2021/03/01 by Ross Maller, Maller, Ross, Sidney I. Resnick +3
Computer Science · Mathematics · #62F03 (Secondary) #62N01 (Primary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2103.01337
openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate finite sample and asymptotic distributions for the largest censored and uncensored survival times, and some related statistics, from a sample of survival data generated according to an iid censoring model. These statistics are important for assessing whether there is sufficient followup in the sample to be confident of the presence of immune or cured individuals in the population. A key structural result obtained is that, conditional on the value of the largest uncensored survival time, and knowing the number of censored observations exceeding this time, the sample partitions into two independent subsamples, each subsample having the distribution of an iid sample of censored survival times, of reduced size, from truncated random variables. This result provides valuable insight into the construction of censored survival data, and facilitates the calculation of explicit finite sample formulae. We illustrate for distributions of statistics useful for testing for sufficient followup in a sample, and apply extreme value methods to derive asymptotic distributions for some of those.