A comprehensive back-calculation framework for estimation and prediction of HIV/AIDS in India

HIV incubation period is the random time between the HIV-infection and the onset of clinical AIDS. Distribution of this non-negative random variable is known as HIV incubation period distribution. The Back-calculation method reconstructs the past pattern of HIV infection and predicts the future number of AIDS cases with the present infection status. It depends on three important factors: incubation distribution, incidence curve and observed number of AIDS cases over time. This method is very popular and requires less information and assumptions. Lack of information about incubation distribution, the effect of intervention therapy on incubation period, and errors in reported AIDS incidence leads to uncertainties associated with this method. The incubation distribution is assumed to be exactly known in back-calculation methodology. Incubation period of HIV is very long and highly variable within and between cohorts. The current prevalence of HIV-infection and the corresponding pattern of incidence from the beginning of the epidemic to the present time are mainly estimated by means of back-calculation method. It calculates the most likely temporal distribution of infected individuals compatible with the number of observed AIDS cases starting from the suitable estimate of the incubation period, derived from the available data. Most of the projections formulated the problem of estimation of future AIDS cases as estimation of parameters in multinomial likelihood with unknown sample size by EM algorithm. In this paper the various approaches for modeling the incubation distribution are compared using real and simulated data under various infection density distributions. The projected minimum AIDS cases in India based on the reported data for the years 2003, 2004, 2005 and 2006 are around 27000, 44000, 70000 and 113000 respectively. The corresponding figures based on the adjusted data are around 67000,100000,150000 and 230000 respectively.