Studies of the biology of aging (both experimental and evolutionary) frequently involve the estimation of parameters arising in various multi-parameter survival models such as the Gompertz or Weibull distribution. Standard parameter estimation methodologies, such as maximum likelihood estimation (MLE) or nonlinear regression (NLR), require knowledge of the actual life spans or their explicit algebraic equivalents in order to provide reliable parameter estimates. Many fundamental biological discussions and conclusions are highly dependent upon accurate estimates of these survival parameters (this has historically been the case in the study of genetic and environmental effects on longevity and the evolutionary biology of aging). In this article, we examine some of the issues arising in the estimation of gerontologic survival model parameters. We not only address issues of accuracy when the original life-span data are unknown, we consider the accuracy of the estimates even when the exact life spans are known. We examine these issues as applied to known experimental data on diet restriction and we fit the frequently used, two-parameter Gompertzian survival distribution to these experimental data. Consequences of methodological misuse are demonstrated and subsequently related to the values of the final parameter estimates and their associated errors. These results generalize to other multiparametric distributions such as the Weibull, Makeham, and logistic survival distributions.
Attempts to understand aging processes often involve life-span measurements from which a survival curve is constructed and model parameters estimated. The parameter estimates are then compared, and conclusions concerning the underlying biological processes are subsequently deduced, based upon the magnitude of the parameter differences. In this article we discuss the role of sample size and sample fluctuation on the parameter estimates and the profound effect that these factors may play in our arrival at meaningful biological conclusions. We then extend this discussion to examine one methodology that can help select sample sizes for specific parametric survival models.
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