Estimation of HIV infection and incubation via state space models

By using the state space model (Kalman filter model) of the HIV epidemic, i n this paper we have developed a general Bayesian procedure to estimate sim ultaneously the HIV infection distribution, the HIV incubation distribution , the numbers of susceptible people, infective people and AIDS cases. The b asic approach is to use the Gibbs sampling method combined with the weighte d bootstrap method. We have applied this method to the San Francisco AIDS i ncidence data from January 1981 to December 1992. The results show clearly that both the probability density function of the HIV infection and the pro bability density function of the HIV incubation are curves with two peaks. The results of the HIV infection distribution are clearly consistent with t he finding by Tan et al. [W.Y. Tan, S.C. Tang, S.R. Lee, Estimation of HIV seroconversion and effects of age in San Francisco homosexual populations, J. Appl. Slat. 25 (1998) 85]. The results of HIV incubation distribution se em to confirm the staged model used by Satten and Longini [G. Satten, I. Lo ngini, Markov chain with measurement error: estimating the 'true' course of marker of the progression of human immunodeficiency virus disease, Appl. S tat. 45 (1996) 275]. (C) 2000 Elsevier Science Inc. All rights reserved.