NON-PARAMETRIC INFERENCE OF A FAILURE TIME DISTRIBUTION WHEN THE FAILURE TIMES ARE ESTIMATED

✍ Scribed by HYUNGJIN MYRA KIM; STEPHEN W. LAGAKOS

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 925 KB
• Volume: 15
• Category: Article
• ISSN: 0277-6715
• DOI: 10.1002/(sici)1097-0258(19961130)15:22<2475::aid-sim465>3.0.co;2-x

✦ Synopsis

We consider the estimation of a failure time distribution F when, instead of N i.i.d. realizations TI, T z , .. . , T N from F, the observations consist of estimates of the Ti. If the T i could be observed, a natural non-parametric estimator of F would be the Kaplan-Meier estimator. Thus, we examine the properties of the Kaplan-Meier estimator based on the estimates of the Ti. We also consider a weighted Kaplan-Meier estimator which gives more emphasis to those estimated times based on more information. We evaluate the small sample bias and precision of F when the estimated failure times arise from additive or multiplicative error structures. Because this problem has particular application in the study of non-compliance of subjects in clinical trials, we also investigate the bias and precision of the estimators of the distribution function based on a complex error structure that would arise in the non-compliance setting. Here T i denotes the unobserved time to non-compliance for the ith subject, and is estimated using repeated observations from a laboratory marker whose behaviour is affected by non-compliance. The techniques are illustrated with the results of a recent AIDS clinical trial.