Statistical modeling of causal effects in continuous time

By J. Lok. 2004

47 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

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Citations in the corpus

Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations (2020, background): “Schulam & Saria (2017) build upon work from Lok et al. (2008); Arjas & Parner (2004) and use marked point processes and Gaussian processes to learn causal effects in continuous-time data.”
Learning Treatment-Response Models from Multivariate Longitudinal Data (2017, background): “…worth noting that in the potential outcomes framework, estimation of the causal effect is precluded by the need to justify a set of generally untestable assumptions (Gill and Robins, 2001); e.g., see Lok (2008); Schulam and Saria (2017) for assumptions needed for continuous-time potential outcomes.”
Reliable Decision Support using Counterfactual Models (2017, methodology): “mes are measured and actions are taken at irregular, discrete points in continuous-time. The CGP builds on previous ideas in continuous-time causal inference (e.g. Robins 1997, Arjas and Parner 2004, Lok 2008), but is unique in that it can predict the full counterfactual trajectory of a time-depende”
Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms (2014, background): “28 Although we have only considered an example above, it is clearly a general feature that the local dynamic eﬀects would be ‘‘smeared out’’ when considering a longer time interval.”
A martingale approach to continuous-time marginal structural models (2009, unknown): “J. Lok has developed continuous time versions of such models, using counting processes and martingale theory, see [ Lok08 ].”
What-If Reasoning with Counterfactual Gaussian Processes (2017, methodology): “The CGP builds on previous ideas in continuous-time causal inference (e.g., Robins 1997, Arjas and Parner 2004, Lok 2008), but is unique in that it can predict the full counterfactual trajectory ; we combined marked point processes (MPP) with GPs to model observational traces , and described three…”