Marginal structural models and causal inference in epidemiology

In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverse-probability-of-treatment weighted estimators.     

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。     

Marginal structural models application to estimate the effects of antiretroviral therapy in 5 cohorts of HIV seroconverters

OBJECTIVES: Standard methods to evaluate population effectiveness of treatments in observational studies have important limitations to appropriately adjust for time-dependent confounders. In this paper, we describe a recently developed methodological approach, marginal structural models (MSM), and use it to estimate the effectiveness of highly active antiretroviral therapy (HAART) on AIDS or death incidence. SUBJECTS AND METHODS: We analyzed all subjects followed after 1997 as part of the GEMES project (comprised by several cohorts of HIV seroconverters in Spain) and who had not used HAART before the start of follow-up. To estimate the effect of HAART on AIDS or death incidence, we estimated the parameters of a marginal structural Cox model by fitting an inverse probability weighted logistic regression model. The estimation of the weights was based on CD4 count, time since seroconversion, sex, age, transmission category and previous treatment. RESULTS: 917 eligible subjects were followed for an average of 3.4 years and we observed 139 events. 42.1% of the participants received HAART during the study. The estimated rate ratio was 1.01 (95% confidence interval [CI], 0.68-1.49) using a Cox model without covariates and 0.90 (95% CI, 0.61-1.32) using a Cox model with time-dependent covariates. The causal rate ratio estimated for MSM was 0.74, (95% CI, 0.49-1.12). CONCLUSIONS: The beneficial effect of HAART estimated by the MSM, but largely missed by conventional methods, is consistent with the findings of previous randomized studies. The MSM appropriately adjusted for the time-dependent covariate CD4 count, which is both a time-varying confounder and is affected by prior treatment.     

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.     

Estimating the causal effect of zidovudine on CD4 count with a marginal structural model for repeated measures

Even in the absence of unmeasured confounding factors or model misspecification, standard methods for estimating the causal effect of a time-varying treatment on the mean of a repeated measures outcome (for example, GEE regression) may be biased when there are time-dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment. In contrast, the recently developed marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. We describe an MSM for repeated measures that parameterizes the marginal means of counterfactual outcomes corresponding to prespecified treatment regimes. The parameters of MSMs are estimated using a new class of estimators - inverse-probability of treatment weighted estimators. We used an MSM to estimate the effect of zidovudine therapy on mean CD4 count among HIV-infected men in the Multicenter AIDS Cohort Study. We estimated a potential expected increase of 5.4 (95 per cent confidence interval -1.8,12.7) CD4 lymphocytes/l per additional study visit while on zidovudine therapy. We also explain the theory and implementation of MSMs for repeated measures data and draw upon a simple example to illustrate the basic ideas.     

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.     

Marginal structural models for case-cohort study designs to estimate the association of antiretroviral therapy initiation with incident AIDS or death

To estimate the association of antiretroviral therapy initiation with incident acquired immunodeficiency syndrome (AIDS) or death while accounting for time-varying confounding in a cost-efficient manner, the authors combined a case-cohort study design with inverse probability-weighted estimation of a marginal structural Cox proportional hazards model. A total of 950 adults who were positive for human immunodeficiency virus type 1 were followed in 2 US cohort studies between 1995 and 2007. In the full cohort, 211 AIDS cases or deaths occurred during 4,456 person-years. In an illustrative 20% random subcohort of 190 participants, 41 AIDS cases or deaths occurred during 861 person-years. Accounting for measured confounders and determinants of dropout by inverse probability weighting, the full cohort hazard ratio was 0.41 (95% confidence interval: 0.26, 0.65) and the case-cohort hazard ratio was 0.47 (95% confidence interval: 0.26, 0.83). Standard multivariable-adjusted hazard ratios were closer to the null, regardless of study design. The precision lost with the case-cohort design was modest given the cost savings. Results from Monte Carlo simulations demonstrated that the proposed approach yields approximately unbiased estimates of the hazard ratio with appropriate confidence interval coverage. Marginal structural model analysis of case-cohort study designs provides a cost-efficient design coupled with an accurate analytic method for research settings in which there is time-varying confounding.     

