Mean square error of estimates of HIV prevalence and short-term AIDS projections derived by backcalculation

We simulated multinomial AIDS incidence counts from 27 'representative' AIDS epidemics that spanned a period corresponding to previous applications of backcalculation (1 January 1977 to 1 July 1987) and assessed mean square error for several back-calculated estimators of HIV prevalence and short-term AIDS projections. Estimators were based on flexible model selection procedures that chose the best-fitting non-negatively constrained model of the infection curve from a family of possible step-function models. Selection of the best-fitting model from a family of four-step models each with a long last step of width of 4 or 4.5 years offered a favourable tradeoff between bias and variance when compared with selection from families of models with three steps or from families with a short last step. Five-step models performed as well as four-step models. Three-step models had substantially larger mean square error in some epidemic situations. Percentage root mean square error (PRMSE) for estimates of cumulative HIV prevalence as of 1 January 1985 was less than 14 per cent over a range of hypothetical epidemics of N = 50,000 infected individuals. PRMSE for short-term projections was less than 18 per cent. Estimates of cumulative HIV prevalence as of 1 July 1987 were substantially more uncertain and had a PRMSE of 33 per cent in the unfavourable case of a rapidly rising HIV epidemic. Estimates of cumulative HIV prevalence as of 1 July 1987 were positively biased in HIV epidemics with a rapidly decreasing recent HIV incidence rate and negatively biased in rapidly increasing HIV epidemics. Despite these uncertainties, we obtained useful estimates even for HIV epidemics with as few as 5000 infected individuals.