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.     

Estimating long‐term treatment effects in observational data: A comparison of the performance of different methods under real‐world uncertainty

In the presence of time‐dependent confounding, there are several methods available to estimate treatment effects. With correctly specified models and appropriate structural assumptions, any of these methods could provide consistent effect estimates, but with real‐world data, all models will be misspecified and it is difficult to know if assumptions are violated. In this paper, we investigate five methods: inverse probability weighting of marginal structural models, history‐adjusted marginal structural models, sequential conditional mean models, g‐computation formula, and g‐estimation of structural nested models. This work is motivated by an investigation of the effects of treatments in cystic fibrosis using the UK Cystic Fibrosis Registry data focussing on two outcomes: lung function (continuous outcome) and annual number of days receiving intravenous antibiotics (count outcome). We identified five features of this data that may affect the performance of the methods: misspecification of the causal null, long‐term treatment effects, effect modification by time‐varying covariates, misspecification of the direction of causal pathways, and censoring. In simulation studies, under ideal settings, all five methods provide consistent estimates of the treatment effect with little difference between methods. However, all methods performed poorly under some settings, highlighting the importance of using appropriate methods based on the data available. Furthermore, with the count outcome, the issue of non‐collapsibility makes comparison between methods delivering marginal and conditional effects difficult. In many situations, we would recommend using more than one of the available methods for analysis, as if the effect estimates are very different, this would indicate potential issues with the analyses.     

Approches d’analyse causale en épidémiologie

Epidemiological research is mostly based on observational studies. Whether such studies can provide evidence of causation remains discussed. Several causal analysis methods have been developed in epidemiology. This paper aims at presenting an overview of these methods: graphical models, path analysis and its extensions, and models based on the counterfactual approach, with a special emphasis on marginal structural models. Graphical approaches have been developed to allow synthetic representations of supposed causal relationships in a given problem. They serve as qualitative support in the study of causal relationships. The sufficient-component cause model has been developed to deal with the issue of multicausality raised by the emergence of chronic multifactorial diseases. Directed acyclic graphs are mostly used as a visual tool to identify possible confounding sources in a study. Structural equations models, the main extension of path analysis, combine a system of equations and a path diagram, representing a set of possible causal relationships. They allow quantifying direct and indirect effects in a general model in which several relationships can be tested simultaneously. Dynamic path analysis further takes into account the role of time. The counterfactual approach defines causality by comparing the observed event and the counterfactual event (the event that would have been observed if, contrary to the fact, the subject had received a different exposure than the one he actually received). This theoretical approach has shown limits of traditional methods to address some causality questions. In particular, in longitudinal studies, when there is time-varying confounding, classical methods (regressions) may be biased. Marginal structural models have been developed to address this issue. In conclusion, “causal models”, though they were developed partly independently, are based on equivalent logical foundations. A crucial step in the application of these models is the formulation of causal hypotheses, which will be a basis for all methodological choices. Beyond this step, statistical analysis tools recently developed offer new possibilities to delineate complex relationships, in particular in life course epidemiology.     

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.     

Longitudinal structural mixed models for the analysis of surgical trials with noncompliance

Patient noncompliance complicates the analysis of many randomized trials seeking to evaluate the effect of surgical intervention as compared with a nonsurgical treatment. If selection for treatment depends on intermediate patient characteristics or outcomes, then 'as-treated' analyses may be biased for the estimation of causal effects. Therefore, the selection mechanism for treatment and/or compliance should be carefully considered when conducting analysis of surgical trials. We compare the performance of alternative methods when endogenous processes lead to patient crossover. We adopt an underlying longitudinal structural mixed model that is a natural example of a structural nested model. Likelihood-based methods are not typically used in this context; however, we show that standard linear mixed models will be valid under selection mechanisms that depend only on past covariate and outcome history. If there are underlying patient characteristics that influence selection, then likelihood methods can be extended via maximization of the joint likelihood of exposure and outcomes. Semi-parametric causal estimation methods such as marginal structural models, g-estimation, and instrumental variable approaches can also be valid, and we both review and evaluate their implementation in this setting. The assumptions required for valid estimation vary across approaches; thus, the choice of methods for analysis should be driven by which outcome and selection assumptions are plausible.     

