Jackknife Estimator of Logistic Transformation from Truncated Data

In medical follow-up, equipment lifetesting, various military situations, and other fields, one often desires to calculate survival probability as a function of time, p(t). If the observer is able to record the time of occurrence of the event of interest (called a 'death'), then an empirical, non-parametric estimate may simply by obtained from the fraction of survivors after various elapsed times. The estimation is more complicated when the data are truncated, i.e., when the observer loses track of some individuals before death occurs. 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 jackknife estimators of logistic trans-formation and compares it to the product-limit method. A computer simulation is used to generate the times of death and truncation from a variety of assumed distributions.