Estimation of confidence bands using non-parametric test for the survival curve obtained in the Thalassaemia (Major) clinical trial
by
Girishkumar Chhaganlal Bhimani
Statistic Department, Saurashtra University, Rajkot(Gujrat), INDIA

In many clinical survivorship studies, a certain number of patients being followed many months or years after the pre selected endpoint of the study. The main advantage of Kaplan-Meier product limit estimation procedure is that, we can obtain a confidence band for the survival curve till the largest, or at least next to largest known survival time, a time that may be substantially exceed the highest reliable interval endpoint under the life table procedure.

S(t) is survival curve, in a population from which a study group of N patients has been randomly drawn. The product limit estimate SN(t) defined by Kaplan-Meier equation is point estimate of S(t). A confidence band for the entire survival curve is a paired step function, with step occurs at every known survival times. Here problem is to define the paired step function, such that we can enclose the S(t) within it, with (1-a) 100% confidence. This bands will be nonparametric, as there is no assumption made about the mathematical form of the S(t). When all the survival times are known, width of the confidence band is constant over all the time. When the survival time is being censored, we get more and more wider bands with time. In this investigation we have obtained the confidence bands for those survival curves using Kaplan-Meier product limit estimates. We utilized two methods for obtaining the confidence bands. They are Asymptotic Kolmogrov and Hall - Wellner methods.

Date received: July 19, 2003