We used dried blood spot (DBS) specimens which were collected in the longitudinal population-based HIV surveillance conducted by the Africa Centre for Health and Population Studies (Africa Centre), University of KwaZulu-Natal [21]. The HIV surveillance area is located near the market town of Mtubatuba in the Umkhanyakude district of KwaZulu-Natal. The area is 438 square kilometers in size; it has a population of approximately 85,000 almost exclusively Zulu-speaking people who are members of about 11,000 households [22]. In 2004, the overall HIV prevalence among residents in the surveillance area was 27% in women (15 to 49 years of age) and 14% in men (15 to 54 years of age) [19]. The surveillance methods have been described elsewhere [20], [23]. Ethics permission for the HIV surveillance at the Africa Centre was obtained from the Research Ethics Committee at the College of Health Sciences, University of KwaZulu-Natal. All participants in the study provided written informed consent for the analysis of their samples.

All women aged 15–49 years and all men aged 15–54 years who were resident in the surveillance area at the time of visit of an HIV surveillance fieldworker were eligible for HIV testing. Different samples were used for the different analyses conducted for this article. The samples for estimation of the long-term FPR consisted of cBED assay results for blood specimens contributed by individuals who tested HIV positive in the surveillance in the time period from June 2003 through June 2006. In order to be included in the sample, the specimens had to meet the following criteria. First, they were follow-up specimens from individuals who had previously tested HIV-positive in the surveillance. Second, the time period between the first positive HIV test and the follow-up specimen exceeded the maximum BED progression time. Third, the specimen was the earliest follow-up specimen that met the second criterion. Our count of long-term false-positive individuals included all individuals who were classified as recently HIV-infected and had been infected for longer than the maximum BED progression time, i.e. it included both non-progressors and regressors.

For the further cBED assay analyses we used a maximum BED progression time of 306 days (sample size n = 1,065) as baseline assumption. In order to assess the sensitivity of the long-term FPR to the assumed maximum BED progression time, we varied progression time length from 250 to 400 days in daily intervals. Table 1 shows sample size and the number of individuals who were falsely identified as recently HIV-infected for the BED progression times when the long-term FPR reaches its maximum and minimum and for all progression times in ten-day intervals from 250 to 400 days.

For the HIV incidence estimation based on longitudinal HIV status information, we included all individuals who tested at least twice for HIV in the period from June 2003 through June 2006 and whose first HIV test in this period was negative (4,869 individuals observed over 7,685 person-years). As in previous studies of HIV incidence based on data from longitudinal HIV surveillances [24], [25], [26], [27], [28], for the purpose of estimating exposure time, we used the mid-date between the last available negative HIV test and the first available positive HIV test as an estimate of the date of seroconversion. In addition, in order to test the robustness of the longitudinally measured HIV incidence estimates to changes in the assumption about seroconversion dates, we re-estimated HIV incidence using the most extreme assumptions about the seroconversion date that are possible given the interval-censored information on seroconversion dates. At the one extreme, we assumed that all individuals in the longitudinal sample who seroconverted did so on the day immediately after the day of their last HIV-negative test. At the other extreme, we assumed that all individuals who seroconverted did so on the day of their first HIV-positive test. Under changes in the assumption of date of seroconversion, these two extremes yield maximum and minimum estimates of longitudinally measured incidence.

For the cross-sectional cBED-based HIV incidence estimation, we used the first available HIV test for all individuals tested in the time period January 2005 through June 2006 (n = 11,755), i.e. the period in which all second HIV tests of the people included in the longitudinal HIV incidence analysis took place. Thus, all 4,869 individuals in the longitudinal sample are also included in the sample for the cBED assay-based analysis.

HIV status was determined by antibody testing with a broad-based HIV-1/HIV-2 enzyme-linked immunosorbent assay (ELISA; Vironostika, Organon Teknika, Boxtel, the Netherlands) followed by a confirmatory ELISA (GAC-ELISA; Abbott, Abbott Park, Illinois, USA) [23]. If HIV-positive status was confirmed, we used another spot from the same filter paper as used for the initial test in order to conduct the cBED assay (cEIA; Calypte® HIV-1 BED Incidence EIA, Calypte Biomedical Corporation, Maryland, USA). HIV-specific IgG were detected by the BED-biotin peptide, followed by a colour reaction with streptavidin-peroxidase. The optical density values were normalized in every run using a calibrator (normalized OD (ODn) = mean specimen OD/mean calibrator OD). Specimens with ODn less than or equal to 1.2 during an initial cBED screening test were confirmed by further cBED testing of the sample in triplicate. We took the median value of the three confirmatory test results as the final ODn value. As specified by the manufacturer, an HIV-1-positive specimen for which the cBED assay gave a final ODn of less than or equal to 0.8 was considered to be a specimen of recent HIV-1 infection. Otherwise, the specimen was classified as a non-recent infection [5].

