Abstract #300850

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JSM 2003 Abstract #300850
Activity Number: 219
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 9:00 AM to 10:50 AM
Sponsor: Section on Statistics in Epidemiology
Abstract - #300850
Title: On the Current, Excess, and Total Llife Distributions When Renewal Process Reaches a Special Event
Author(s): Ruiguang Song*+ and John M. Karon
Companies: Center for Disease Control and Prevention and Centers for Disease Control and Prevention
Address: 1600 Clifton Rd., NE, Atlanta, GA, 30333,
Keywords: renewal process ; equilibrium ; constant hazard ; survival time ; gamma distribution
Abstract:

When a renewal process has reached equilibrium, the current, excess, and total life distributions are well-known. If the time for a renewal process is bounded, then these distributions can be obtained by solving the renewal equation. An explicit solution of the renewal equation is available only for a few special cases. In this study, we consider the application of renewal theory to the detection of a chronic disease, in particular, HIV. People at risk are tested repeatedly until a positive result is observed. Under the condition that the hazard for each person at risk is constant over time, we provide explicit formulas for the distributions associated with the last intertest interval and show that the equilibrium can be reached by the time of onset of the disease when the infection hazard is small. For HIV, a recent infection can be distinguished from a long standing infection by applying a less sensitive test. We derive the probability distributions for the last intertest interval for persons detected with recent or long standing infection. We discuss applications of these results to estimating HIV incidence.

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