Exact and Asymptotic Tests for Sufficient Followup in Censored Survival Data

TL;DR

This paper develops exact and asymptotic statistical tests to determine if there is sufficient followup in censored survival data, which is crucial for identifying immune or cured individuals in medical studies.

Contribution

It introduces a detailed analysis of a specific test statistic for followup sufficiency, providing exact finite sample and asymptotic distributions, and evaluates its power.

Findings

Derived exact finite sample distribution of the test statistic

Established asymptotic distribution for large samples

Assessed the test's power relative to followup levels

Abstract

The existence of immune or cured individuals in a population and whether there is sufficient followup in a sample of censored observations on their lifetimes to be confident of their presence are questions of major importance in medical survival analysis. So far only a few candidates have been put forward as possible test statistics for the existence of sufficient followup in a sample. Here we investigate one such statistic and give a detailed analysis, obtaining an exact finite sample as well as asymptotic distributions for it, and use these to calculate the power of the test as a function of the followup in the sample.