The serorevertion and the survival related to HIV infection among children: Statistical modeling applied to retrospective data collection

We are interested in describing the biological phenomenon of the time of serorevertion or death due to AIDS. By the serorevertion, we mean the cleansing of maternally derived antibodies against HIV by seropositive children without HIV infection, and the survival is related to how long HIV infected children survive. In order to perform a posteriori descriptions of retrospective data related to babies from HIV infected mothers, we develop a simple statistical methodology. The resulting statistical model is a function of two parameters named half-age and phenomenon-gauge. The modelʹs parameters are fitted to the collection of seropositive childrenʹs data by the maximum likelihood estimation method. We compare this parametric estimation with nonparametric Kaplan-Meier estimation with respect to the half-age.