A cautionary note concerning the use of stabilized weights in marginal structural models

Talbot, Denis; Atherton, Juli; Rossi, Antônio; Bacon, Simon; Lefebvre, Geneviève

doi:10.1002/sim.6378

Cited by 12 publications

(12 citation statements)

References 17 publications

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“…This scenario is taken from the work of Talbot et al The relationships between the variables are as follows:

\begin{matrix} alignleft \\ align-1 & align-2 L_{1} \sim N (0, 1), \\ align-1 & align-2 P (X_{1} = 1) = expit (0.5 L_{1}) \\ align-1 & align-2 L_{1}^{'} = X_{1} + L_{1} + ε_{L_{1}^{'}} \\ align-1 & align-2 L_{2} = 0.5 X_{1} + ε_{L_{2}} \\ align-1 & align-2 P (X_{2} = 1) = expit (0.5 X_{1} + 0.5 L_{1}^{'} + 0.5 L_{2}) \\ align-1 & align-2 Y = X_{2} + 0.5 L_{1} + L_{2} + ε_{Y}, \end{matrix}

where

expit false(a false) = \frac{e^{a}}{1 + e^{a}}

ε_{L_{1}}, ε_{L_{1}^{'}}, ε_{L_{2}}, ε_{Y}

are

scriptN false(0, 1 false)

independent random variables. In this scenario, the standard, stabilized and marginal stabilized weights are defined as

\begin{matrix} alignleft \\ align-1 w_{i} & align-2 = 1 ... \end{matrix}

…”

Section: Simulation Studymentioning

confidence: 99%

“…The specification of the structural outcome model, which links the outcome to the exposure history, has been the subject of much methodological work during the last few years. For instance, it has been observed that biased inferences may be obtained when the model considers only a part of the exposure history . It has also been suggested that employing a marginal stabilized weight IPTW estimator may provide some robustness to misspecifications in this instance .…”

Section: Introductionmentioning

confidence: 99%

“…For instance, it has been observed that biased inferences may be obtained when the model considers only a part of the exposure history . It has also been suggested that employing a marginal stabilized weight IPTW estimator may provide some robustness to misspecifications in this instance . Platt et al have proposed an information criterion for MSMs ( QIC w ) inspired by Akaike's information criterion to help in selecting a best fitting model among a set of candidate specifications for the structural outcome model .…”

Section: Introductionmentioning

confidence: 99%

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A test for the correct specification of marginal structural models

Sall

Aubé

Trudel

et al. 2019

Statistics in Medicine

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Marginal structural models (MSMs) allow estimating the causal effect of a time-varying exposure on an outcome in the presence of time-dependent confounding. The parameters of MSMs can be estimated utilizing an inverse probability of treatment weight estimator under certain assumptions. One of these assumptions is that the proposed causal model relating the outcome to exposure history is correctly specified. However, in practice, the true model is unknown.We propose a test that employs the observed data to attempt validating the assumption that the model is correctly specified. The performance of the proposed test is investigated with a simulation study. We illustrate our approach by estimating the effect of repeated exposure to psychosocial stressors at work on ambulatory blood pressure in a large cohort of white-collar workers in Québec City, Canada. Code examples in SAS and R are provided to facilitate the implementation of the test. KEYWORDS causal inference, marginal structural models, model specification Abbreviations: ABP, ambulatory blood pressure; IPTW, inverse probability of treatment weight; MSMs, marginal structural models. 3168

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“…This scenario is taken from the work of Talbot et al The relationships between the variables are as follows:

\begin{matrix} alignleft \\ align-1 & align-2 L_{1} \sim N (0, 1), \\ align-1 & align-2 P (X_{1} = 1) = expit (0.5 L_{1}) \\ align-1 & align-2 L_{1}^{'} = X_{1} + L_{1} + ε_{L_{1}^{'}} \\ align-1 & align-2 L_{2} = 0.5 X_{1} + ε_{L_{2}} \\ align-1 & align-2 P (X_{2} = 1) = expit (0.5 X_{1} + 0.5 L_{1}^{'} + 0.5 L_{2}) \\ align-1 & align-2 Y = X_{2} + 0.5 L_{1} + L_{2} + ε_{Y}, \end{matrix}

where

expit false(a false) = \frac{e^{a}}{1 + e^{a}}

ε_{L_{1}}, ε_{L_{1}^{'}}, ε_{L_{2}}, ε_{Y}

are

scriptN false(0, 1 false)

independent random variables. In this scenario, the standard, stabilized and marginal stabilized weights are defined as

\begin{matrix} alignleft \\ align-1 w_{i} & align-2 = 1 ... \end{matrix}

…”

Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A test for the correct specification of marginal structural models

Sall

Aubé

Trudel

et al. 2019

Statistics in Medicine

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“…As an example, let us consider a simple marginal structural model y (Platt et al 2013, Talbot et al 2015, where y (h) i is a potential outcome for the i-th sample with the treatment x (h) , t (h) i is an indicator which is 1 if the treatment x (h) is received and 0 otherwise, and ε i is an error. In this model, y (Rosenbaum and Rubin 1983) is commonly used.…”

Section: Introductionmentioning

confidence: 99%

A $C_p$ criterion for semiparametric causal inference

Baba

Kanemori²,

Ninomiya

2017

Biometrika

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Summary For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator as a $C_{p}$ criterion using an ignorable treatment assignment condition. Simulation shows that the proposed criterion outperforms a conventional one by providing smaller squared errors and higher frequencies of selecting the true model in all the settings considered. Moreover, in a real-data analysis we found a clear difference between the two criteria.

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“…

In their recent paper, Talbot et al [1] argue that the use of the stabilized weights in marginal structural models (MSMs) possibly yields biased inferences while the use of the standard unstabilized weights does not. They conclude that analysts should avoid using the common stabilized weights when the analyses target the estimation of the current or most recent treatment effect.

…”

mentioning

confidence: 99%

Comments on ‘A cautionary note concerning the use of stabilized weights in marginal structural models’ by D. Talbot, J. Atherton, A. M. Rossi, S. L. Bacon, and G. Lefebvre

Taguri

2015

Statistics in Medicine

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In their recent paper, Talbot et al. [1] argue that the use of the stabilized weights in marginal structural models (MSMs) possibly yields biased inferences while the use of the standard unstabilized weights does not. They conclude that analysts should avoid using the common stabilized weights when the analyses target the estimation of the current or most recent treatment effect. In this letter, I would like to clarify why this phenomenon was observed in their simulation study and question about the authors' conclusion. I here assume that the models for the treatment probabilities P (First, as Talbot et al. note, their example in Section 3 is too simple and artificial because in this situation, time-dependent confounding does not occur (that is, the treatment process is causally exogenous [2]) and a traditional regression model yields a consistent causal treatment effect estimate. Under the occurrence of time-dependent confounding, both the standard and stabilized weights yield consistent estimates under the no unmeasured confounders assumption and correct model specification of the MSM [3]. Thus, these two estimates can be asymptotically different only under the model misspecification as long as there are no unmeasured confounders. While I agree with Talbot et al. that the robustness of the weights to misspecification of the MSM is desirable, they do not give any theoretical justification on why the standard weights showed such a robustness in their simulations.To clarify why this result was observed, it is convenient to consider the pseudo-populations constructed by weighting each subject in the population by their subject-specific inverse probability of treatment weighting [3][4][5]. As shown in Lemma 1.2 of Robins [3], the following equation holds in the absence of unmeasured confounders:where E sw [.] and E w [.] mean that expectations are taken with respect to the pseudo-population created by sw and w, respectively. From (1), we can consider MSMs as ordinary regression models (that is, association models) for the pseudo-populations. The only difference between the two pseudo-populations is that in the stabilized pseudo-population P swwhile in the unstabilized pseudo-population P w ( A k = a k |Ā k−1 =ā k−1 ,L k =l k ) = 0.5, for k = {0, … , K}, respectively [3,4]. The important consequence of using these different weights in this context is that the treatmentsĀ are mutually independent in the unstabilized pseudo-population with w, but generally not in the stabilized pseudo-population with sw. This explains the simulation results of Talbot et al.For example, in their simulation Scenario 3, the true MSM is

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A cautionary note concerning the use of stabilized weights in marginal structural models

Cited by 12 publications

References 17 publications

A test for the correct specification of marginal structural models

A test for the correct specification of marginal structural models

A $C_p$ criterion for semiparametric causal inference

Comments on ‘A cautionary note concerning the use of stabilized weights in marginal structural models’ by D. Talbot, J. Atherton, A. M. Rossi, S. L. Bacon, and G. Lefebvre

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