Model fitting and hypothesis testing for age-specific mortality data

Abstract

Demographic studies focusing on age‐specific mortality rates are becoming increasingly common throughout the fields of life‐history evolution, ecology and biogerontology. Well‐defined statistical techniques for quantifying patterns of mortality within a cohort and identifying differences in age‐specific mortality among cohorts are needed. Here I discuss using maximum likelihood (ML) statistical methods to estimate the parameters of mathematical models, which are used to describe the change in mortality with age. ML provides a convenient and powerful framework for choosing an adequate mortality model, estimating model parameters and testing hypotheses about differences in parameters among experimental or ecological treatments. Simulations suggest that experiments designed to estimate age‐specific mortality should involve at least 100‐500 individuals per cohort per treatment. Significant bias in the estimation of model parameters is introduced when the mortality model is misspecified and samples are too small to detect the true mortality pattern. Furthermore, the lack of simple and efficient procedures for comparing different mortality models has forced the use of the Gompertz model, which specifies an exponentially increasing mortality with age, and which may not apply to the majority of experimental systems.

Lifespan modification by glucose and methionine in Drosophila melanogaster fed a chemically defined diet

“…Scatter plot of observed mortality rates -lnμ x (triangles) and projected mortality curves (lines) as a function of age. The projected mortality curves are fitted according to the parameters derived from the Gompertz-Makeham models given in Table 3 using a maximum likelihood procedure and facilitates hypothesis testing of whether the fitted models differ by experimental treatment (Pletcher 1999;Pletcher et al 2000). Mortality models fitted with the WinModest program established that the GompertzMakeham function provided the best fit model for all diets.…”

Quantitative genetic tests of recent senescence theory: age-specific mortality and male fertility in Drosophila melanogaster

“…For the inbreeding load analysis (see below), we pooled all cages within a genotype to calculate the mortality. We used Winmodest (Pletcher, 1999), a maximumlikelihood estimator of parametric mortality models, to fit age at death data to the Gompertz model…”

Age‐specific metabolic rates and mortality rates in the genusDrosophila

“…Deaths summed over all ages from each cohort estimate the initial cohort size N 0 ; the number alive N x at age x was calculated from N x−1 less the deaths from the period x − 1 to x. Mortality rate was estimated as (1) Lee, 1992), where ∆x is the interval over which deaths are observed. From the distribution of deaths per interval, maximum likelihood methods executed in Winmodest (see Pletcher, 1999) estimated mortality parameters of the Gompertz-Makeham model:…”

“…The exponent b can be interpreted as the 'demographic rate of aging' (MRDT, Finch et al, 1990). WinModest (Pletcher, 1999) was also used to estimate mean life span for each species and sex, and to evaluate hypotheses on homogeneity of the Gompertz mortality parameters among species. WinModest provides unbiased estimates and incorporates censored data.…”