Modelling Survivorship Kinetics: A Two-Parameter Model

Abstract

A mathematical model of survivorship kinetics is presented. It takes into account both deterministic and stochastic aspects of survival curves. Earlier reports [Piantanelli: Arch Gerontol Geriatr 1986;5:107–118; Piantanelli: Ann NY Acad Sci 1988; 521:99–109] described a model capable of making distinct predictions on the mean and standard deviation of an index of physiological function, fitting data even in the tail of survivorship curves, and accounting for the selection of the cohort at advanced ages. However, it contains four parameters whose biological interpretation is unclear. In the present paper we propose a modification of the model which maintains the main characteristics of the previous one and, in addition, results in two significant improvements. First, the number of free parameters is reduced to only two, making much easier both their estimation and interpretation, particularly when the model is applied to data from various animal groups manipulated in different ways. Second, it is possible to relate the parameters to well-defined deterministic and stochastic factors: specifically, a deterministic component describing the environmental and genetic influence on physiological functions, and a stochastic component representing the fluctuating interactions of the living organism and its environment.

Air pollution and daily mortality: a hypothesis concerning the role of impaired homeostasis.

“…The rate of decline in pulmonary function as measured by the annual loss of the 1-sec forced expiratory volume does accelerate with advancing age: Depending on the statistical model used, the rate of decline may be about 4.5-fold greater at age 75 than at age 25 (20).The topography of survival is well documented. It appears similar for humans (21,22), rodents (23), and a variety of short-lived invertebrates (24,25) and may be considered generic. In general, four stages can be identified: an initial gradual linear decline followed by an inflection or transitional stage, an exponential decline, and, finally, a reverse inflection.…”

Fatigue analysis and fracture toughness of graphene reinforced carbon fibre polymer composites

“…To plot this equation, the fatigue lives for a specific stress level are arranged in ascending order. The empirical survivorship function L R for each fatigue life data at a specific stress level were obtained from the following relationship 46 :…”

Noninvasive Neonatal Thymus Graft into the Axillary Cavity Extends the Lifespan of Old Mice

“…8 Thus, we decided to compare the survival of mice after grafting two neonatal thymi into the axillary cavities, as previously suggested for the transplant of other tissues with an endocrine role. 14 Also, in this case, conventional nonparametric tests did not show any significant change in survival between grafted old mice versus controls; however, survival analysis performed with a Piantanelli-sensitive parametric model 15,16 suggests that this kind of approach may be considered as a starting point for rejuvenating interventions. The very small difference between the two curves, which is not statistically significant according to the Kaplan-Meier analysis with log rank test, would have hardly an interest per se.…”

“…Survival data were analyzed using both Kaplan-Meier analysis (SPSS 14.0 package) and a parametric mathematical model of survivorship proposed by Piantanelli et al 15,16 The method is based on two parameters as described in Box 1.…”