Different formulae that use information obtained from the cBED assay have been proposed to estimate HIV incidence from cross-sectional surveys. These formulae provide incidence estimates expressed either as a rate, Î_r, (expressed, for instance, in number of new HIV infections per 100 person-years) [18] or as the probability that in a given year a person will acquire HIV, i.e. an incidence proportion, Î_p, (expressed, for instance, in number of new HIV infections per 100 people per year) [6], [7]. Some of us have previously derived a formula from first principles to estimate HIV incidence based on the cBED assay [18], and have commented on the assumptions made in different formulae [29], [30]. Here, we implemented four different formulae found in the literature. The formula for HIV incidence derived by McDougal and colleagues (McDougal formula) [6] iswhere R is the number of people who were classified as recently HIV-infected by the cBED assay and N is the number of individuals who tested HIV-negative. The mean window period of the cBED assay, , is “the mean period of time from initial seroconversion to reaching an ODn of 0.800” expressed in years in people who progress above the BED threshold [6]. The “adjustment factor”takes into account that the cBED assay does not have perfect specificity or sensitivity, P is the total number of people who tested HIV-positive, σ is the sensitivity of the cBED assay, ε₁ is the short-term FPR (i.e. over the period [, ]), and ε₂ is the long-term FPR (i.e. over all times ). Note that the short- and long-term specificities, ρ₁ and ρ₂, are related to the FPRs by ρ₁ = 1−ε₁ and ρ₂ = 1−ε₂, respectively. The formula of Hargrove and colleagues (Hargrove formula) [7] iswhile the formula derived by McWalter and Welte (McWalter/Welte formula) [18] is

In addition, we implemented a simplified version of the McDougal formula. The adjustment factor used in the formula can be simplified tousing the identitywhich requires no more assumptions than are used by McDougal and colleagues [29], [30].

Note that in order to implement any of the above four formulae, estimates of the long-term FPR ε₂ and the window period are required. For our baseline estimation, we use an of 153 days, i.e. the window period that is recommended by the manufacturer of the commercially available cBED assay. Most previous studies reporting HIV incidence based on the cBED assay have used window periods between 150 and 160 days [6], [9], [12], [13], [14], [15], [16], [31], [32], [33], [34], [35]. A few studies have used a window period of 180 days [8], [10], [11], and a recent study from Zimbabwe calibrated a window period of 187 days in postpartum mothers enrolled in a Vitamin-A intervention trial [7]. In order to test whether our results are robust to changes in the window period estimate, we repeated our analyses with window periods of 180 and 187 days. The Hargrove and McDougal formulae require that the maximum BED progression time is twice the window period. The estimate of the long-term FPR thus depends on the choice of the window period (see Table 1).

Note also that the Hargrove, McWalter/Welte and simplified McDougal formulae do not require estimates of σ and ε₁, which – unlike ε₂ – cannot be calibrated from longitudinal data if the intervals between the last negative and the first positive HIV test in seroconverters are of the order of one year [30]. The mean period of follow-up among seroconverters in our study was 1.4 years; we thus used estimates of σ (0.7680) and ε₁ (0.2770) from another study in order to implement the McDougal formula [6] (compare also [10]).

The McWalter/Welte formula expresses HIV incidence as a rate, i.e. as the number of HIV seroconversions per person-time at risk, while all other formulae express HIV incidence as an incidence proportion, i.e. the number of HIV seroconversions within a specified time period divided by the size of the population initially at risk. In order to directly compare all HIV incidence estimates in our study, we expressed the estimates based on the McWalter/Welte formula and the longitudinally measured HIV incidence both as rates (per 100 person-years) and as incidence proportions (per 100 people per year). We translated the rate estimates into proportions, assuming that the incidence rate, Î_r, is constant over time T, by using the relationship

The authors of the four different formulae do not use equivalent methods for the calculation of confidence intervals (CIs). Thus, uncertainty analysis on the incidence estimates was performed as follows. Any observed proportion of HIV-negative, cBED-recent and cBED-non-recent individuals is an unbiased estimate of the underlying population proportions. Given an observed occurrence of the population proportions and the sample size, all attainable draws of the three counts can be enumerated and assigned their respective trinomial probability. Hence an exact cumulative probability distribution of attainable values of the incidence estimator can be computed. For each incidence estimate, we quote the estimator evaluated at the observed counts (the maximum likelihood estimate) and a confidence interval expressed as the central 95^th percentile.

To control for differences in the sex-age composition between the sample used in the longitudinal HIV incidence estimation and the sample used in the cBED assay-based estimation, we weighted the sex- and five-year age group-specific longitudinal mean incidence rates by the proportions of individuals in each of the sex-age groups in the sample used for the cBED assay-based estimationwhere Î_rs is the sex-age adjusted mean incidence rate, w_si are the proportions of individuals in each sex-age group in the cBED assay sample, and Î_ri are the sex-age specific mean incidence rates. We estimated the variance of Î_rs, var(Î_rs), asassuming that the number of HIV incident cases, Ĉ_i, is Poisson distributed [36]. We calculated the 95% confidence limits for Î_rs using the method based on gamma distributions described in Anderson and Rosenberg [37].

