Multinomial analysis of smoothed HIV back-calculation models incorporatinguncertainty in the AIDS incidence

Back-calculation models, developed to reconstruct the past trend of human i mmunodeficiency virus (HIV) and to project future acquired immunodeficiency syndrome incidence (AIDS), are usually and unrealistically based on the as sumption that the observed AIDS counts are independently distributed accord ing to a Poisson process. In contrast, we argue that a multinomial framewor k is more suitable to this situation, leading to a natural covariance struc ture. The ill-conditioned nature of the problem is solved by modelling the HIV parameters according to a cubic spline function to reduce the dimension ality of the parameter space and obtain smoother parameter estimates. We ap plied a regression spline technique which yields to a computationally stabl e basis incorporating the incubation period in the new design matrix. We di rectly incorporate the reporting delay distribution in the AIDS incidence d ata, leading to a more complex formulation of the variance and covariance m odel that is adapted to the iteratively reweighted least square (IRLS) algo rithm. In this case we obtain more accurate estimates of the standard error of the HIV incidence, especially in the most recent time. Our model, which uses a cubic spline reparameterization based on a multinomial probability distribution, is applied to the AIDS epidemic data in Italy. Copyright (C) 2001 John Wiley & Sons, Ltd.