MARKER-DEPENDENT HAZARD ESTIMATION - AN APPLICATION TO AIDS

The acquired immunodeficiency syndrome (AIDS) results from infection w ith the human immunodeficiency virus (HIV). The time of infection is g enerally unknown since transmission usually occurs during the course o f repeated sexual contacts or needle sharing. Brookmeyer and Gail desc ribe the biases that may arise in survival analyses using the recruitm ent time rather than the unknown infection time as the origin in preva lent cohorts of HIV-infected individuals. We apply a non-parametric ha zard estimator, introduced by Nielsen, that assumes the hazard of an A IDS diagnosis depends upon the unknown time of infection solely throug h the value of possibly multidimensional markers of HIV-disease progre ssion such as CD4+ T lymphocyte cell counts. Essentially, we estimate the hazard for a specific marker value y by dividing the number of occ urrences among subjects with marker measurements in a neighbourhood of y by the total risk time in that neighbourhood. We present this estim ator, which relies upon kernel estimator techniques to produce a smoot h estimate, within a counting process framework. We apply this method to marker data from the San Francisco Men's Health Study.