Counting the number of DBS specimens classified as recently HIV-infected by the cBED assay in the sample of all individuals who had a previous positive HIV test more than 306 days before the date of the cBED assay-tested specimen, we obtained a long-term FPR of 0.0169 (95% CI 0.0100–0.0266). When we varied the length of the maximum BED progression time from 250 to 400 days (in daily intervals), we found that the estimate of the long-term FPR did not change significantly over the time interval, with minimum and maximum long-term FPRs of 0.0164 (95% CI 0.0097–0.0257) and 0.0190 (95% CI 0.0104–0.0317), respectively (Table 1).

Of the 4,869 individuals included in the sample for longitudinal HIV incidence measurement, 224 people seroconverted in 7,685 person-years. Assuming that seroconversion occurred at the mid-date between the last available negative HIV test and the first available positive HIV test, longitudinally measured crude HIV incidence was 2.87 per 100 people per year (95% CI 2.53–3.27) (Table 2). Longitudinally measured HIV incidence increased to 3.09 per 100 people per year (95% CI 2.69–3.52), when we adjusted it to the age-sex distribution of the sample for the cBED assay-based incidence estimate.

Of the 11,755 individuals included in the sample for the cBED assay-based HIV incidence measurement, 9,236 tested HIV- negative and 2,519 HIV-positive. Of the individuals who tested HIV-positive, 165 were classified in cBED assay testing as recently HIV-infected and the remainder as non-recently infected. For given ε₂ and , the four different formulae to calculate HIV incidence from cBED assay measurement produced very similar results. Using the baseline estimate for of 153 days and the locally measured ε₂ of 0.0169, HIV incidence point estimates (per 100 people per year) varied between 3.03 (95% CI 2.44–3.63; McDougal formula) and 3.19 (95% CI 2.57–3.82; Hargrove formula) (Table 2). The cBED assay-based HIV incidence estimates were thus very similar in magnitude and did not differ significantly from the estimates based on longitudinal measurement (crude and sex-age adjusted) (Table 2). Furthermore, when we implemented the cBED assay formulae using the lower bound or upper bound of the 95% CI of the locally measured long-term FPR (0.0100–0.0266), the cBED assay-based HIV incidence estimates did not differ significantly from the estimates based on longitudinal measurement. By contrast, when we implemented the cBED assay formulae using the externally measured long-term FPR of 0.0560 [6], all four cBED assay-based HIV incidence estimates were significantly lower than the longitudinal estimates (Table 2).

Our finding that the cBED assay-based HIV incidence estimate was not significantly different from the longitudinal HIV incidence estimate did not change when we applied the window periods of 180 and 187 days (and their corresponding long-term FPRs of 0.0182 and 0.0177 (see Table 1)). Using the McWalter/Welte formula, the cBED assay-based HIV incidence was estimated at 2.63 per 100 people per year (95% CI 2.10–3.18) with a 180-day window period and at 2.56 per 100 people per year (95% CI 2.04–3.08) with a 187-day window period. Neither of these estimates was significantly different from the longitudinally measured HIV incidence estimates or from the cBED assay-based incidence estimates based on a 153-day window period (see Table 2).

As described above, we conducted sensitivity analysis of the longitudinally measured HIV incidence estimate by changing the assumption about seroconversion dates. Assuming that all seroconverters became HIV-seropositive on the day following the last negative HIV test, crude HIV incidence was estimated at 2.97 per 100 person-years (95% CI 2.61–3.39). Assuming, on the other hand, that all seroconverters became HIV-seropositive on the day of their first positive HIV test, crude HIV incidence was estimated at 2.85 per 100 person-years (95% CI 2.51–3.25). The longitudinal HIV incidence estimates were thus highly robust to changes in the approach to computing the seroconversion date. Even under the most extreme possible assumptions, the mean HIV incidence changed by only 2% of the estimate based on the mid-date assumption, as reported in Table 2.

When we stratified HIV incidence by sex and five-year age group (starting at 15 years of age), we found that none of the cBED assay-based sex and age-specific estimates differed significantly from the corresponding longitudinally measured sex and age-specific estimates. However, our samples in each of the sex-age groups were too small to detect significant differences with reasonable confidence. The coefficients of variation (CVs) of the sex-age specific cBED assay-based HIV incidence estimates ranged from 18% to 203%; in 13 of the 15 sex-age groups the CVs were larger than 25%; in 10 sex-age groups the CVs were larger than 50%; and in 4 sex-age groups they were larger than 100%.