The Annals of Statistics
- Ann. Statist.
- Volume 36, Number 3 (2008), 1464-1507.
Statistical modeling of causal effects in continuous time
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.
Ann. Statist., Volume 36, Number 3 (2008), 1464-1507.
First available in Project Euclid: 26 May 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62P10: Applications to biology and medical sciences
Secondary: 62M99: None of the above, but in this section
Lok, Judith J. Statistical modeling of causal effects in continuous time. Ann. Statist. 36 (2008), no. 3, 1464--1507. doi:10.1214/009053607000000820. https://projecteuclid.org/euclid.aos/1211819571