The purpose of this research is to extend my earlier research in non- and semi-parametric methods for the analysis of health studies with incomplete data, to methods for addressing a number of important unsolved problems for drawing causal inferences-from complex longitudinal observational and randomized studies with time-varying exposures or treatments. In this regard, to reflect the extended work scope of this project, its title has been amended to """"""""Methods for Analysis with Missing and/or Censored Data and for Causal Inference"""""""". The proposed methodology adequately adjusts for time-dependent confounding factors;that is, for risk factors for outcomes that also predict subsequent treatment. The main emphasis is in the estimation of new classes of causal models that are specifically tailored to answer each of the causal inquiries in this grant.
The first aim i s to develop methodology for estimating, from observational data, optimal dynamic treatment regimes that use partial covariate information. I will derive estimators of the parameters of a new class of models, the """"""""dynamic regime structural models"""""""". The new models are specifically tailored to the estimation of optimal dynamic regimes out of a set of simple, realistically enforceable, regimes.
The second aim i s to develop methods for the testing and estimation, from observational studies, of the direct effect of a treatment on an outcome when a second treatment is fixed at a pre-specified dose regimen. The proposed models facilitate the conduct of a sensitivity analysis that quantifies how one's inference concerning the direct effect of a treatment of interest varies as a function of the magnitude of confounding due to unmeasured factors.
The third aim i s to develop methods for estimating, from a double-blind randomized trial, treatment effects in the subset of the population in which a post-randomization event would occur under both treatments.
Tfte fourth aim i s to develop a theory of efficient, non-root-n consistent estimation based on higher order influence functions. This theory extends the theory of semi-parametric efficient root-n consistent estimation to allow for the construction of non-root-n estimators that are consistent under generally weaker assumptions. This theory is particularly, useful for constructing honest confidence intervals for the average treatment effect in the presence of such high-dimensional pre-treatment confounding factors that root-n estimation of the treatment effect is precluded.
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