Extremes of Censored and Uncensored Lifetimes in Survival Data
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The i.i.d. censoring model for survival analysis assumes two independent sequences of i.i.d. positive random variables, (T_i^*)_1< i< n and (U_i)_1< i< n. The data consists of observations on the random sequence (T_i=min(T_i^*,U_i) together with accompanying censor indicators. Values of T_i with T_i^*< U_i are said to be uncensored, those with T_i^*> U_i are censored. We assume that the distributions of the T_i^* and U_i are in the domain of attraction of the Gumbel distribution and obtain the asymptotic distributions, as sample size n→∞, of the maximum values of the censored and uncensored lifetimes in the data, and of statistics related to them. These enable us to examine questions concerning the possible existence of cured individuals in the population.
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