A comparison of methods for estimating mortality parameters from survival data

Abstract

The Gompertz mortality function, R m = R 0e αt , is frequently used to describe changes in mortality rate ( R m ) with time ( t). In this paper, four methods for determining the best fit values of the two parameters, R 0 and α, are compared. Three of the four methods use the Gompertz mortality function with mortality rate estimates derived from survival data to determine the best fit values of the two parameters. All three confront problems. The fourth method uses the Gompertz survival function, which can be derived from the Gompertz mortality function and which allows one to use survival data directly. It thereby avoids the problems and generally gives the best estimates for the two parameters. The use of the mortality function, with mortality rate estimates, confronts four distinct problems. One of these is caused by time intervals when zero organisms die. A second is caused by errors produced in estimating mortality rates from survival data. If too high a proportion of a population die in a given time interval, the mortality rate estimates are too low. A third problem is the sensitivity of the mortality-equation-based analyses to values at the end of the survival curve, where scatter in mortality values tends to be greater. A final problem occurs when time intervals greater than one time unit (day, week, year, etc.) are used in the analysis. Such problems with the use of mortality rates to estimate parameter values are revealed when the calculated parameters are used to produce a survival curve, or when known values of R 0 and α are used to generate survival data. This paper introduces a non-linear regression analysis, using a Simplex algorithm to fit parameters R 0 and α in the Gompertz Survival function and concludes that it gives more reliable and consistent results with a variety of data than do three methods that use the mortality function.