Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 106, Issue 496, Pages 1434-1449Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/jasa.2011.tm10156
Keywords
Cox regression model; Increasing failure rate; Nonparametric likelihood; Profile likelihood; Right-censored data
Categories
Funding
- Seniors' Independence Research Program, through the National Health Research and Development Program of Health Canada [6606-3954-MC(S)]
- Pfizer Canada through Medical Research Council/Pharmaceutical Manufacturers Association of Canada Health Activity [6603-1417-302(R)]
- Bayer Incorporated
- British Columbia Health Research Foundation [38(93-2), 34(96-1)]
- National Institute of Health [R01-CA079466]
Ask authors/readers for more resources
Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, and epidemiological, genetic, and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimation and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization algorithms for estimations based on full likelihoods involving infinite-dimensional parameters under three settings for length-biased data: estimating nonparametric distribution function, estimating nonparametric hazard function under an increasing failure rate constraint, and jointly estimating baseline hazards function and the covariate coefficients under the Cox proportional hazards model. Extensive empirical simulation studies show that the maximum likelihood estimators perform well with moderate sample sizes and lead to more efficient estimators compared to the estimating equation approaches. The proposed estimates are also more robust to various right-censoring mechanisms. We prove the strong consistency properties of the estimators, and establish the asymptotic normality of the semiparametric maximum likelihood estimators under the Cox model using modern empirical processes theory. We apply the proposed methods to a prevalent cohort medical study. Supplemental materials are available online.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available