Performance of principal scores to estimate the marginal compliers causal effect of an intervention

We examine the properties of principal scores methods to estimate the causal marginal odds ratio of an intervention for compliers in the context of a randomized controlled trial with non‐compliers. The two‐stage estimation approach has been proposed for a linear model by Jo and Stuart (Statistics in Medicine 2009; 28 :2857–2875) under a principal ignorability (PI) assumption. Using a Monte Carlo simulation study, we compared the performance of several strategies to build and use principal score models and the robustness of the method to violations of underlying assumptions, in particular PI. Results showed that the principal score approach yielded unbiased estimates of the causal marginal log odds ratio under PI but that the method was sensitive to violations of PI, which occurs in particular when confounders are omitted from the analysis. For principal score analysis, probability weighting performed slightly better than full matching or 1:1 matching. Concerning the variables to be included in principal score models, the lowest mean squared error was generally obtained when using the true confounders. Using variables associated with the outcome only but not compliance however yielded very similar performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Marginal structural models for estimating the effect of highly active antiretroviral therapy initiation on CD4 cell count

The effect of highly active antiretroviral therapy (HAART) on the evolution of CD4-positive T-lymphocyte (CD4 cell) count among human immunodeficiency virus (HIV)-positive participants was estimated using inverse probability-of-treatment-and-censoring (IPTC)-weighted estimation of a marginal structural model. Of 1,763 eligible participants from two US cohort studies followed between 1996 and 2002, 60 percent initiated HAART. The IPTC-weighted estimate of the difference in mean CD4 cell count at 1 year among participants continuously treated versus those never treated was 71 cells/mm3 (95% confidence interval: 47.5, 94.6), which agrees with the reported results of randomized experiments. The corresponding estimate from a standard generalized estimating equations regression model that included baseline and most recent CD4 cell count and HIV type 1 RNA viral load as regressors was 26 cells/mm3 (95% confidence interval: 17.7, 34.3). These results indicate that nonrandomized studies of HIV treatment need to be analyzed with methods (e.g., IPTC-weighted estimation) that, in contrast to standard methods, appropriately adjust for time-varying covariates that are simultaneously confounders and intermediate variables. The 1-year estimate of 71 cells/mm3 was followed by an estimated continued increase of 29 cells/mm3 per year (estimated effect at 6 years: 216 cells/mm3), providing evidence that the large short-term effect found in randomized experiments persists and continues to improve over 6 years.     

An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies

Relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death. We propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors. The baseline hazard was modelled until 10 years follow-up using parametric continuous functions. Six models including cubic regression splines were considered and the Akaike Information Criterion was used to select the final model. This approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information. Splines were also used to model simultaneously non-linear effects of continuous covariates and time-dependent hazard ratios. This led to a graphical representation of the hazard ratio that can be useful for clinical interpretation. Estimates of these models were obtained by likelihood maximization. We showed that these estimates could be also obtained using standard algorithms for Poisson regression.     

From biographical disruption to biographical reinforcement: the case of HIV-positive men

In-depth interviews were conducted with 44 asymptomatic HIV-positive men infected through homosexual relations or medical treatment for haemophilia. The objective was to better understand interrelations between: the consequences of infection on everyday life; the meanings given to being HIV-positive; and the reconstruction of identities. The consequences for everyday life are examined in relation to: the importance of keeping one's immune status secret; self-imposed restraints and the constraints ensuing from the immune status; and the resources interviewees tapped to cope with their new situation. The meanings given to infection arose as these men reinterpreted their individual and collective pasts. This biographical reconstruction reinforced components of identity that, prior to HIV-infection, had been built around haemophilia or homosexuality. This is what is called biographical reinforcement, a notion developed in relation to biographical disruption.     

Estimating the effect of zidovudine on Kaposi's sarcoma from observational data using a rank preserving structural failure-time model

Researchers commonly express scepticism about using observational data to estimate the effect of a treatment on an outcome the treatment is intended to affect. In this paper, we consider using data from the Multicenter AIDS Cohort Study (MACS) to determine whether zidovudine prevents the development of Kaposi's sarcoma among HIV-positive gay men. Several methodologic issues common to observational data characterized the study: information on potentially important confounders was missing at some study visits; investigators did not always know the time of changes in treatment level, nor the value of confounders at that time, and the censoring process depended strongly on time-varying covariates related to outcome. We describe application to our data of Robins' paradigm for defining, modelling and estimating the effect of a time-varying treatment and show how to modify his approach to deal with the methodologic issues we have mentioned. Further, we demonstrate that relative risk regression is less well equipped to deal with these issues. We compare our results to the findings from randomized trials, and conclude that observational studies may sometimes be useful in evaluating the effect of treatment on an intended outcome. © 1998 John Wiley & Sons, Ltd.     

Risk construction in the reinfection discourses of HIV-positive men

Interviews with HIV-positive gay and bisexual men in Toronto show a widespread attentiveness to the question of HIV reinfection or super-infection as a concern in safer sex decision-making. Examination of HIV reinfection discourses shows how sero-positive men find themselves at the nexus of expert knowledge and responsibilizing trends in relying on, interpreting, and extending medical evidence in constructing risk for self and others. While not an issue that overrides all others, reinfection concerns play a salient role among the reasons mentioned by those practising safe sex, and are often weighed against competing incentives and discourses by those who do not.     

