A martingale approach to continuous-time marginal structural models

By K. Røysland. 2009

52 citations recorded by the source corpus.

Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. The key point is that this can be understood in terms of Girsanov's change of measure. This offers a mathematical interpretation of marginal structural models that has not been available before. We consider both a model of an observational study and a model of a hypothetical randomized trial. These models correspond to different martingale measures -- the observational measure and the randomized trial measure -- on some underlying space. We describe situations where the randomized trial measure is absolutely continuous with respect to the observational measure. The resulting continuous-time likelihood ratio process with respect to these two probability measures corresponds to the weights in discrete-time marginal structural models. In order to do inference for the hypothetical randomized trial, we can simulate samples using observational data weighted by this likelihood ratio.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/518b72e303f62b162eaf095ccd65bc465800b420

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In Statistics and Probability

1. O. Aalen
2. B. Ledergerber
3. J. M. Gran
4. K. Røysland
5. Niels Richard Hansen
6. Søren Wengel Mogensen

Citations in the corpus

• History of applications of martingales in survival analysis. (2010, unknown): “More recently new developments in causal inference using martingale theory were developed by Røyseland [77] and Ryalden et al. [78].”
• Counterfactual analyses with graphical models based on local independence (2011, background): “this strategy actually works. We will provide some rigorous conditions for such re-weighting to be achievable. A similar exposition has not been carried out in the literature before, except partly in [25] and [7]. A probability distribution on the underlying sample space that would govern the freque”
• Causality, mediation and time: a dynamic viewpoint (2012, methodology): “A detailed analysis of the marginal structural model using local independence and δ-separation is given by Røysland (2011).”