#### Title

Locally Efficient Estimation in Censored Data Models: Theory and Examples

#### Abstract

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that 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 one-step estimators that are efficient at a chosen 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. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.

#### Suggested Citation

van der Laan, Mark J.; Gill, Richard D.; and Robins, James M., "Locally Efficient Estimation in Censored Data Models: Theory and Examples" (March 2000). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 85.

http://biostats.bepress.com/ucbbiostat/paper85

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## Comments

Paper copy is available from biostat@berkeley.edu