2019
RP, Kyle; EEM, Moodie; MB, Klein; M, Abrahamowicz
Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators Journal Article
In: American Journal of Epidemiology, 2019.
Abstract | Links | BibTeX | Tags: Causal inference, Fractional polynomials, Marginal structural models, Model misspecification, Splines
@article{RP2019,
title = {Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators},
author = {Kyle RP and Moodie EEM and Klein MB and Abrahamowicz M},
url = {https://pubmed.ncbi.nlm.nih.gov/30649165/},
doi = {10.1093/aje/kwz004},
year = {2019},
date = {2019-06-01},
journal = {American Journal of Epidemiology},
abstract = {Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate Lt and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of Lt when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.},
keywords = {Causal inference, Fractional polynomials, Marginal structural models, Model misspecification, Splines},
pubstate = {published},
tppubtype = {article}
}
Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate Lt and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of Lt when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.
2016
Kyle, Ryan P.; Moodie, Erica E. M.; Klein, Marina B.; Abrahamowicz, Michał
Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models Journal Article
In: American Journal of Epidemiology , 2016.
Abstract | Links | BibTeX | Tags: Causal inference, Marginal structural models, Measurement error, Simulations, Time-varying covariates
@article{Kyle2016,
title = {Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models},
author = {Ryan P. Kyle and Erica E. M. Moodie and Marina B. Klein and Michał Abrahamowicz},
url = {https://www.ncbi.nlm.nih.gov/pubmed/27416840},
doi = {10.1093/aje/kww068},
year = {2016},
date = {2016-08-15},
journal = {American Journal of Epidemiology },
abstract = {Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014.
© The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.},
keywords = {Causal inference, Marginal structural models, Measurement error, Simulations, Time-varying covariates},
pubstate = {published},
tppubtype = {article}
}
Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014.
© The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
© The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
2015
Saarela, Olli; Stephens, David A.; Moodie, Erica E. M.; Klein, Marina B.
On Bayesian estimation of marginal structural models Journal Article
In: Biometrics, 2015.
Abstract | Links | BibTeX | Tags: Bayesian inference, Causal inference, Inverse probability weighting, Longitudinal data, Marginal structural models, Posterior predictive inference, Variance estimation
@article{Saarela2015,
title = {On Bayesian estimation of marginal structural models},
author = {Olli Saarela and David A. Stephens and Erica E. M. Moodie and Marina B. Klein},
url = {https://www.ncbi.nlm.nih.gov/pubmed/25677103},
doi = {10.1111/biom.12269},
year = {2015},
date = {2015-06-15},
journal = {Biometrics},
abstract = {The purpose of inverse probability of treatment (IPT) weighting in estimation of marginal treatment effects is to construct a pseudo-population without imbalances in measured covariates, thus removing the effects of confounding and informative censoring when performing inference. In this article, we formalize the notion of such a pseudo-population as a data generating mechanism with particular characteristics, and show that this leads to a natural Bayesian interpretation of IPT weighted estimation. Using this interpretation, we are able to propose the first fully Bayesian procedure for estimating parameters of marginal structural models using an IPT weighting. Our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities, answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in Bayesian inference of marginal treatment effects. The proposed approach is compared to existing methods in simulated data, and applied to an analysis of the Canadian Co-infection Cohort.
© 2015, The International Biometric Society.},
keywords = {Bayesian inference, Causal inference, Inverse probability weighting, Longitudinal data, Marginal structural models, Posterior predictive inference, Variance estimation},
pubstate = {published},
tppubtype = {article}
}
The purpose of inverse probability of treatment (IPT) weighting in estimation of marginal treatment effects is to construct a pseudo-population without imbalances in measured covariates, thus removing the effects of confounding and informative censoring when performing inference. In this article, we formalize the notion of such a pseudo-population as a data generating mechanism with particular characteristics, and show that this leads to a natural Bayesian interpretation of IPT weighted estimation. Using this interpretation, we are able to propose the first fully Bayesian procedure for estimating parameters of marginal structural models using an IPT weighting. Our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities, answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in Bayesian inference of marginal treatment effects. The proposed approach is compared to existing methods in simulated data, and applied to an analysis of the Canadian Co-infection Cohort.
© 2015, The International Biometric Society.
© 2015, The International Biometric Society.
2014
Moodie, Erica E. M.; Stephens, David A.; Klein, Marina B.
In: Statistics in Medicine, vol. 33, no. 8, pp. 1409-1425, 2014.
Abstract | Links | BibTeX | Tags: Causal inference, Completing risks, Confounding, Failure-time data, Intermediate variables, Inverse-probability weighting, Longitudinal data, Marginal structural models, Multiple-outcome data, Simulation, Survival analysis, Time-dependent confounding
@article{Moodie2014,
title = {A marginal structural model for multiple-outcome survival data:assessing the impact of injection drug use on several causes of death in the Canadian Co-infection Cohort},
author = {Erica E. M. Moodie and David A. Stephens and Marina B. Klein},
url = {https://www.ncbi.nlm.nih.gov/pubmed/24272681},
doi = {10.1002/sim.6043},
year = {2014},
date = {2014-04-15},
journal = {Statistics in Medicine},
volume = {33},
number = {8},
pages = {1409-1425},
abstract = {It is often the case that interest lies in the effect of an exposure on each of several distinct event types. For example, we are motivated to investigate in the impact of recent injection drug use on deaths due to each of cancer, end-stage liver disease, and overdose in the Canadian Co-infection Cohort (CCC). We develop a marginal structural model that permits estimation of cause-specific hazards in situations where more than one cause of death is of interest. Marginal structural models allow for the causal effect of treatment on outcome to be estimated using inverse-probability weighting under the assumption of no unmeasured confounding; these models are particularly useful in the presence of time-varying confounding variables, which may also mediate the effect of exposures. An asymptotic variance estimator is derived, and a cumulative incidence function estimator is given. We compare the performance of the proposed marginal structural model for multiple-outcome data to that of conventional competing risks models in simulated data and demonstrate the use of the proposed approach in the CCC.},
keywords = {Causal inference, Completing risks, Confounding, Failure-time data, Intermediate variables, Inverse-probability weighting, Longitudinal data, Marginal structural models, Multiple-outcome data, Simulation, Survival analysis, Time-dependent confounding},
pubstate = {published},
tppubtype = {article}
}
It is often the case that interest lies in the effect of an exposure on each of several distinct event types. For example, we are motivated to investigate in the impact of recent injection drug use on deaths due to each of cancer, end-stage liver disease, and overdose in the Canadian Co-infection Cohort (CCC). We develop a marginal structural model that permits estimation of cause-specific hazards in situations where more than one cause of death is of interest. Marginal structural models allow for the causal effect of treatment on outcome to be estimated using inverse-probability weighting under the assumption of no unmeasured confounding; these models are particularly useful in the presence of time-varying confounding variables, which may also mediate the effect of exposures. An asymptotic variance estimator is derived, and a cumulative incidence function estimator is given. We compare the performance of the proposed marginal structural model for multiple-outcome data to that of conventional competing risks models in simulated data and demonstrate the use of the proposed approach in the CCC.
[wpcode id=”2390″]