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We consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications. Copyright (c) 2014 John Wiley & Sons, Ltd. We consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications.

Background Studies of Nordic twins suggest an increased genetic influence on mortality with age. Contrary to this, the heterogeneity hypothesis predicts that the mortality of individuals carrying a "frail" or "risky" genotype in a population will approach that of non-carriers with age due to selection pressure. The ApoE ε4 allele is associated with increased mortality risk and its effect has been suggested to decrease with age. Here we investigated the effect of ApoE ε4 allele on survival in a sample of the healthiest and long-lived Danes. Methods The study population comprised Danes born in 1905 and a replicate sample of the 1895 cohort. For the 1905 cohort, a total of 350 carriers and 1256 non-carriers of the ApoE ε4 allele were followed from 1998 until death or end of follow-up. Cox regressions models were used for the analysis. Results Of the 1606 persons with known ApoE ε4 status in 1998, 1546 had died at the end of the ten years follow up. Carriers of the ApoE ε4 allele had an increased mortality compared to non-carriers and the influence of ApoE status on mortality increased in the age interval 92-103. For the covariates, sex and independency status, the difference in relative risk for death between groups decreased with advancing age. Conclusions Our findings of increasing influence of ApoE ε4 allele on mortality with age do not support previous findings of decreased influence ApoE ε4 allele on mortality with age and alternative models such as the multi-factorial threshold models should be considered for understanding the genetic effects on mortality at advanced age.

New approaches are needed to explore the different ways in which genes affect the human life span. One needs to assess the genetic effects themselves, as well as gene–environment interactions and sex dependency. In this paper, we present a new model that combines both genotypic and demographicinformation in the estimation of the geneticinfluence on life spans. Based on Cox'sproportional hazard assumption, the modelmeasures the risks for each gene as well as forgene–environment and gene–sex interactions,while controlling for confounding factors. Atwo-step MLE is introduced to obtain anon-parametric form of the baseline hazardfunction. The model is applied to genotypicdata from Italian centenarian studies toestimate relative risks of candidate genes,risks due to interactions and initialfrequencies of different genes in thepopulation. Results from models that either door do not take into consideration individualheterogeneity are compared. It is shown thatignoring the existence of heterogeneity canlead to a systematic underestimation of geneticeffects and effects due to interactions.

1. A graphic technique is presented in which data on age-specific reproduction of individuals are portrayed using: (i) a horizontal life line, the length of which is proportional to individual longevity; (ii) colour-coded segments depicting the level of reproduction at each age; and (iii) a cohort survival schedule created by rank-ordering individual life lines from shortest- to longest-lived. 2. The resulting graphic, referred to as an event history diagram, portrays data at the individual level and thus allows visual comparisons of detailed life-history patterns such as age of first reproduction, longevity, ages of high, medium, low and zero reproduction, and post-reproductive period. 3. Example graphs are shown for reproductive and longevity data gathered on 1000 medfly females. The average female lived 35.6 days and laid 759.3 eggs and therefore the graphs display information for 35 600 fly days and the age-distribution of laying for 759 300 eggs. 4. Because the graphics provide a means for visualizing large amounts of data precisely and efficiently, they reveal details and nuances in the data that are not apparent from conventional graphic methods. 5. The advantages of longitudinal data gathered on individuals and reasons why visualizing individual-level data is important are discussed.

OBJECTIVE--To test the validity of the fetal origins hypothesis and the classic twin method. DESIGN--Follow up study of pairs of same sex twins in which both twins survived to age 6. SETTING--Denmark. SUBJECTS--8495 twin individuals born 1870-1900, followed through to 31 December 1991. MAIN OUTCOME MEASURES--Mortality calculated on a cohort basis. RESULTS--Mortality among twins and the general population was not significantly different except among females aged 60-89, in whom mortality among twins was 1.14 times (SE 0.03) higher than in the general population. Mortality among female dizygotic twins was 1.77 times (0.18) higher than among monozygotic twins at age 30-59. Otherwise, mortality for monozygotic and dizygotic twins did not consistently differ after age 6. CONCLUSION--According to the fetal origins hypothesis the risk of adult morbidity and mortality is heightened by retardation in intrauterine growth. Twins, and in particular monozygotic twins, experience growth retardation in utero. The findings in the present study suggest that the fetal origins hypothesis is not true for the retardation in intrauterine growth experienced by twins. Furthermore, the data are inconsistent with the underlying assumption of a recent claim that the classic twin method is invalid for studies of adult diseases. The present study is, however, based on the one third of all pairs of twins in which both twins survived to age 6. The possible impact of this selection can be evaluated in future studies of cohorts of younger twins with lower perinatal and infant mortality.