Change Points in the Series of T4 Counts Prior to AIDS

The absolute number of T4 cells has been established as an important clinical marker of disease progression to acquired immunodeficiency syndrome (AIDS) in persons infected with human immunodeficiency virus (HIV). Series of T4 counts are analyzed from the 131 homosexual men who entered the New York Blood Center Study in 1984, mostly seropositive for HIV, and who developed AIDS as participants by 1990. These series exhibit a gradual decline of the log(T4) count followed by a more rapid decline close to the time of the development of AIDS. Empirical Bayes and hierarchical Bayes change point models are proposed to estimate the distribution of the time before AIDS when this rapid decline begins. Results using the EM Algorithm and Markov chain Monte Carlo indicate that the mean change point occurs approximately 1 year before diagnosis with a standard deviation of 9 months. Detection of a change point may indicate that an AIDS diagnosis is increasingly likely for an individual HIV-positive but AIDS-free.