Statistical modeling of causal effects in continuous time. (English) Zbl 1360.62511
Summary: 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.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62N02 | Estimation in survival analysis and censored data |
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