SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch, South Africa.
Received 4 February, 2009
Revised 1 June, 2009
Accepted 9 June, 2009
Correspondence to John W. Hargrove, PhD, SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, 19 Jonkershoekweg, Stellenbosch 7600, South Africa. Tel: +27 21 808 2589; fax: +27 21 808 2586
Brookmeyer concludes that adjustments to capture enzyme immunoassay (BED-CEIA or simply BED) HIV incidence estimates ‘do not increase … accuracy’ , that the ‘mathematical implication of the Hargrove assumption is that ϵ is 0’, where ϵ is the probability that a person HIV-positive for more than twice the window period tests recent by BED . Moreover, the ‘Hargrove adjustment has a mathematical error that can cause significant underestimation of HIV incidence rates’. Increased accuracy could, however, be achieved ‘through improvements in the estimates of the mean window period’ .
These claims can be dismissed by considering their implications for our analysis. We found a 2.2-fold discrepancy between unadjusted BED (7.6%) and follow-up (3.4%) incidence, estimated over 12 months postpartum. Both estimates used the same cohort, obviating any concerns regarding differential effects of selection bias and adherence . This led to the suggested adjustment
for the annualized risk of HIV infection as estimated by BED:
for Ω mean window, N HIV-negative cases, P positive, R recent by BED. If, as Brookmeyer suggests, ϵ ≡ 0, the BED incidence estimates can indeed only be matched to the follow-up values by changing Ω. Solving (1) for Ω with ϵ = 0, N = 6595, R = 279 and I (the follow-up incidence) = 0.034, gives
This window is 2.3 times our estimated mean of 187 days, and more than 20% longer than the longest window among all cases where BED normalized optical density (ODn) ever exceeded the 0.8 cut-off (fig. 1 in ). A window of 439 days is also incompatible with Brookmeyer's conclusion that ‘false positives exactly counterbalance false negatives ’ (cf quadrants D and B in Fig. 1a below).
When ϵ = 0, our baseline BED incidence was an impossibly high 9.5% and, against reasonable expectation, was a nondecreasing function of age, independent of the assumed value of Ω (Fig. 1b). Conversely, the Hargrove adjustment, with ϵ = 0.052, gave plausible incidence estimates, decreasing with age as expected .
Thus, insisting that ϵ = 0 implies unrealistically long estimates of the mean window period and an inappropriate age-specific incidence function. The problem can be resolved by considering the results for 918 HIV positive women whose baseline CD4 level (<350 cells/μl) suggested that the majority had already been HIV positive for more than 2 years. One year later, when most had then been positive for more than 3 years, 35 tested recent by BED. This implies at least one of the following scenarios: There are window periods more than 3 years, contrary to Brookmeyer's assumption but consistent with other evidence (Fig. 1a); in some cases ODn had declined secondarily, as noted previously . Brookmeyer ignored the latter scenario, which can result in long-term false-recent cases, regardless of the window period. In any event, therefore, ϵ is greater than 0, negating the basis of Brookmeyer's argument and his criticisms of the McDougal and Hargrove adjustments.
Regardless of the above arguments, the results in Brookmeyer's Table 1 are invalid, as is his statement that the ‘Hargrove adjustment (with ϵ = 0.052) will give a negative estimate of incidence if the true HIV incidence rate is 1% per year and if the percentage of the population with longstanding prevalent infections of greater than 3 years duration is 10% or more.’ In both cases, the hypothetical population has been synthesized assuming ϵ = 0, but then the Hargrove adjustment is estimated assuming ϵ = 0.052. The resulting under-estimate of incidence stems from this inconsistency, not from an error in the Hargrove adjustment.
Whereas improved mean window estimates are highly desirable they will not, by themselves, result in accurate HIV incidence estimates from the BED method. Until, therefore, we can unequivocally identify long-term HIV infections, BED HIV incidence estimates must be adjusted, using a good estimate of the long-term specificity (1 – ϵ) appropriate for the study population .
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2. Hargrove JW, Humphrey JH, Mutasa K, Parekh BS, McDougal JS, Ntozini R, et al
. Improved HIV-1 incidence estimates using the BED capture enzyme immunoassay. AIDS 2008; 22:511–518.