| 1. |
- Belzile, L. R., et al.
(författare)
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Human mortality at extreme age
- 2021
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Ingår i: Royal Society Open Science. - : The Royal Society. - 2054-5703. ; 8:9
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Tidskriftsartikel (refereegranskat)abstract
- We use a combination of extreme value statistics, survival analysis and computer-intensive methods to analyse the mortality of Italian and French semi-supercentenarians. After accounting for the effects of the sampling frame, extreme-value modelling leads to the conclusion that constant force of mortality beyond 108 years describes the data well and there is no evidence of differences between countries and cohorts. These findings are consistent with use of a Gompertz model and with previous analysis of the International Database on Longevity and suggest that any physical upper bound for the human lifespan is so large that it is unlikely to be approached. Power calculations make it implausible that there is an upper bound below 130 years. There is no evidence of differences in survival between women and men after age 108 in the Italian data and the International Database on Longevity, but survival is lower for men in the French data.
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| 2. |
- Belzile, Léo R., et al.
(författare)
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Is There a Cap on Longevity? A Statistical Review
- 2022
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Ingår i: Annual Review of Statistics and Its Application. - : Annual Reviews. - 2326-8298 .- 2326-831X. ; 9, s. 21-45
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Forskningsöversikt (refereegranskat)abstract
- There is sustained and widespread interest in understanding the limit, if there is any, to the human life span. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social security systems. A central question is whether the endpoint of the underlying lifetime distribution is finite. Recent analyses of data on the oldest human lifetimes have led to competing claims about survival and to some controversy, due in part to incorrect statistical analysis. This article discusses the particularities of such data, outlines correct ways of handling them, and presents suitable models and methods for their analysis. We provide a critical assessment of some earlier work and illustrate the ideas through reanalysis of semisupercentenarian lifetime data. Our analysis suggests that remaining life length after age 109 is exponentially distributed and that any upper limit lies well beyond the highest lifetime yet reliably recorded. Lower limits to 95% confidence intervals for the human life span are about 130 years, and point estimates typically indicate no upper limit at all.
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| 3. |
- Rootzén, Holger, 1945, et al.
(författare)
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Efficient estimation of the number of false positives in high-throughput screening
- 2015
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Ingår i: Biometrika. - : Oxford University Press (OUP). - 0006-3444 .- 1464-3510. ; 102:3, s. 695-704
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Tidskriftsartikel (refereegranskat)abstract
- This paper develops tail estimation methods to handle false positives in multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom, and where the true null distribution may differ from the theoretical one. We show that the number of false positives, conditional on the total number of positives, has an approximately binomial distribution, and we find estimators of the distribution parameter. We also develop methods for estimation of the true null distribution, as well as techniques to compare it with the theoretical one. Analysis is based on a simple polynomial model for very small p-values. Asymptotics that motivate the model, properties of the estimators, and model-checking tools are provided. The methods are applied to two large genomic studies and an fMRI brain scan experiment.
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| 4. |
- Rootzén, Holger, 1945, et al.
(författare)
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Human life is unlimited - but short
- 2017
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Ingår i: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 20:4, s. 713-728
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Tidskriftsartikel (refereegranskat)abstract
- Does the human lifespan have an impenetrable biological upper limit which ultimately will stop further increase in life lengths? This question is important for understanding aging, and for society, and has led to intense controversies. Demographic data for humans has been interpreted as showing existence of a limit, or even as an indication of a decreasing limit, but also as evidence that a limit does not exist. This paper studies what can be inferred from data about human mortality at extreme age. We find that in western countries and Japan and after age 110 the risk of dying is constant and is about 47% per year. Hence data does not support that there is a finite upper limit to the human lifespan. Still, given the present stage of biotechnology, it is unlikely that during the next 25 years anyone will live longer than 128 years in these countries. Data, remarkably, shows no difference in mortality after age 110 between sexes, between ages, or between different lifestyles or genetic backgrounds. These results, and the analysis methods developed in this paper, can help testing biological theories of aging and aid confirmation of success of efforts to find a cure for aging.
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| 5. |
- Rootzen, Holger, 1945, et al.
(författare)
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Rejoinder to discussion of the paper “Human life is unlimited - but short”
- 2018
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Ingår i: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 21:3, s. 415-424
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Tidskriftsartikel (refereegranskat)abstract
- What can be learned from data about human survival at extreme age? In this rejoinder we give our views on some of the issues raised in the discussion of our paper Rootzén and Zholud (Extremes 20(4), 713–728, 2017).