Use of econometric models to estimate expenditure shares

Objective. To investigate the use of regression models to calculate disease-specific shares of medical expenditures.
Data Sources/Study Setting. Medical Expenditure Panel Survey (MEPS), 2000–2003.
Study Design. Theoretical investigation and secondary data analysis.
Data Collection/Extraction Methods. Condition files used to define the presence of 10 medical conditions.
Principal Findings. Incremental effects of conditions on expenditures, expressed as a fraction of total expenditures, cannot generally be interpreted as shares. When the presence of one condition increases treatment costs for another condition, summing condition-specific shares leads to double-counting of expenditures.
Conclusions. Condition-specific shares generated from multiplicative models should not be summed. We provide an algorithm that allows estimates based on these models to be interpreted as shares and summed across conditions.     

A weighting approach to causal effects and additive interaction in case-control studies: marginal structural linear odds models

Estimates of additive interaction from case-control data are often obtained by logistic regression; such models can also be used to adjust for covariates. This approach to estimating additive interaction has come under some criticism because of possible misspecification of the logistic model: If the underlying model is linear, the logistic model will be misspecified. The authors propose an inverse probability of treatment weighting approach to causal effects and additive interaction in case-control studies. Under the assumption of no unmeasured confounding, the approach amounts to fitting a marginal structural linear odds model. The approach allows for the estimation of measures of additive interaction between dichotomous exposures, such as the relative excess risk due to interaction, using case-control data without having to rely on modeling assumptions for the outcome conditional on the exposures and covariates. Rather than using conditional models for the outcome, models are instead specified for the exposures conditional on the covariates. The approach is illustrated by assessing additive interaction between genetic and environmental factors using data from a case-control study.     

Optimal probability weights for estimating causal effects of time-varying treatments with marginal structural Cox models

Marginal structural Cox models have been used to estimate the causal effect of a time-varying treatment on a survival outcome in the presence of time-dependent confounders. These methods rely on the positivity assumption, which states that the propensity scores are bounded away from zero and one. Practical violations of this assumption are common in longitudinal studies, resulting in extreme weights that may yield erroneous inferences. Truncation, which consists of replacing outlying weights with less extreme ones, is the most common approach to control for extreme weights to date. While truncation reduces the variability in the weights and the consequent sampling variability of the estimator, it can also introduce bias. Instead of truncated weights, we propose using optimal probability weights, defined as those that have a specified variance and the smallest Euclidean distance from the original, untruncated weights. The set of optimal weights is obtained by solving a constrained quadratic optimization problem. The proposed weights are evaluated in a simulation study and applied to the assessment of the effect of treatment on time to death among people in Sweden who live with human immunodeficiency virus and inject drugs.     

已知和未知自身感染状况的男男性行为人群HIV阳性者性行为特征分析

近年来男男性行为者(MSM)人群中HIV感染呈上升趋势,与其多性伴、高频次的无保护性行为密切相关;本研究选择北京地区,分别对HIV阳性告知前的MSM和已知自身感染HIV阳性MSM两组群体开展了横断面调查,比较其性行为特征的差异,为开展有效的行为干预和心理支持提供依据.     

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.     

应用受访者驱动抽样估计青岛市男男性行为者人群规模

目的  探索受访者驱动抽样(respondent-driven sampling, RDS)在男男性行为者(men who have sex with men, MSM)人群规模估计中的应用经验并估计青岛市MSM人群规模, 为青岛市艾滋病疫情估计和资源分配提供参考。方法  采用RDS于2022年8-10月招募青岛市MSM参与调查, 收集一般人口学特征及社交网络规模信息。采用RDS Analyst 0.72软件评估RDS招募效果, 通过定性访谈了解青岛市MSM人群参与调查的意愿及其对激励措施的态度, 利用连续抽样人群规模估计法估计青岛市MSM人群规模。结果  共招募671人参与研究, 其中种子10名, 种子所在招募链的人数均>20人, 招募轮次为4~14轮不等。研究对象的年龄组、婚姻状况、受教育程度及户籍地构成在第5~10轮达到均衡, 人口学特征的同质性系数均接近1。10名访谈对象均表示无论是否有激励措施都愿意参与此类调查。连续抽样人群规模估计法基于研究对象自我报告的社交网络规模及基于可见度估计的青岛市MSM人数为分别为80 405~93 410人和69 284~80 236人, 占青岛市成年男性人口的比例分别为1.88%~2.19%和1.62%~1.88%。结论  RDS在MSM人群的招募效果较好, 应用基于RDS的连续抽样人群规模估计法估计的青岛市MSM占当地成年男性人口的比例为1.62%~2.19%。