Optimisation as a statistical estimation tool: an example in estimating the AIDS treatment-free incubation period distribution

Abstract

The identification of the AIDS incubation period distribution, together with its parameters, is a vital component of any epidemiological model designed to portray scenarios concerning future trends in reported AIDS cases or to evaluate intervention strategies. The Transfusion-Associated dataset of AIDS cases in the U.S.A. can be utilised in this identification process. By employing an appropriate system dynamics software tool an optimisation approach to the fitting process has been conducted. However, although the task of interpreting a best fit using parametric methods is hampered because, in particular, the data are right-censored, the results do provide a template against which to judge the effects of recent treatment advances in delaying progression to AIDS. As a case study in system dynamics optimisation, this demonstrates the need to use a powerful tool with care: considerations other than the best objective function, together with its resultant parameter set, have to be taken into account. The results show that a three-stage distribution, with unequal phases at each stage, is an appropriate incubation time model to employ in situations where projections of future AIDS incidence are being attempted. The work is also an affirmation of the utility of the system dynamics approach insofar as real-world complications can be easily handled in model formulation. Copyright © 1999 John Wiley & Sons, Ltd.