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CC BY V4.0, Open Access
Journal article
Splitting the sample at the largest uncensored observation
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.28(4), pp.2234-2259
2022
Abstract
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 follow-up 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 by calculating distributions of statistics useful for testing for sufficient follow-up in a sample, and apply extreme value methods to derive asymptotic distributions for some of those.
Details
- Title
- Splitting the sample at the largest uncensored observation
- Authors/Creators
- Ross Maller - Australian National UniversitySidney Resnick - Cornell UniversitySoudabeh Shemehsavar - University of Tehran
- Publication Details
- Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.28(4), pp.2234-2259
- Publisher
- Bernoulli Society for Mathematical Statistics and Probability
- Number of pages
- 26
- Identifiers
- 991005618226407891
- Murdoch Affiliation
- College of Science, Technology, Engineering and Mathematics
- Language
- English
- Resource Type
- Journal article
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- 9 Mathematics
- 9.92 Statistical Methods
- 9.92.220 Robust Estimation
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