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About 3,349 papers for “Marginal structural model”

Structural Breaks and Model Selection With Marginal Likelihoods

Wolfgang Polasek, Lei Ren · 1997

We consider AR processes with a possible break (regime shifts) at an unknown break point m. We derive the conjugate Bayesian analysis for informative and non-informative priors and allow also for heteroskedasticity in the regimes. Using the model selection approach of Chib (1995) we derive the marginal likelihood for all models with unknown lag length. The approach is also extended for the break point model of VAR processes which is formulated as a multivariate normal-Wishart models. We demonstrate the model selection ability of our approach by a simulated example and for Swiss macro-economic time series involving GNP and consumption. Keywords: marginal likelihood criterion, univariate and multivariate regime shifts, order estimation in AR models, heteroskedasticity 1 Introduction Structural breaks are a frequent feature of macro-economic time series. Many procedures have been suggested to obtain satisfying models for time series with a break point. Popular methods are the CUSUM t...

Cited by 0

A marginal structural model for partial compliance in SMARTs

William J. Artman, Indrabati Bhattacharya, Ashkan Ertefaie et al. · The Annals of Applied Statistics · 2024

The cyclical and heterogeneous nature of many substance use disorders highlights the need to adapt the type and/or the dose of treatment to accommodate the specific and changing needs of individuals. The Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE) is a sequential multiple assignment randomized trial (SMART) that provided longitudinal data for constructing dynamic treatment regimes (DTRs) to improve patients' engagement in therapy. However, the high rate of noncompliance and lack of analytic tools to account for noncompliance has impeded researchers from using the data to achieve the main goal of the trial; namely, construction of individually tailored DTRs. We address this by defining our target parameter as the mean outcome under different DTRs for potential compliance strata and propose a marginal structural model with principal stratification to estimate this quantity. We model the principal strata using a Bayesian semiparametric approach. An important feature of our work is that we consider partial rather than binary compliance strata, which is more relevant in longitudinal studies. We assess the performance of our method through simulation. We illustrate its application on ENGAGE and demonstrate the optimal DTRs depend on compliance strata compared with ignoring compliance information as in intention-to-treat analyses.

Cited by 1Open access

A marginal structural model for normal tissue complication probability

Thai-Son Tang, Zhihui Liu, Ali Hosni et al. · Biostatistics · 2024

The goal of radiation therapy for cancer is to deliver prescribed radiation dose to the tumor while minimizing dose to the surrounding healthy tissues. To evaluate treatment plans, the dose distribution to healthy organs is commonly summarized as dose-volume histograms (DVHs). Normal tissue complication probability (NTCP) modeling has centered around making patient-level risk predictions with features extracted from the DVHs, but few have considered adapting a causal framework to evaluate the safety of alternative treatment plans. We propose causal estimands for NTCP based on deterministic and stochastic interventions, as well as propose estimators based on marginal structural models that impose bivariable monotonicity between dose, volume, and toxicity risk. The properties of these estimators are studied through simulations, and their use is illustrated in the context of radiotherapy treatment of anal canal cancer patients.

Cited by 0Open access

A marginal structural model for normal tissue complication probability

Thai-Son Tang, Zhihui Liu, Ali Hosni et al. · arXiv (Cornell University) · 2023

The goal of radiation therapy for cancer is to deliver prescribed radiation dose to the tumor while minimizing dose to the surrounding healthy tissues. To evaluate treatment plans, the dose distribution to healthy organs is commonly summarized as dose-volume histograms (DVHs). Normal tissue complication probability (NTCP) modelling has centered around making patient-level risk predictions with features extracted from the DVHs, but few have considered adapting a causal framework to evaluate the safety of alternative treatment plans. We propose causal estimands for NTCP based on deterministic and stochastic interventions, as well as propose estimators based on marginal structural models that impose bivariable monotonicity between dose, volume, and toxicity risk. The properties of these estimators are studied through simulations, and their use is illustrated in the context of radiotherapy treatment of anal canal cancer patients.

