aSouth African Centre for Epidemiological Modelling and Analysis, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch, South Africa
bZVITAMBO Project, Borrowdale, Harare, Zimbabwe.
Received 14 March, 2010
Accepted 23 March, 2010
Correspondence to Brian G. Williams, South African Centre for Epidemiological Modelling and Analysis, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, 19 Jonkershoek Road, Stellenbosch 7600, South Africa. E-mail: BrianGerardWilliams@gmail.com
Hargrove and Humphrey  have recently shown that mortality among postpartum women in Zimbabwe is significantly higher in HIV-positive compared with HIV-negative women, even for those with the highest CD4+ cell counts. Here, we present a model that predicts the observed dependence of mortality on CD4+ cell counts and further clarifies the result.
There is increasing evidence that the prognosis for people infected with HIV is worse if they defer the start of antiretroviral therapy  but the improvement in survival declines as CD4+ cell counts increase . In these studies, the comparison was among HIV-positive people with different CD4+ cell counts. However, in the study by Hargrove and Humphrey , the comparison is with HIV-negative women and even those with a CD4+ cell count greater than 600 cells/μl suffer a six-fold greater mortality at 1 year. The data are replotted in Fig. 1 with the CD4+ cell count categories chosen so that each of the 10 categories has as close as possible to one-tenth of the total number of deaths to ensure that the confidence limits on each data point are similar.
We use a previously published model  to fit the CD4+ cell count distribution of HIV-negative women in the study to a log-normal distribution giving a median value of 798 cells/μl and a standard deviation of 0.42 (test of deviance, P = 0.062). We allow the CD4+ cell count to drop by 25% immediately after seroconversion and to decline linearly to death thereafter . We assume that survival after infection follows a Weibull distribution with a median of 10 years and a shape parameter of 2.25  and is independent of the CD4+ cell count at seroconversion . The model has been used to predict the distribution of CD4+ cell counts in HIV-positive populations in Zambia and in South Africa  and to predict the probability distribution of the rate of decline of CD4+ cell counts . We use a Monte Carlo integration to estimate the mortality at 1 year for women as a function of their CD4+ cell counts.
As shown in Fig. 1, the model predicts the observed data quite accurately. The model has no free parameters that have been adjusted to improve the fit. The lower horizontal line in Fig. 1 is the observed mortality of 0.14% in HIV-negative women at 1 year. The upper horizontal line is the asymptotic value of the mortality in HIV-positive women, calculated from the model, which at 1 year is 0.35%. As women with a very high CD4+ cell count must have been infected very recently, the asymptote is given by the survival 1 year after seroconversion. This does not depend on the details of the model and can be calculated directly from the Weibull survival function.
For women with a CD4+ cell count of 100, 200, 500, 1000 and 2000 cells/μl, the model suggests that the mortality at 1 year is 101, 25, 6.1, 3.9 and 2.9 times greater than in HIV-negative women. Even at the highest CD4+ cell counts, the mortality of HIV-positive women is 2.5 times the mortality in HIV-negative women.
This model facilitates estimation of the expected mortality of HIV-positive people as a function of their CD4+ cell counts, provided the distribution of CD4+ cell counts is known for HIV-negative people in the same population. The model also illustrates the magnitude of reduced mortality risk that may result from HAART according to CD4 cell count. The relative benefit of initiating treatment declines as the CD4+ cell count increases in agreement with studies [2,3] that included only HIV-positive people. But even though the mortality among women who start at 600 cells/μl is only 15% greater than the mortality among those that start at 500 cells/μl, the mortality in both cases is five to six times greater than in HIV-negative women. Initiating treatment even at the very highest CD4 cell counts is likely to yield important survival benefits for postpartum women.
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