Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models
This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates...
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doaj-fe06d732bc3549cc97265be5e25b419b2021-09-06T19:40:27ZengDe GruyterJournal of Causal Inference2193-36772193-36852014-09-012214718510.1515/jci-2013-0007Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working ModelsPetersen Maya0Schwab Joshua1Gruber Susan2Blaser Nello3Schomaker Michael4van der Laan Mark5Division of Biostatistics, University of California, Berkeley, CA, USADivision of Biostatistics, University of California, Berkeley, CA, USADepartment of Epidemiology, Harvard School of Public Health, Boston, MA, USAInstitute of Social and Preventive Medicine (ISPM), University of Bern, Bern, SwitzerlandCentre for Infectious Disease Epidemiology & Research, University of Cape Town, Cape Town, South AfricaDivision of Biostatistics, University of California, Berkeley, CA, USAThis paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.https://doi.org/10.1515/jci-2013-0007dynamic regimesemiparametric statistical modeltargeted minimum loss based estimationconfoundingright censoring |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Petersen Maya Schwab Joshua Gruber Susan Blaser Nello Schomaker Michael van der Laan Mark |
spellingShingle |
Petersen Maya Schwab Joshua Gruber Susan Blaser Nello Schomaker Michael van der Laan Mark Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models Journal of Causal Inference dynamic regime semiparametric statistical model targeted minimum loss based estimation confounding right censoring |
author_facet |
Petersen Maya Schwab Joshua Gruber Susan Blaser Nello Schomaker Michael van der Laan Mark |
author_sort |
Petersen Maya |
title |
Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models |
title_short |
Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models |
title_full |
Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models |
title_fullStr |
Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models |
title_full_unstemmed |
Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models |
title_sort |
targeted maximum likelihood estimation for dynamic and static longitudinal marginal structural working models |
publisher |
De Gruyter |
series |
Journal of Causal Inference |
issn |
2193-3677 2193-3685 |
publishDate |
2014-09-01 |
description |
This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart. |
topic |
dynamic regime semiparametric statistical model targeted minimum loss based estimation confounding right censoring |
url |
https://doi.org/10.1515/jci-2013-0007 |
work_keys_str_mv |
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1717768533197193216 |