We derive information bounds for the regression parameters in Cox models when data are missing at random. These calculations are of interest for understanding the behavior of efficient estimation in case-cohort designs, a type of two-phase design often used in cohort studies. The derivations make use of key lemmas appearing in Robins, Rotnitzky and Zhao [J. Amer. Statist. Assoc. 89 (1994) 846–866] and Robins, Hsieh and Newey [J. Roy. Statist. Soc. Ser. B 57 (1995) 409–424], but in a form suited for our purposes here. We begin by summarizing the results of Robins, Rotnitzky and Zhao in a form that leads directly to the projection method which will be of use for our model of interest. We then proceed to derive new information bounds for the regression parameters of the Cox model with data Missing At Random (MAR). In the final section we exemplify our calculations with several models of interest in cohort studies, including an i.i.d. version of the classical case-cohort design of Prentice [Biometrika 73 (1986) 1–11] and Self and Prentice [Ann. Statist. 16 (1988) 64–81].
Publié le : 2004-04-14
Classification:
Case-cohort design,
Cox model,
efficient score,
efficient influence function,
information bound,
integral equation,
least favorable direction,
martingale operators,
mean residual life operators,
missing at random,
regression models,
scores,
stratification,
survival analysis,
tangent set,
tangent space,
62E17,
65D20
@article{1083178944,
author = {Nan, Bin and Emond, Mary J. and Wellner, Jon A.},
title = {Information bounds for Cox regression models with missing data},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 723-753},
language = {en},
url = {http://dml.mathdoc.fr/item/1083178944}
}
Nan, Bin; Emond, Mary J.; Wellner, Jon A. Information bounds for Cox regression models with missing data. Ann. Statist., Tome 32 (2004) no. 1, pp. 723-753. http://gdmltest.u-ga.fr/item/1083178944/