Dependent HIV incidences in back-projection of AIDS incidence data

Techniques for reconstructing plausible HIV incidence curves from AIDS incidence data are called methods of back-projection, or back-calculation. Approaches to back-projection tend to make the simplifying assumption that the quarterly HIV incidences are independent, which is not even approximately true. Here we investigate whether smoothed non-parametric back-projection based on this simplifying assumption gives sensible back-projections and appropriate measures of precision for these reconstructed HIV incidence curves. Simple models for HIV transmission are shown to have much greater variation than the corresponding non-homogeneous Poisson process arising from the independence assumption. Nevertheless, bearing in mind that the objective is to reconstruct the HIV epidemic curve for the current epidemic, it is argued that such back-projection does give sensible HIV curves. This conclusion is supported by a simulation study, which also finds that confidence intervals for the HIV incidences are wider for transmission data than those determined from independent Poisson data.