Uncertainty in estimates of HIV prevalence derived by backcalculation

The incidence of consistently defined acquired immunodeficiency syndrome (AIDS) among adults in the United States was used to "backcalculate" the prevalence of human immunodeficiency virus (HIV) as of January 1, 1985, and July 1, 1987. The sensitivity of estimates to random and systematic sources of uncertainty was assessed. Using a "standard" incubation distribution with a 10-year median time-to-AIDS, we estimated that 544,000 persons were infected as of January 1, 1985, and that 992,000 persons were infected as of July 1, 1987. Variation from model selection and fitting was only 2% and 5%, respectively. Perturbations of the AIDS incidence counts to reflect plausible reporting biases reduced prevalence estimates by as much as 9.6% and 16.0%, respectively. Uncertainty about the incubation distribution had an even greater impact. A "plausible range" of prevalence estimates was calculated using alternative "Fast" and "Slow" incubation distributions. The plausible range varied from 415,000 to 760,000 persons in 1985 and from 737,000 to 1.4 million persons in July 1987. Inclusion of AIDS incidence counts beyond mid-1987 can lead to serious underestimates of prevalence, because use of zidovudine and other therapies beginning in mid-1987 has lengthened the incubation distribution in many severely immunodepressed persons without AIDS.