General Departmental Seminar Series
Locally Efficient Estimation in Censored Data Models
Mark Van Der Laan, Departments of Biostatistics
and Statistics, UC-Berkeley
Friday, April 20, 2001, 12:00-1:00 pm
3285 Medical Sciences Center
1300 University Avenue
In many applications the observed data can be viewed as a censored high dimensional full data random variable $X$. In particular, causal inference can be viewed as a missing data problem in which one only observes the treatment specific outcome corresponding with the treatment the subject actually received. By the curse of dimensionality it is typically not possible to construct estimators which are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of doubly robust one-step estimators which are efficient at a user supplied submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. As examples, we will focus on estimation with 1) current status data on time till onset of tumor (or time till HIV-infection in AIDS-partner studies) 2) multivariate right-censored data and 3) causal inference data structures, where we allow in all data structures the presence of time-dependent covariates.
Joint work: James Robins, Harvard School of Public Health.
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