Locally efficient estimation with bivariate right-censored data

• 成果类型: Article
• 署名作者: Quale, Christopher M.; Van der Laan, Mark J.; Robins, James R.
• 署名单位: Novo Nordisk; University of California System; University of California Berkeley; Harvard University; Harvard T.H. Chan School of Public Health
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000000212
• 发表日期: 2006
• 页码: 1076-1084
• 关键词: survival function; inference; models; npmle

摘要

Estimation of the survival curve for independently right-censored bivariate failure time data is a problem that has been studied extensively over the past 20 years. In this article we propose a new class of estimators for the bivariate survivor function based on locally efficient (LE) estimation. The LE estimator takes bivariate estimators F, and G,, of the distributions of the time variables (T-1, T-2) and the censoring variables (C-1, C-2), and maps them to the resulting estimator LE. If F, and G, are appropriate consistent estimators of F and G, then LE will be nonparametrically efficient (thus the term locally efficient). However, if either F-n or G(n) (but not both) is not a consistent estimator of F or G, then S-LE will still be consistent and asymptotically normally distributed. We propose a locally efficient estimator that uses a consistent, nonparametric estimator for G and allows the user to supply lower-dimensional (semiparametric or parametric) working model for F. Because the estimator that we choose for G is consistent, the resulting LE estimator will always be consistent and asymptotically normal, and our simulation studies have indicated that using a lower-dimensional model for F gives excellent small-sample performance. In addition, our algorithm for calculation of the efficient influence curve at true distributions for F and G computes the efficiency bound for the model that can be used to calculate relative efficiencies for any bivariate estimator. In this article we introduce the LE estimator for bivariate right-censored data, present an asymptotic result, present the results of simulation studies, and perform a brief data analysis illustrating the use of the LE estimator.