Risk of HIV infection as a function of the duration of intravenous drug use: a non-parametric Bayesian approach

We analyse the elapsed time between intravenous (IV) drug initiation and HIV infection in a cohort of 972 injecting drug users attending a hospital detoxification unit. We use the time of seroconversion instead of the time of HIV infection because the date of HIV infection is rarely known and the gap between these two times is negligible (around one to three months). Although seroconversion time cannot be determined exactly, it can be inferred at least to within an interval. This seroconversion interval is determined from the dates of HIV antibody tests, if available. The data is consequently interval-censored. We estimate the distribution function of the elapsed time from IV drug initiation to seroconversion as well as the risk of seroconversion by means of a non-parametric Bayesian approach. The analysis is conducted according to the following four calendar periods: before or at 1980; between 1981 and 1985; between 1986 and 1991; after or at 1992 where the IV drug use was initiated. The methodology used is based on an alternating conditional sampling algorithm. The Bayesian approach allows not only the incorporation of prior beliefs about the distribution function, but also the analysis of the risk of seroconversion without assuming restrictive parametric models. Furthermore, the estimator for the distribution function is smooth and thus differences between groups can be easily interpreted.