Nonparametric estimation from censored data.

Abstract

For nearly two decades we have witnessed an intensive development of a statistical methodology for assessing length of life and reliability of performance from empirical data. The initial stimulus for research on statistical problems in life testing and reliability came from the need to answer pressing practical questions which could not be treated by the existing statistical techniques. Because life and performance tests are so time consuming and expensive to run, it is a practical necessity to terminate them as soon as possible. For the statistician this means developing estimation and decision procedure for data, which are severely curtailed in one way or another long before all items on test have actually failed. The estimation is more complicated when the data are truncated, i.e. when the observer loses track of some individuals before death occur. The product limit method of Kaplan and Meier is one way of estimating p(t) when the mechanism causing truncation is independent of the mechanism causing death . This paper proposes alternative estimators and compares them to the product limit method. A computer simulation is used to generate the times of death and truncation from a variety of assumed distributions. No single estimator gives the best fit to the "true" distribution of death under all situations. However, other estimators are shown to be better than the product limit estimator under all of the assumed situations.