Logarithmic relationship of the CD4 count to survival in patients with human immunodeficiency virus infection

Abstract

Background: Survival, and the incidence of events that define the acquired immunodeficiency syndrome (AIDS), are known to be inversely related to the CD4 count in patients with human immunodeficiency virus infection. We wished to quantify this relationship more precisely, particularly for patients with CD4 counts of less than 50/mm3.

Methods: Prospective surveillance for survival and for all AIDS-defining events was performed on all 2682 patients with human immunodeficiency virus infection who had at least one CD4 count performed at a large urban public hospital during a 3-year period. Product-limit survival and incidence of AIDS-defining events were calculated as a function of baseline CD4 count.

Results: The 1-year product-limit survival was 17% +/- 6% for patients after a baseline CD4 count of 1 to 4/mm3; 44% +/- 6% after a count of 5 to 9/mm3; 48% +/- 5% after a count of 10 to 19/mm3; 51% +/- 4% after a count of 20 to 39/mm3; 62% +/- 5% after a count of 40 to 59/mm3; 71% +/- 4% after a count of 60 to 99/mm3; 79% +/- 3% after a count of 100 to 199/mm3; and 92% +/- 2% after a count of 200 to 499/mm3. One-year survival and baseline CD4 count were related by the following formula: percent 1-year survival = 10 + 32(log10 CD4 count) (R2 = .97; P < .001). The 1-year incidence of a first AIDS-defining event and baseline CD4 count were related by the following formula: percent developing AIDS in 1 year = 104-36(log10 CD4 count) (R2 = .89; P < .001). Similar relationships were calculated between the logarithm of the baseline CD4 count and the 1-year incidence of most AIDS-defining events. These relationships were linear over the CD4 range of 1 to 499/mm3 and over follow-up periods of 6 months to 2 years.

Conclusions: The relationship of the CD4 count to survival, and to the incidence of AIDS-defining events, is logarithmic. This relationship helps explain the substantial differences in 1-year survival associated with baseline CD4 counts in the range below 50/mm3.