Detection of hormesis effect in longevity: simulation approach for heterogeneous population Anatoli I. Michalski a,1 , Anatoli I. Yashin b, * a Institute of Control Sciences, Profsoyuznaya 65, 117806, Moscow, Russia b Max Planck Institute for Demographic Research, 114 Doberaner Str., D-18057 Rostock, Germany Received 3 November 2000; received in revised form 16 July 2001; accepted 17 August 2001 Abstract Manifestation of hormesis in longevity was modelled by modification of the mortality rate during and after the period of a stress factor action. In heterogeneous population this can lead to observation of unchanged mortality during action of the stress and decrease in mortality after stress period. Stochastic simulations were made to investigate the possibility of detecting the hormesis effect on the basis of the stress-control longitudinal data. The goal of the stochastic simulation was to investigate the role in the hormesisdetectionofcontrolandstressedgroupsize,ofpopulationheterogeneityvariancevalue,ofstress and hormesis attributable risks as well as the role of a prior information about the survival in the control group. It was demonstrated that if the attributable risks for stress and hormesis effects are approximately equal, then in both ‘high’ and ‘low’ heterogeneous populations the hormesis phenomenon is detected with probability higher than 75% even in relatively ‘small’ groups of 50 subjects. In case of ‘weak’ effect the hormesisphenomenonisnotdetectedina‘highlyheterogeneous’populationeveninagroupcomposedof 1000 subjects. In a ‘low heterogeneous’ population the hormesis phenomenon is detected with probability higherthan70%whenthegroupsizeisnotlessthan200subjects.Informationaboutthesurvivalincontrol group did not play a critical role in all experiments and exact survival curve may be replaced by the tra- ditional Kaplan–Meier estimate. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Stress experiments; Longevity; Hormesis identification; Heterogeneity; Simulation Mathematical Biosciences 175 (2002) 57–66 www.elsevier.com/locate/mbs * Corresponding author. Tel.: +49-381 208 1106; fax: +49-381 208 1169. E-mail addresses: mikhalsk@ipu.rssi.ru (A.I. Michalski), yashin@demogr.mpg.de (A.I. Yashin). 1 Tel.: +7-095 334 8820; fax: +7-095 420 2016. 0025-5564/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0025-5564(01)00083-9