Median time from seroconversion to AIDS in Italian HIV-positive haemophiliacs: different parametric estimates

The purpose of this study was to estimate the median incubation time between human immunodeficiency virus (HIV) infection and onset of acquired immunodeficiency syndrome (AIDS), using three parametric models and six estimates of seroconversion time. Study subjects were 732 HIV-positive haemophiliacs enrolled in the Italian Registry of patients with congenital coagulation disorders. Seroconversion time was estimated for each subject according to six different criteria, based on three distributions of seroconversion (uniform, uniform on three sub-intervals and truncated Weibull) and two indices synthesizing each distribution (median and median of three random values). The estimated seroconversion times were subsequently used as starting points in the analysis of incubation. This was performed applying Kaplan-Meier non-parametric survival analysis, and fitting to incubation data three probability density functions, representing three different situations with respect to the hazard of developing AIDS following seroconversion (namely Weibull (WE), generalized exponential (GE) and log-logistic (LL)). The cumulative incidence over an 8-year period ranged from 14.9 to 17.8 per cent when applying the Kaplan-Meier method, from 14.1 to 17.2 per cent when using the WE function, from 14.5 to 17.3 per cent when using the GE function and from 14.4 to 17.3 per cent when using the LL function, depending on the estimate of seroconversion time used. Similarly, the median incubation times ranged from 12.6 to 15.0 years with the WE function, from 14.0 to 16.5 years with the GE function, and from 13.4 to 16.1 years with the LL function. The presence of a bound on the increase of the hazard function seems to affect the incubation more strongly than the eventual decrease following the attainment of the maximum risk. This may be due to the decrease in the hazard beginning when most of the seropositive subjects have already developed AIDS.