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April 2004 Information bounds for Cox regression models with missing data
Bin Nan, Mary J. Emond, Jon A. Wellner
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Ann. Statist. 32(2): 723-753 (April 2004). DOI: 10.1214/009053604000000157


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].


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Bin Nan. Mary J. Emond. Jon A. Wellner. "Information bounds for Cox regression models with missing data." Ann. Statist. 32 (2) 723 - 753, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1097.62097
MathSciNet: MR2060175
Digital Object Identifier: 10.1214/009053604000000157

Primary: 62E17
Secondary: 65D20

Keywords: Case-cohort design , Cox model , efficient influence function , efficient score , 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

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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