Static and dynamic models of interdisease competition: past and projected mortality from amyotrophic lateral sclerosis and multiple sclerosis.

Longitudinal Gompertzian analysis is an effective method for determining both the pure probability of death for a given condition and the size of inherently susceptible subpopulations [1]. Gompertzian analysis has been used in this study to provide the parameters necessary to construct a stationary population lifetable (static model) of mortality for amyotrophic lateral sclerosis (ALS) and for multiple sclerosis (MS). The static model demonstrates the relative effect of changing general mortality upon the mortality from each specific disease in a situation where interdisease competition is continuously changing. In order to represent mortality in a real population more closely (where age structure is not the result of mortality rates alone) a dynamic model was constructed for both conditions using the age distributions of the population of England and Wales. The quality of the model was verified by comparison of estimated mortality with historical data from the last three decades. The dynamic model has then been used to estimate mortality from each condition over the next three decades on the basis of population projections made by the Central Statistical Office [2], assuming no major change in the factors which lead to either condition. This analysis demonstrates both the theoretical applicability and practical capabilities of Gompertz-derived mortality models for analysing changing mortality patterns.