Open Access
June 2008 Statistical modeling of causal effects in continuous time
Judith J. Lok
Ann. Statist. 36(3): 1464-1507 (June 2008). DOI: 10.1214/009053607000000820


This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321–334, (1998b) Encyclopedia of Biostatistics 6 4372–4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372–4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.


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Judith J. Lok. "Statistical modeling of causal effects in continuous time." Ann. Statist. 36 (3) 1464 - 1507, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1360.62511
MathSciNet: MR2418664
Digital Object Identifier: 10.1214/009053607000000820

Primary: 62P10
Secondary: 62M99

Keywords: Causality in continuous time , counterfactuals , longitudinal data , observational studies

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 3 • June 2008
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