Testing a Model of Aging in Animal Experiments

Abstract

A stochastic model of aging is developed in terms of accumulation and expression of intracellular lesions caused by environment or intrinsic genetic program. In contrast to the commonly used Gompertz-Makeham approach to the parametric analysis of mortality data, the model yields a hazard function that is bounded from above. For testing the model in experiments aimed at studying animal longevity, a Kolmogorov-type statistical test is presented with regard to the hypothesis involving unknown parameters. Examples concerning longevity of intact animals of two different species, as well as the effect of a prolonged irradiation at a low dose rate, are given to illustrate the model application and goodness-of-fit testing. The results of the analysis of published data show that the rate of lesion formation is not sustained at a constant level throughout life, though in some cases its variations with age can be considered negligible.

Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth

“…Later, the Gompertzian deterministic model was found to fit well diverse growth phenomena in nature, including tumor and embryonic growth. To the best of our knowledge, there have been few attempts to give biological theoretical grounding to the Gompertzian model (cf., Bass and Green, 1989;Qi et al, 1993;Tyurin et al, 1995) in spite of its extensive use in biological and medical research. Especially in experimental oncology, the Gompertzian model is most widely used to describe in vivo tumor growth.…”

A Modified Stochastic Gompertz Model for Tumour Cell Growth

“…Despite their simplicity, such models of tumour growth make possible the description of the principal regularities and provide effective guidelines for cancer therapy, drug development and clinical decision-making [19]. In the past two decades, the deterministic Gompertz law of population growth has been widely used to describe in vivo tumour growth in experimental oncology [2,5,10,18,20,22]. If xðtÞ is the size of the tumour cell at time t, then the Gompertz law models the cell growth by the equation…”

Estimation of the hazard function in a semiparametric model with covariate measurement error

“…This latter is commonly used in analysis of mortality data (see [37]). We refer to [2,10,17] for discussions on parametric survival time models and their advantages.…”