Cited by 0Open access

An Application of Model-Fitting Procedures for Marginal Structural Models

Kathleen Mortimer, Romain Neugebauer, Mark van der Laan et al. · American Journal of Epidemiology · 2005

Marginal structural models (MSMs) are being used more frequently to obtain causal effect estimates in observational studies. Although the principal estimator of MSM coefficients has been the inverse probability of treatment weight (IPTW) estimator, there are few published examples that illustrate how to apply IPTW or discuss the impact of model selection on effect estimates. The authors applied IPTW estimation of an MSM to observational data from the Fresno Asthmatic Children's Environment Study (2000-2002) to evaluate the effect of asthma rescue medication use on pulmonary function and compared their results with those obtained through traditional regression methods. Akaike's Information Criterion and cross-validation methods were used to fit the MSM. In this paper, the influence of model selection and evaluation of key assumptions such as the experimental treatment assignment assumption are discussed in detail. Traditional analyses suggested that medication use was not associated with an improvement in pulmonary function--a finding that is counterintuitive and probably due to confounding by symptoms and asthma severity. The final MSM estimated that medication use was causally related to a 7% improvement in pulmonary function. The authors present examples that should encourage investigators who use IPTW estimation to undertake and discuss the impact of model-fitting procedures to justify the choice of the final weights.

Cited by 108Open access

Doubly robust estimation under a possibly misspecified marginal structural Cox model

Jiyu Luo, Denise Rava, Jelena Bradić et al. · Biometrika · 2024

Summary In this article we consider the marginal structural Cox model, which has been widely used to analyse observational studies with survival outcomes. The standard inverse probability weighting method under the model hinges on a propensity score model for the treatment assignment and a censoring model that incorporates both the treatment and the covariates. In such settings model misspecification can often occur, and the Cox regression model’s non-collapsibility has historically posed challenges when striving to guard against model misspecification through augmentation. We introduce a novel joint augmentation to the martingale-based full-data estimating functions and develop rate double robustness, which allows the use of machine learning and nonparametric methods to overcome the challenges of non-collapsibility. We closely examine its theoretical properties to guarantee root-$ n $ inference for the estimand. The estimator extends naturally to estimating a time-average treatment effect when the proportional hazards assumption fails, and we show that it satisfies both the assumption-lean and the well-specification criteria in the context of a causal estimand for censoring survival data; that is, it is a functional of the potential outcome distributions only and does not depend on the treatment assignment mechanism, the covariate distribution or the censoring mechanism. The martingale-based augmentation approach is also applicable to many semiparametric failure time models. Finally, its application to a dataset provides insights into the impact of mid-life alcohol consumption on mortality in later life.

Cited by 5Open access

The Effect of Serious Offending on Health: A Marginal Structural Model

Baćak, Valerio, Karim, Mohammad Ehsanul · Sage Journals Data · 2018

In this study, we contribute to the emerging scholarship at the intersection of crime and health by estimating the effect of serious offending on offenders’ health. By building on sociological stress research, we identify and adjust for the key life course processes that may intervene on the pathway from offending to health using a rich set of measures available in the panel data from the National Longitudinal Study of Adolescent to Adult Health. Because offending and health share many causes and consequences, a critical challenge is accounting for confounding and mediation that unfold over time. We adjust for these time-varying processes by estimating repeated measures marginal structural models with inverse probability of treatment weights. The results show that offending over the life course is adversely linked to health but not uniformly across race and gender.

