# BED estimates of HIV incidence must be adjusted

HIV Laboratory Branch, Division of HV/AIDS, Centers for Disease Control and Prevention, Atlanta, Georgia, USA.

Received 23 March, 2009

Revised 24 May, 2009

Accepted 3 June, 2009

Correspondence to John S. McDougal, MD, Mailstop A25, Centers for Disease Control and Prevention, 1600 Clifton Rd, Atlanta, GA 30333, USA. Tel: +1 404 639 4158; e-mail: JSM3@cdc.gov

Brookmeyer ^{[1]} questions the need for an adjustment to the BED estimate of incidence if a more inclusive estimate of the mean window period was used. Furthermore, he states that the McDougal adjustment has no net effect and that the Hargrove adjustment has a mathematical error ^{[2,3]}. Hargrove ^{[4]} has lodged a compelling rebuttal. Herein, we clarify the derivation of the of the McDougal adjustment and demonstrate that the variable influence of false-recent prevalent specimens cannot be corrected with a single fixed window period.

Following infection, the immune response to the BED antigen is manifested as progressively higher optical density (OD) responses. The mean time from initial infection to surpassing an arbitrary OD response (0.800) is known as the window (*Î¼*), and patients who register an OD less than 0.800 are considered recently infected. The frequency of people who register recent divided by the mean window (*Î¼*) is the estimate of incidence (new infections per person per unit of time).

Our model of the distribution of an HIV-seropositive population (*N*_{spos}) versus duration of infection is shown in Fig. 1. Duration of infection is plotted as multiples of the window *Î¼*. For a given interval, the number testing recent (graph c) is the product of the number seropositve (graph a) and the proportion recent (graph b). The proportion testing recent was determined for each of three intervals by integration of the plot from 0â€“1 *Î¼* (sensitivity), 1â€“2 *Î¼* (1 âˆ’ specificity 1), and higher than 2 *Î¼* (1 âˆ’ specificity 2).

The adjustment derives from an equation where the proportion of seropositive specimens observed to be recent by testing (*P*_{o}) is related to the true proportion recent (*P*_{t}) through the expected sensitivity/specificity performance of the assay (Fig. 1).

This equation has four terms representing, from left to right, the total number that test recent, the number in the first window that test recent (true recent), the number in the second window that test recent (false recent), and the number in the remainder (>2 *Î¼*) that test recent (false recent). The latter is overlooked by Brookmeyer. The equation can be rearranged and simplified as:

*P*_{t}/*P*_{o} is a dimensionless ratio by which the observed proportion or number recent is multiplied to give the true proportion or number.

We agree that false-negative specimens in the first window (1 âˆ’ sensitivity) and false-recent specimens in the second window (1 âˆ’ specificity 1) tend to cancel each other out with a combined effect of near zero (Fig. 1). The inclusion of sensitivity and specificity 1 in the formula mathematically dictates the size of the population in the first two windows and, by subtraction, the size of the remaining prevalent (>2 *Î¼*) population. Nevertheless, the net effect of the adjustment is not zero. Brookmeyer ignores the adjustment for long-term specimens (>2 *Î¼*) that test false-recent [the fourth term in Eq. (1)]. The number of long-term infected (>2 *Î¼*) specimens that may be misclassified as recent can easily outnumber specimens in the first two windows. The prime determinant of the magnitude of this distortion is prevalence. Brookmeyer proposes that these â€˜prevalent false-recentâ€™ patients ultimately surpass the cut-off (within 3 years) and that a more appropriate and inclusive window would accommodate them. Two populations with the same incidence but different prevalence should register the same incidence value. In Brookmeyer's own example of two populations with the same incidence but different prevalence (Table 1 from ^{[1]}), the hypothetical example did not allow a false-recent rate in the prevalent specimens, and thus the unadjusted incidence rates agreed. Had he modeled the population with a false-recent rate in prevalent specimens, as actually occurs, there would have been concordance in the adjusted rates. Although it is possible to adjust the window to give any desired incidence, there is no way a single window can be appropriate for calculations involving differing numbers of long-term recent specimens.

A central feature of the Brookmeyer thesis is the assumption that all HIV-infected people mount a BED response that eventually crosses the cut-off within 3 years after infection. To affirm this finding, BED testing of specimens documented to be more than 3 years after infection is required. Unfortunately, we do not have many informative specimens needed to resolve this issue. We have examined 27 specimens from people documented to be 3 or more years after infection: 26 tested nonrecent and one had an OD of 0.800. However, Laeyendecker *et al.* ^{[5]} reported a group of 16 patients referred to as elite suppressors [low viral load, normal CD4, no antiretroviral (ARV) and infected at least 10 years]. Half of them tested recent. Clearly, not all patients are above the cut-off by 3 or more years.

There are practical barriers to obtaining an uncensored window that spans the 0â€“3-year postinfection period. Slow responders are infrequent and collections containing the required serial specimens are not readily available. Unless the window for these patients and their frequency are accurately known, there is risk of a disproportionate influence on the mean window. The issue of available and informative datasets is further complicated by the increasing use of ARV therapy in people with prevalent infection. Current window calculations are based mostly on serial data that are less than 1 year after infection, more specifically 0â€“2 window periods after infection. Data are plentiful and, in this region, are less likely to be influenced by factors that are unrelated to an orderly biological response to the BED antigen, and span the decision point (the cut-off). It may be more efficient and feasible to use the window determined with robust serial data, and let the adjustment correct for prevalent false-recent specimens. Elimination of people with AIDS, those on ARV therapy, those with confirmed or self-reported HIV seropositivity of at least a year's duration will refine incidence estimates. However, until and unless we can identify long-term infections and remove them from the calculation of incidence, there will be a need for some sort of correction.

Although the theory is sound and the mathematics valid, the Hargrove/McDougal adjustments are not definitive. The paramount uncertainty is the derivation of an assigned false-recent rate in prevalent infections [(1 âˆ’ specificity 2) for McDougal or *ϵ* for Hargrove] that is relevant to the population being tested. One testing strategy is to revisit the seropositive members of a cross-sectional population 1 year after the initial collection, retest with the BED assay, determine the rate of BED-recent specimens, and use this as the assigned value of (1 âˆ’ specificity 2) or *ϵ*. This approach has been documented to result in valid incidence values ^{[2]}.

## References

*et al*. Improved HIV-1 incidence estimates using the BED capture enzyme immunoassay. AIDS 2008; 22:511.

*et al*. Comparison of HIV Type 1 incidence observed during longitudinal follow-up with incidence estimated by cross-sectional analysis using the BED capture enzyme immunoassay. AIDS Res Hum Retroviruses 2006; 22:945â€“952.

**BED estimates of HIV incidence must be adjusted [letter to the editor].**

*AIDS*2009;

**23**:2061â€“2062.

*et al.*

**Decreasing HIV incidence and prevalence at the Johns Hopkins Emergency Department with a concurrent increase of virally suppressed HIV-infected individuals**[abstract]. In:

*16th Conference on Retroviruses and Opportunistic Infections*; 8â€“11 February 2009; Montreal, Canada; abstract 1045.