational epidemiologic results usually include a point estimate, a measure of random error such as a frequentist confidence interval, and a qualitative discussion of study limitations. Without randomization of study subjects to exposure groups, inference from study results requires an educated guess about the strength of the systematic errors compared with the strength of the exposure effects. Although quantitative methods to make these educated guesses exist, the conventional approach is qualitative, which reduces the educated guessing to a problem of reasoning under uncertainty. In circumstances such as these, humans predictably reason poorly. Heuristics and resulting biases that simplify the judgmental tasks tend to underestimate the systematic error, underestimate the uncertainty, and focus the inference on the study's specific evidence while excluding countervailing external information. Common warnings to interpret results with trepidation are an ineffective solution. The methods that quantify systematic error and uncertainty challenge the analyst to specify the alternative explanations for associations that are otherwise too readily judged causal.