Cited by 0Open access

Marginal structural Cox proportional hazards model for data with measurement errors

Ming Geng · D-Scholarship@Pitt (University of Pittsburgh) · 2015

In causal inference, interest often lies in estimating the joint effect of treatment on outcome at different time points. Marginal structural models are particularly useful for this purpose when a time-dependent confounder exists in the causal path between the treatment assigned in the previous time and the outcome. These models provide a consistent estimate when treatment is measured perfectly. In practice however, treatment may be subject to measurement error. Many studies have shown that measurement error in treatment can result in underestimating its effect. One approach proposed in the literature for correcting this problem is the marginal structural measurement-error model. It requires using a validation data set in which both the true treatment and the observed treatment are available to correct the bias. In this study, we developed a new method which combines the marginal structural Cox proportional hazards model, the regression calibration method, and the Bayesian method to account for measurement error in treatment without the need for a validation data set. Moreover, instead of fitting a traditional pooled logistic regression model, a weighted Cox proportional hazards model is implemented to reduce bias. The performance of our proposed method was assessed through the simulation study. Our simulation results show that the bias is reduced even with an approximate value of the parameter of the prior distribution. Our sensitivity analysis also shows that the estimated treatment effect is robust to the choice of the prior distribution. We applied our proposed method to estimate the effect of highly active antiretroviral therapy on the incidence of acquired immune deficiency syndrome or death among HIV-positive patients using a data set in which the observed treatment assignment was subject to misclassification. Public Health Significance: Measurement errors can happen in medical studies despite good intentions. In general, either a validation data set or the replicates of the observed predictor are needed to correct for bias in estimation. Our study provides a new method in causal inference for correcting bias caused by measurement errors when investigators only have the main data set in which the observed treatment is measured only once at each time point.

Cited by 0Open access

Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model

Michael Rosenblum, Mark J. van der Laan · The International Journal of Biostatistics · 2010

Targeted maximum likelihood estimation is a versatile tool for estimating parameters in semiparametric and nonparametric models. We work through an example applying targeted maximum likelihood methodology to estimate the parameter of a marginal structural model. In the case we consider, we show how this can be easily done by clever use of standard statistical software. We point out differences between targeted maximum likelihood estimation and other approaches (including estimating function based methods). The application we consider is to estimate the effect of adherence to antiretroviral medications on virologic failure in HIV positive individuals.

Cited by 68Open access

CoxAIPW: Doubly Robust Inference for Cox Marginal Structural Model with Informative Censoring

Jiyu Luo, Dennis Rava, Ronghui Xu · 2023

Doubly robust estimation and inference of log hazard ratio under the Cox marginal structural model with informative censoring. An augmented inverse probability weighted estimator that involves 3 working models, one for conditional failure time T, one for conditional censoring time C and one for propensity score. Both models for T and C can depend on both a binary treatment A and additional baseline covariates Z, while the propensity score model only depends on Z. With the help of cross-fitting techniques, achieves the rate-doubly robust property that allows the use of most machine learning or non-parametric methods for all 3 working models, which are not permitted in classic inverse probability weighting or doubly robust estimators. When the proportional hazard assumption is violated, CoxAIPW estimates a causal estimated that is a weighted average of the time-varying log hazard ratio. Reference: Luo, J. (2023). Statistical Robustness - Distributed Linear Regression, Informative Censoring, Causal Inference, and Non-Proportional Hazards [Unpublished doctoral dissertation]. University of California San Diego.; Luo &amp; Xu (2022) &lt;<a href="https://doi.org/10.48550%2FarXiv.2206.02296" target="_top">doi:10.48550/arXiv.2206.02296</a>&gt;; Rava (2021) &lt;<a href="https://escholarship.org/uc/item/8h1846gs" target="_top">https://escholarship.org/uc/item/8h1846gs</a>&gt;.

