FEATURES OF GOMPERTZ FUNCTIONS IN MODELING MORTALITY RATES
Author(s)
Wendland G1, Lauterbach K2, 1Guido Wendland, Cologne, NW, Germany; 2University of Cologne, Cologne, Germany
Presentation Documents
OBJECTIVES: Despite their surprisingly good fit of current mortality data, Gompertz-functions are rather seldom used in outcome research. The main objective is to show some interesting methodological features of the Gompertz function encouraging a more wide-spread use in modeling mortality rates beyond the time frame of clinical trials. METHODS: Current mortality data of the Statistical Yearbook of Germany are closely fitted by Gompertz functions (Rx =R0 exp(bx), x=age) which involves estimating parameters b und R0 by non-linear iterative regression. Several authors have observed that in a series of Gompertz-functions from the same underlying population (i.e life tables from different years, different subgroups, different regions etc.) the two parameters are closely related as: ln R0=ab + ß, where a <0, ß € IR. Based on this relation, it is shown how to determine Gompertz functions for specific study cohorts by specifying a standardised mortality ratio (SMR) at a certain age. In practical applications this SMR can be estimated from clinical trials data. RESULTS: All Gompertz-functions satisfying the relation ln R0=ab + ß intersect at (-a, exp(ß)). If the SMR is fixed at an age of x' then a Gompertz-function satisfying this condition is given by b2=ln(SMR)/(x'+?a) + b1, and R20=exp(ab2) exp(ß)?, where (b2, R20) is the pair of parameters of the new Gompertz-function, and the pair (b1,R10) belongs to the baseline Gompertz-function. Furthermore it holds that the hazard ratio at any age is given by the ratio (R20/R10)x/a + 1. CONCLUSIONS: The more frequent use of Gompertz-Functions in the area of modeling is motivated by the good fit of mortality data in the general population. Furthermore, this analysis shows how these results can be extended to specific subgroups of patients, when clinical trials data only provide little mortality data. The analysis of high-risk groups in disease prevention seems a sensible context for applying these results.
Conference/Value in Health Info
2002-05, ISPOR 2002, Arlington, VA, USA
Value in Health, Vol. 5, No. 3 (May/June 2002)
Code
PMI26
Topic
Methodological & Statistical Research
Topic Subcategory
Modeling and simulation
Disease
Multiple Diseases