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| 6. |
- Rootzén, Holger, 1945, et al.
(författare)
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Tail estimation for window censored processes
- 2016
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Ingår i: Technometrics. - : Informa UK Limited. - 0040-1706 .- 1537-2723. ; 58:1
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Tidskriftsartikel (refereegranskat)abstract
- This paper develops methods to estimate the tail and full distribution of the lengths of the 0-intervals in a continuous time stationary ergodic stochastic process which takes the values 0 and 1 in alternating intervals. The setting is that each of many such 0-1 processes have been observed during a short time window. Thus the observed 0-intervals could be non-censored, right censored, left censored or doubly censored, and the lengths of 0-intervals which are ongoing at the beginning of the observation window have a length-biased distribution. We exhibit parametric conditional maximum likelihood estimators for the full distribution, develop maximum likelihood tail estimation methods based on a semi-parametric generalized Pareto model, and propose goodness of fit plots. Finite sample properties are studied by simulation, and asymptotic normality is established for the most important case. The methods are applied to estimation of the length of off-road glances in the 100-car study, a big naturalistic driving experiment. Supplementary materials that include MatLab code for the estimation routines and a simulation study are available online.
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| 7. |
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| 8. |
- Zholud, Dmitrii, 1984
(författare)
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Extreme Value Analysis of Huge Datasets: Tail Estimation Methods in High-Throughput Screening and Bioinformatics
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents results in Extreme Value Theory with applications to High-Throughput Screening and Bioinformatics. The methods described here, however, are applicable to statistical analysis of huge datasets in general. The main results are covered in four papers. The first paper develops novel methods to handle false rejections in High-Throughput Screening experiments where testing is done at extreme significance levels, with low degrees of freedom, and when the true null distribution may differ from the theoretical one. We introduce efficient and accurate estimators of False Discovery Rate and related quantities, and provide methods of estimation of the true null distribution resulting from data preprocessing, as well as techniques to compare it with the theoretical null distribution. Extreme Value Statistics provides a natural analysis tool: a simple polynomial model for the tail of the distribution of p-values. We exhibit the properties of the estimators of the parameters of the model, and point to model checking tools, both for independent and dependent data. The methods are tried out on two large scale genomic studies and on an fMRI brain scan experiment. The second paper gives a strict mathematical basis for the above methods. We present asymptotic formulas for the distribution tails of probably the most commonly used statistical tests under non-normality, dependence, and non-homogeneity, and derive bounds on the absolute and relative errors of the approximations. In papers three and four we study high-level excursions of the Shepp statistic for the Wiener process and for a Gaussian random walk. The application areas include finance and insurance, and sequence alignment scoring and database searches in Bioinformatics.
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| 9. |
- Zholud, Dmitrii, 1984
(författare)
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Extremes of Shepp statistics for Gaussian random walk
- 2009
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Ingår i: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 12:1, s. 1-17
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Tidskriftsartikel (refereegranskat)abstract
- Let (xi(i), i >= 1) be a sequence of independent standard normal random variables and let S-k = Sigma(k)(i=1)xi(i) be the corresponding random walk. We study the renormalized Shepp statistic M-T((N)) = 1/root N (1 <= k <= TN 1 <= L <= N)max max (Sk+L-1 - Sk-1) and determine asymptotic expressions for P(M-T((N)) > u) when u, N and T -> infinity in a synchronized way. There are three types of relations between u and N that give different asymptotic behavior. For these three cases we establish the limiting Gumbel distribution of M-T((N)) when T, N -> infinity and present corresponding normalization sequences.
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| 10. |
- Zholud, Dmitrii, 1984
(författare)
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Extremes of Shepp statistics for the Wiener process
- 2008
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Ingår i: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 11:4, s. 339-351
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Tidskriftsartikel (refereegranskat)abstract
- Define Y(t)= max 0 ≤ s ≤1 W(t+s)-W(t), where W(̇) is a standard Wiener process. We study the maximum of Y up to time T: MT= max 0 ≤t ≤ T Y(t) and de termine an asymptotic expression for P (MT>u) when u → ∞. Further we establish the limiting Gumbel distribution of MT when T → ∞ and present the corresponding normalization sequence. © 2008 Springer Science+Business Media, LLC.
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