Annals of Statistics

Asymptotic theory for the semiparametric accelerated failure time model with missing data

Bin Nan, John D. Kalbfleisch, and Menggang Yu

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Abstract

We consider a class of doubly weighted rank-based estimating methods for the transformation (or accelerated failure time) model with missing data as arise, for example, in case-cohort studies. The weights considered may not be predictable as required in a martingale stochastic process formulation. We treat the general problem as a semiparametric estimating equation problem and provide proofs of asymptotic properties for the weighted estimators, with either true weights or estimated weights, by using empirical process theory where martingale theory may fail. Simulations show that the outcome-dependent weighted method works well for finite samples in case-cohort studies and improves efficiency compared to methods based on predictable weights. Further, it is seen that the method is even more efficient when estimated weights are used, as is commonly the case in the missing data literature. The Gehan censored data Wilcoxon weights are found to be surprisingly efficient in a wide class of problems.

Article information

Source
Ann. Statist., Volume 37, Number 5A (2009), 2351-2376.

Dates
First available in Project Euclid: 15 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247663758

Digital Object Identifier
doi:10.1214/08-AOS657

Mathematical Reviews number (MathSciNet)
MR2543695

Zentralblatt MATH identifier
1173.62073

Subjects
Primary: 62E20: Asymptotic distribution theory 62N01: Censored data models
Secondary: 62D05: Sampling theory, sample surveys

Keywords
Accelerated failure time model case-cohort study censored linear regression Donsker class empirical processes Glivenko–Cantelli class pseudo Z-estimator nonpredictable weights rank estimating equation semiparametric method

Citation

Nan, Bin; Kalbfleisch, John D.; Yu, Menggang. Asymptotic theory for the semiparametric accelerated failure time model with missing data. Ann. Statist. 37 (2009), no. 5A, 2351--2376. doi:10.1214/08-AOS657. https://projecteuclid.org/euclid.aos/1247663758


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