Good Research Practices for Comparative Effectiveness Research: Analytic Methods to Improve Causal Inference from Nonrandomized Studies of Treatment Effects Using Secondary Data Sources: The ISPOR Good Research Practices for Retrospective Database Analysis Task Force Report—Part III

Objectives:  Most contemporary epidemiologic studies require complex analytical methods to adjust for bias and confounding. New methods are constantly being developed, and older more established methods are yet appropriate. Careful application of statistical analysis techniques can improve causal inference of comparative treatment effects from nonrandomized studies using secondary databases. A Task Force was formed to offer a review of the more recent developments in statistical control of confounding.
Methods:  The Task Force was commissioned and a chair was selected by the ISPOR Board of Directors in October 2007. This Report, the third in this issue of the journal, addressed methods to improve causal inference of treatment effects for nonrandomized studies.
Results:  The Task Force Report recommends general analytic techniques and specific best practices where consensus is reached including: use of stratification analysis before multivariable modeling, multivariable regression including model performance and diagnostic testing, propensity scoring, instrumental variable, and structural modeling techniques including marginal structural models, where appropriate for secondary data. Sensitivity analyses and discussion of extent of residual confounding are discussed.
Conclusions:  Valid findings of causal therapeutic benefits can be produced from nonrandomized studies using an array of state-of-the-art analytic techniques. Improving the quality and uniformity of these studies will improve the value to patients, physicians, and policymakers worldwide.     

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.     

Analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules

In this paper, we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials. Unlike a number of methods proposed previously, this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified. In addition, it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously. This is particularly useful if the number of such rules is large, in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer. In addition, such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they immediately give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum. We discuss an inverse-probability-of-treatment-weighted (IPTW) estimator for these causal effect models, which is straightforward to implement using standard statistical software, and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator. The methodology is illustrated in two simulation studies that are intended to mimic an HIV/AIDS trial.     

Who really gets strep sore throat? Confounding and effect modification of a time‐varying exposure on recurrent events

Unmeasured confounding is the fundamental obstacle to drawing causal conclusions about the impact of an intervention from observational data. Typically, covariates are measured to eliminate or ameliorate confounding, but they may be insufficient or unavailable. In the special setting where a transient intervention or exposure varies over time within each individual and confounding is time constant, a different tack is possible. The key idea is to condition on either the overall outcome or the proportion of time in the intervention. These measures can eliminate the unmeasured confounding either by conditioning or by use of a proxy covariate. We evaluate existing methods and develop new models from which causal conclusions can be drawn from such observational data even if no baseline covariates are measured. Our motivation for this work was to determine the causal effect of Streptococcus bacteria in the throat on pharyngitis (sore throat) in Indian schoolchildren. Using our models, we show that existing methods can be badly biased and that sick children who are rarely colonized have a high probability that the Streptococcus bacteria are causing their disease. Published 2016. This article is a U.S. Government work and is in the public domain in the USA     

Weighted causal inference methods with mismeasured covariates and misclassified outcomes

Inverse probability weighting (IPW) estimation has been widely used in causal inference. Its validity relies on the important condition that the variables are precisely measured. This condition, however, is often violated, which distorts the IPW method and thus yields biased results. In this paper, we study the IPW estimation of average treatment effects for settings with mismeasured covariates and misclassified outcomes. We develop estimation methods to correct for measurement error and misclassification effects simultaneously. Our discussion covers a broad scope of treatment models, including typically assumed logistic regression models and general treatment assignment mechanisms. Satisfactory performance of the proposed methods is demonstrated by extensive numerical studies.     

Mediation analysis via potential outcomes models

This paper develops a causal or manipulation model framework for mediation analysis based on the concept of potential outcome. Using this framework, we provide new definitions and measures of mediation. Effects of manipulations are modeled via the linear structural model. Corresponding structural equation models (SEMs), in conjunction with two-stage least-squares estimation and the delta method, are used to perform inference. The methods are applied to data from a study of nursing interventions for postoperative pain. We address the cases of more than two treatment groups, and an interaction among mediators. For the latter, a sensitivity analysis approach to handle unidentified parameters is described. Interpretative advantages of the potential outcomes framework for mediation are emphasized.     

Correcting for non-compliance of repeated binary outcomes in randomized clinical trials: randomized analysis approach

We develop the randomized analysis for repeated binary outcomes with non-compliance. A break randomization-based semi-parametric estimation procedure for both the causal risk difference and the causal risk ratio is proposed for repeated binary data. Although we assume the simple structural models for potential outcomes, we choose to avoid making any assumptions about comparability beyond those implied by randomization at time zero. The proposed methods can incorporate non-compliance information, while preserving the validity of the test of the null hypothesis, and even in the presence of non-random non-compliance can give the estimate of the causal effect that treatment would have if all individuals complied with their assigned treatment. The methods are applied to data from a randomized clinical trial for reduction of febrile neutropenia events among acute myeloid leukaemia patients, in which a prophylactic use of macrophage colony-stimulating factor (M-CSF) was compared to placebo during the courses of intensive chemotherapies.     

