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Estimating the incubation time distribution and expected number of cases of transfusion‐associated acquired immune deficiency syndrome

The number of cases of transfusion‐associated acquired immune deficiency syndrome (TA‐AIDS) that will be seen over the next few years is difficult to estimate, because of the uncertainty about the number of persons infected with the human immunodeficiency virus (HIV) via blood transfusion and about the duration of the incubation period from HIV infection via transfusion to diagnosis of AIDS. Presented here are a mathematical model and nonparametric and parametric statistical analyses of recent data on TA‐AIDS that indicate clearly the existing estimability problems. The methods provide short‐term projections of new TA‐AIDS cases to be reported; the results suggest about 1100 new cases to be reported in the United States between July 1988 and June 1989 and about 1500 more between July 1989 and June 1990. Estimates of the number of eventual TA‐AIDS cases to be seen are considerably more uncertain and require additional assumptions about the incubation distribution. Under the assumption that the probability of an infected person developing AIDS within 8 years of infection is 0.40 (an estimation derived from cohort studies in homosexual men and hemophiliacs), parametric and nonparametric analyses give, respectively, point estimates of 14,300 and 15,000 for the number of eventual cases of AIDS (in the age group 13–69) attributable to infection by blood transfusion prior to July 1985. The parametric analysis gives a corresponding 95 percent confidence interval (12,300, 16,800).