Non-parametric Estimation of a Survival Function with Two-stage Design Studies

• Published in: Scandinavian journal of statistics Vol. 35; no. 2; pp. 193 - 211
• Main Authors: LI, GANG, TSENG, CHI-HONG
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2008; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Aalen estimator; Applications; Bias; censoring; Censorship; Clinical trials; Confidence intervals; Consistent estimators; Epidemiology; Estimation bias; Estimators; Exact sciences and technology; General topics; Kaplan; Kaplan Meier estimator; martingale; Martingales; Mathematics; Medical equipment; Medical sciences; Meier estimator; Nelson; Nonparametric inference; Parametric inference; Perceptron convergence procedure; Probability and statistics; Reliability functions; Sciences and techniques of general use; Statistical methods; Statistical variance; Statistics; Studies; Surveillance; truncation; Biometrics; Kaplan Meier estimator; Parameter estimation; Variance estimation; Bias; Large sample; Non parametric estimation; Nelson-Aalen estimator; Epidemiology; Variance; Marketing; Parametric method; Medical science; censoring; Survival function; Clinical trial; truncation; Survival data; Censored data; Covariance analysis; Statistical estimation; Parametric estimation; Variance analysis; Survival; Confidence interval; Statistical method; Statistical regression; Function estimation; Experimental design; Kaplan-Meier estimator; martingale; Application; Biased estimation
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2007.00581.x

The two-stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right-censored survival data from a two-stage design. A non-parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite-sample bias of the Kaplan-Meier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study.