Testing concordance of instrumental variable effects in generalized linear models with application to Mendelian randomization

Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerable work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent because of the log‐linear approximation of the logistic function. Optimality of such estimators relative to the well‐known two‐stage least squares estimator and the double‐logistic structural mean model is further discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Causal logistic models for non-compliance under randomized treatment with univariate binary response

We propose a method for estimating the marginal causal log-odds ratio for binary outcomes under treatment non-compliance in placebo-randomized trials. This estimation method is a marginal alternative to the causal logistic approach by Nagelkerke et al. (2000) that conditions on partially unknown compliance (that is, adherence to treatment) status, and also differs from previous approaches that estimate risk differences or ratios in subgroups defined by compliance status. The marginal causal method proposed in this paper is based on an extension of Robins' G-estimation approach for fitting linear or log-linear structural nested models to a logistic model. Comparing the marginal and conditional causal log-odds ratio estimates provides a way of assessing the magnitude of unmeasured confounding of the treatment effect due to treatment non-adherence. More specifically, we show through simulations that under weak confounding, the conditional and marginal procedures yield similar estimates, whereas under stronger confounding, they behave differently in terms of bias and confidence interval coverage. The parametric structures that represent such confounding are not identifiable. Hence, the proof of consistency of causal estimators and corresponding simulations are based on two different models that fully identify the causal effects being estimated. These models differ in the way that compliance is related to potential outcomes, and thus differ in the way that the causal effect is identified. The simulations also show that the proposed marginal causal estimation approach performs well in terms of bias under the different levels of confounding due to non-adherence and under different causal logistic models. We also provide results from the analyses of two data sets further showing how a comparison of the marginal and conditional estimators can help evaluate the magnitude of confounding due to non-adherence.     

Bounding causal effects under uncontrolled confounding using counterfactuals

Common sensitivity analysis methods for unmeasured confounders provide a corrected point estimate of causal effect for each specified set of unknown parameter values. This article reviews alternative methods for generating deterministic nonparametric bounds on the magnitude of the causal effect using linear programming methods and potential outcomes models. The bounds are generated using only the observed table. We then demonstrate how these bound widths may be reduced through assumptions regarding the potential outcomes under various exposure regimens. We illustrate this linear programming approach using data from the Cooperative Cardiovascular Project. These bounds on causal effect under uncontrolled confounding complement standard sensitivity analyses by providing a range within which the causal effect must lie given the validity of the assumptions.     

Causal inference in epidemiological studies with strong confounding

One of the identifiability assumptions of causal effects defined by marginal structural model (MSM) parameters is the experimental treatment assignment (ETA) assumption. Practical violations of this assumption frequently occur in data analysis when certain exposures are rarely observed within some strata of the population. The inverse probability of treatment weighted (IPTW) estimator is particularly sensitive to violations of this assumption; however, we demonstrate that this is a problem for all estimators of causal effects. This is due to the fact that the ETA assumption is about information (or lack thereof) in the data. A new class of causal models, causal models for realistic individualized exposure rules (CMRIER), is based on dynamic interventions. CMRIER generalize MSM, and their parameters remain fully identifiable from the observed data, even when the ETA assumption is violated, if the dynamic interventions are set to be realistic. Examples of such realistic interventions are provided. We argue that causal effects defined by CMRIER may be more appropriate in many situations, particularly those with policy considerations. Through simulation studies, we examine the performance of the IPTW estimator of the CMRIER parameters in contrast to that of the MSM parameters. We also apply the methodology to a real data analysis in air pollution epidemiology to illustrate the interpretation of the causal effects defined by CMRIER.     

Links between causal effects and causal association for surrogacy evaluation in a gaussian setting

Two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed: the causal effects paradigm and the causal association paradigm. Each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker (S) for the true outcome of interest (T). We consider the setting in which S and T are Gaussian and are generated from structural models that include an unobserved confounder. Under the assumed structural models, we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks. We review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework. We demonstrate that there is a similarity, but not exact correspondence between the quantities used to evaluate surrogacy within each framework, and show that the conditions for identifiability of the surrogacy parameters are different from the conditions, which lead to a correspondence of these quantities.     

A structural approach to the familial coaggregation of disorders

The demonstration that 2 disorders coaggregate in families is often the first step in the exploration of genetic factors common to the 2 disorders. Previous methods of analyzing familial coaggregation have used either (1) a typical measure of association (eg, the odds ratio) between a disorder in an individual and another disorder in family members, or (2) a linear structural equation model (SEM). The association method accommodates case-control sampling of families, but may not assess the causal effect of interest because it is not based on an underlying causal model. The SEM method is based on a causal model, but cannot easily accommodate case-control sampling or direct effects of 1 disorder on the other within individuals. We develop a new method of analyzing coaggregation based on directed acyclic graphs. Because this method is a generalization of structural equation models and uses measures of association that accommodate case-control sampling and direct effects, it combines the strengths of both previous methods. In the absence of direct effects between disorders, our approach provides a valid estimate of the causal coaggregation effect. In the presence of direct effects, our approach provides an upper-bound estimate and (assuming additive linear effects of latent familial and nonfamilial factors) a lower-bound estimate of the causal coaggregation effect. For illustration, we applied our method to a family study of binge eating disorder and bipolar disorder.