Senescence rates in patients with end‐stage renal disease: a critical appraisal of the Gompertz model

Abstract

SummaryThe most frequently used model to describe the exponential increase in mortality rate over age is the Gompertz equation. Logarithmically transformed, the equation conforms to a straight line, of which the slope has been interpreted as the rate of senescence. Earlier, we proposed the derivative function of the Gompertz equation as a superior descriptor of senescence rate. Here, we tested both measures of the rate of senescence in a population of patients with end-stage renal disease. It is clinical dogma that patients on dialysis experience accelerated senescence, whereas those with a functional kidney transplant have mortality rates comparable to the general population. Therefore, we calculated the age-specific mortality rates for European patients on dialysis (n = 274 221; follow-up = 594 767 person-years), for European patients with a functioning kidney transplant (n = 61 286; followup = 345 024 person-years), and for the general European population. We found higher mortality rates, but a smaller slope of logarithmic mortality curve for patients on dialysis compared with both patients with a functioning kidney transplant and the general population (P < 0.001). A classical interpretation of the Gompertz model would imply that the rate of senescence in patients on dialysis is lower than in patients with a functioning transplant and lower than in the general population. In contrast, the derivative function of the Gompertz equation yielded the highest senescence rates for patients on dialysis, whereas the rate was similar in patients with a functioning transplant and the general population. We conclude that the rate of senescence is better described by the derivative function of the Gompertz equation.

Aging and uremia: Is there cellular and molecular crossover?

“…Aging is characterized by a progressive loss of phy siological integrity, leading to impaired function and increased vulnerability to death [3] . Dialysis dependent patients of any age have an increased risk of mortality when compared to those with a functioning transplant and healthy controls of the same age [4] , and are more susceptible to disease, particularly that of the cardiova scular system: a 2534yearold dialysis patient has a relative risk of cardiovascular mortality similar to that of a > 75yearold in the general population [5] . Furthermore, the prognosis for chronic kidney disease (CKD) patients is still extremely poor and has not improved greatly despite many treatment advances: CKD patients receiving dialysis aged 50 and under are likely to live 30 years less than agematched people without CKD [5] .…”

Malleability of Human Aging<BR> <I>The Curious Case of Old-Age Mortality in Japan</I>

“…Such an explanation, which involves the diverse effects of nutrition, lifestyle, occupation, and so forth, interacting with biochemical stresses and repair mechanisms could be compatible with the strong socioeconomic gradients seen in health and life expectancy. However, although not undisputed (Koopman et al, 2011;Rozing & Westendorp, 2008), it is considered that the slope of log mortality rates is an indicator of the population rate of aging (Finch, 1990), and it should be noted that the progressive reductions of risk between the cohorts reported here bring about either a parallel reduction or a small increase in the gradient of the log-mortality slope.…”

Calculating the Rate of Senescence From Mortality Data: An Analysis of Data From the ERA-EDTA Registry

“…To compare the use of non-modeled mortality rates with the use of modeled mortality rates, the mortality rates were modeled with the Gompertz model and senescence rates were estimated as previously described (14). Considering the applicability of the model, mortality data were included for the ages of 20-85 years (14,18).…”

“…Considering the applicability of the model, mortality data were included for the ages of 20-85 years (14,18). The Gompertz model is mathematically described as m(t) = α e γ t , where m(t) is the mortality rate at age t in years and α and γ are model parameters.…”

“…We apply this method to mortality data of patients with end-stage renal disease who are either on dialysis therapy or have undergone kidney transplantation. Patients on dialysis therapy are biologically and clinically known to suffer from increased senescence rates (12)(13)(14). Mortality rates and senescence rates in patients with a functioning transplant are lower than in those on dialysis (15) and approach those of the general population (14).…”