Marker‐dependent hazard estimation: An application to AIDS

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Abstract
The acquired immunodeficiency syndrome (AIDS) results from infection with the human immunodeficiency virus (HIV). The time of infection is generally unknown since transmission usually occurs during the course of repeated sexual contacts or needle sharing. Brookmeyer and Gail describe the biases that may arise in survival analyses using the recruitment time rather than the unknown infection time as the origin in prevalent cohorts of HIV-infected individuals. We apply a non-parametric hazard estimator, introduced by Nielsen, that assumes the hazard of an AIDS diagnosis depends upon the unknown time of infection solely through the value of possibly multidimensional markers of HIV-disease progression such as CD4+ T lymphocyte cell counts. Essentially, we estimate the hazard for a specific marker value y by dividing the number of occurrences among subjects with marker measurements in a neighbourhood of y by the total risk time in that neighbourhood. We present this estimator, which relies upon kernel estimator techniques to produce a smooth estimate, within a counting process framework. We apply this method to marker data from the San Francisco Men's Health Study.