Open Access
April 2017 Mimicking counterfactual outcomes to estimate causal effects
Judith J. Lok
Ann. Statist. 45(2): 461-499 (April 2017). DOI: 10.1214/15-AOS1433


In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Structural nested models have been applied in this setting. Structural nested models are based on counterfactuals: the outcome a person would have had had treatment been withheld after a certain time. Previous work on continuous-time structural nested models assumes that counterfactuals depend deterministically on observed data, while conjecturing that this assumption can be relaxed. This article proves that one can mimic counterfactuals by constructing random variables, solutions to a differential equation, that have the same distribution as the counterfactuals, even given past observed data. These “mimicking” variables can be used to estimate the parameters of structural nested models without assuming the treatment effect to be deterministic.


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Judith J. Lok. "Mimicking counterfactual outcomes to estimate causal effects." Ann. Statist. 45 (2) 461 - 499, April 2017.


Received: 1 November 2013; Revised: 1 December 2015; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 06754740
MathSciNet: MR3650390
Digital Object Identifier: 10.1214/15-AOS1433

Primary: 62P10
Secondary: 62M99 , 62N02

Keywords: Causality in continuous time , dynamic treatments , longitudinal data , observational studies , panel data , rank preservation , Stochastic differential equations , structural nested models

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 2 • April 2017
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