Mathematics – Statistics Theory
Scientific paper
2009-01-19
Bernoulli 2011, Vol. 17, No. 3, 895-915
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.3150/10-BEJ303 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/10-BEJ303
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.
No associations
LandOfFree
A martingale approach to continuous-time marginal structural models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A martingale approach to continuous-time marginal structural models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A martingale approach to continuous-time marginal structural models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565960