For the continuous-time case, no proofs were known, and the validity of those estimators was only conjectured. We have proved that, at least if there is no unmeasured confounding and in the absence of censoring, structural nested distribution models in continuous time often give rise to estimators for the effect of treatment on the outcome of interest which are consistent and asymptotically normal.
In this talk I will give an outline of the testing- and estimation procedures. I will also present the results of our efforts to mathematically underpin these methods, especially in continuous time, and indicate the main assumptions we made. E.g., we formalized the assumption of no unmeasured confounding in the context of counting processes. I will focus on ideas, and use an example for illustration.
Some references:
Lok, J.J. (2001, May). Statistical modelling of causal effects in time. PhD-thesis, Department of Mathematical Statistics, Free University of Amsterdam, The Netherlands, under supervision of R.D. Gill and A.W. van der Vaart. Also available on the web: http://www.cs.vu.nl/~jjlok .
Robins, J.M., D. Blevins, G. Ritter and M. Wulfsohn (1992). G-estimation of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology 3 (4), pp. 319-336.
Robins, J.M. (1998). Structural nested failure time models. In P. Armitage and T. Colton (Eds.), Survival analysis, Volume 6 of the Encyclopedia of Biostatistics, pp. 4372-4389. Chichester, UK: John Wiley and Sons. Section Eds: P.K. Andersen and N. Keiding.
Last Updated: February 5, 2002