Locally Efficient Median Regression with Random Censoring and Surrogate Markers
Robins and Rotnitzky (1992) proved a general representation theorem for (1) the efficient score and (2) the set of influence functions for regular asymptotically linear (RAL) estimators in arbitrary semiparametric models with (i) the data missing or coarsened at random, and (ii) the probability of observing complete data bounded away from zero. We use this representation theorem to construct locally efficient estimators (at a parametric submodel) in a censored median regression model where the hazard of censoring at u (i) may depend on both the regressors and on the history up to u of a surrogate process of prognostic factors, but (ii) does not further depend on the possibly unobserved failure time. Our model incorporates both the Ying et al. (1994) random censoring model and the Newey and Powell (1990) observed potential censoring time model as special cases.
KeywordsEfficient Score Asymptotic Variance Influence Function Semiparametric Model Median Regression
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