Testing for the presence of immune or cured individuals in censored survival data

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure, or relapse, etc., may be indicated by a relatively high number of individuals with large censored survival times. We summarise some recent theoretical work which justifies analogues of the usual model fitting and testing techniques for such data. In particular, we discuss a 'boundary' test for the presence of immunes in the population and goodness of fit tests for parametric descriptions of the data. The methods are illustrated on some data on the relapse times of leukemia patients.