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Locally Efficient Median Regression with Random Censoring and Surrogate Markers

In: Lifetime Data: Models in Reliability and Survival Analysis

Author

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  • James M. Robins

    (Harvard School of Public Health, Departments of Epidemiology and Biostatistics)

Abstract

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.

Suggested Citation

  • James M. Robins, 1996. "Locally Efficient Median Regression with Random Censoring and Surrogate Markers," Springer Books, in: Nicholas P. Jewell & Alan C. Kimber & Mei-Ling Ting Lee & G. A. Whitmore (ed.), Lifetime Data: Models in Reliability and Survival Analysis, pages 263-274, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-5654-8_35
    DOI: 10.1007/978-1-4757-5654-8_35
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