Cited by 0Open access

Risk Factor Adjustment in Marginal Structural Model Estimation of Optimal Treatment Regimes

Erica E. M. Moodie · Biometrical Journal · 2009

Marginal structural models (MSMs) are an increasingly popular tool, particularly in epidemiological applications, to handle the problem of time-varying confounding by intermediate variables when studying the effect of sequences of exposures. Considerable attention has been devoted to the optimal choice of treatment model for propensity score-based methods and, more recently, to variable selection in the treatment model for inverse weighting in MSMs. However, little attention has been paid to the modeling of the outcome of interest, particularly with respect to the best use of purely predictive, non-confounding variables in MSMs. Four modeling approaches are investigated in the context of both static treatment sequences and optimal dynamic treatment rules with the goal of estimating a marginal effect with the least error, both in terms of bias and variability.

Cited by 8

Accuracy of Conventional and Marginal Structural Cox Model Estimators: A Simulation Study

Yongling Xiao, Michał Abrahamowicz, Erica E. M. Moodie · The International Journal of Biostatistics · 2010

Marginal structural models (MSM) provide a powerful tool to control for confounding by a time-dependent covariate without inappropriately adjusting for its role as a variable affected by treatment (Hernán et al., 2000). In this paper, we demonstrate that it is possible to fit a marginal structural Cox model directly, rather than the typical approach of using pooled logistic regression, using the weighted Cox proportional hazards function that has been implemented in standard software. To evaluate the performance of the marginal structural Cox model directly via inverse probability of treatment weighting, we conducted several simulation studies based on two data-generating models: one which replicates the simulations of Young et al. (2009) and an additional, more clinically plausible approach which mimics survival data with time-dependent confounders and time-varying treatment. Using the simulations, we illustrate the limitations of the conventional time-dependent Cox model and the MSM fitted via pooled logistic regression. Furthermore, we propose two novel normalized weights with the goal of reducing the MSM estimators' variability. The performance of the normalized weights is evaluated alongside the usual unstabilized and stabilized weights.

Cited by 81Open access

Impact of mis‐specification of the treatment model on estimates from a marginal structural model

Geneviève Lefebvre, Joseph A. Delaney, Robert W. Platt · Statistics in Medicine · 2008

Inverse probability of treatment weighted (IPTW) estimation for marginal structural models (MSMs) requires the specification of a nuisance model describing the conditional relationship between treatment allocation and confounders. However, there is still limited information on the best strategy for building these treatment models in practice. We developed a series of simulations to systematically determine the effect of including different types of candidate variables in such models. We explored the performance of IPTW estimators across several scenarios of increasing complexity, including one designed to mimic the complexity typically seen in large pharmacoepidemiologic studies.Our results show that including pure predictors of treatment (i.e. not confounders) in treatment models can lead to estimators that are biased and highly variable, particularly in the context of small samples. The bias and mean-squared error of the MSM-based IPTW estimator increase as the complexity of the problem increases. The performance of the estimator is improved by either increasing the sample size or using only variables related to the outcome to develop the treatment model. Estimates of treatment effect based on the true model for the probability of treatment are asymptotically unbiased.We recommend including only pure risk factors and confounders in the treatment model when developing an IPTW-based MSM.

Cited by 65

Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures

Babette Brumback, Miguel A. Hernán, Sebastien Haneuse et al. · Statistics in Medicine · 2004

Robins introduced marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators for the causal effect of a time-varying treatment on the mean of repeated measures. We investigate the sensitivity of IPTW estimators to unmeasured confounding. We examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user-specified function. We present augmented IPTW estimators of MSM parameters and prove their consistency for the causal effect of an MSM, assuming a correct confounding bias function for unmeasured confounding. We apply the methods to assess sensitivity of the analysis of Hernán et al., who used an MSM to estimate the causal effect of zidovudine therapy on repeated CD4 counts among HIV-infected men in the Multicenter AIDS Cohort Study. Under the assumption of no unmeasured confounders, a 95 per cent confidence interval for the treatment effect includes zero. We show that under the assumption of a moderate amount of unmeasured confounding, a 95 per cent confidence interval for the treatment effect no longer includes zero. Thus, the analysis of Hernán et al. is somewhat sensitive to unmeasured confounding. We hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications.

Cited by 207