Of the roughly 1550 persons known to be infected with the HIV virus in Israel (where HIV is reportable), about 40% are recent immigrants from Ethiopia (1,2). With a population of approximately 60,000 persons (1,3), the prevalence of known HIV infection in Ethiopian immigrants to Israel is about 1%. However, virtually all of these infections occurred in adult Ethiopian immigrants who arrived in Israel since May 1991 (1,4). Approximately 25,000 persons arrived in Israel during this recent immigration, whereas 70% of the Ethiopian population in Israel is >15 years of age (3), raising the prevalence to about 3.5% in persons in this group. A similar prevalence was observed in the HIV testing of adult Ethiopian immigrants at the Rambam Medical Center in 1995: 54 of 1757 tests (3.1%) were HIV-positive. This circumstance has led to various public health decisions, including a ban on blood donated by Ethiopian immigrants to the Israeli blood supply (1,5,6), and establishment of special HIV prevention programs targeting Ethiopian immigrants (7,8).

Unknown, however, is the incidence rate of new HIV infections per uninfected person per unit of time in the population of Ethiopian immigrants. Although the prevalence of HIV indicates the extent to which the infection has penetrated a population, it is the incidence rate that is crucial for monitoring the spread of an infectious disease, and for understanding and evaluating preventive measures. For example, the ability of infected, donated blood to avoid detection depends crucially on the time since infection, for the major cause of false-negative testing results is that standard antibody tests fail during the "window period" of roughly 3 weeks from the moment of infection until the development of antibodies. Relatively "old" infections are reliably detected with standard antibody tests, although random errors do sometimes occur (9-11). Recent infections in which the time of donation remains within the window period constitute the danger to the blood supply, and it is the incidence of infection that determines the likelihood of finding an infected donor in the window period (9-11). Assuming that other factors, such as HIV prevalence, remain the same, the lower the incidence, the lower the risk will be.

With respect to evaluation of behavioral interventions to prevent HIV transmission, of interest is the number of infections averted by the prevention programs in question. To estimate this quantity, one requires a measure of the number of infections that could conceivably be prevented, as well as the relative reduction in this number that can arguably be attributed to prevention activities. This latter quantity can be estimated from evaluation data (12,13). HIV prevalence is not an appropriate measure for evaluation purposes, however, for one cannot prevent infections that have already occurred. The incidence rate, which reflects the number of new infections occurring in the population, does provide an appropriate benchmark.

Estimating HIV incidence rates typically requires for mation of cohort studies, in which initially uninfected persons are retested over time to determine the number of new infections relative to the person-days of study in the cohort (14,15). Such studies are difficult to implement, expensive, and time consuming. To our knowledge, no such cohort study has been attempted in Ethiopian immigrants to Israel.

Fortunately, indirect methods do exist. When reliable prevalence measures are available over time for a given population, it is possible to estimate statistically the parameters of a mathematical model to obtain an HIV incidence estimate (16,17). A new class of "snapshot estimators" based on markers of HIV progression such as p24 antigen or percentage of CD4 enable the statistical estimation of published and recent HIV incidence (18,19). We have applied such indirect methods to obtain estimates of recent HIV incidence in Ethiopian immigrants to Israel.

The HIV incidence rate in Ethiopian immigrants who have arrived since 1991 and currently reside in Israel was estimated using snapshot estimators (19). The basic idea is to estimate the fraction of currently infected persons with marker values (%CD4 in this application) above a certain threshold, and then ask what the rate of new infections must be to observe the current marker data. As detailed in the study of Kaplan and Brookmeyer (19), the recent incidence rate, denoted by r, can be estimated as Equation [1] where p is the HIV prevalence, is the fraction of HIV-infected persons with percentage CD4 values above some cutoff (e.g., 30%), and is the average length of time that CD4 percentage remains above this cutoff following infection. As shown in Kaplan and Brookmeyer (19), this formula approximates the incidence rate at some time () in the past, where the specific value of depends on the cutoff employed.

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Equation 1

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Implementing this approach required analysis of percentage of CD4 progression data over time for a sample of infected adult Ethiopians. Such data have been compiled as part of an ongoing study of HIV-infected Ethiopian immigrants at the Rambam Medical Center since mid-1991 (4). We examined 175 percentage CD4 measurements for 41 individuals believed to have been infected between mid-1990 and mid-1991 and modeled the probability of observing percentage CD4 values in excess of cutoffs ranging from 25% to 35% over time from infection using quadratic logistic models of the form Equation [2] where x is the number of months that have passed since the assumed date of infection, taken as January 1, 1991. Quadratic logistic models have previously been shown to provide excellent fits to %CD4 progression data in injection drug users (19). Assuming that the date of infection equals January 1, 1991 amounts to midpoint imputation of the date of infection between July 1, 1990 and June 30, 1991, and introduces only minimal bias to our analysis (17).

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Equation 2

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For each cutoff considered, we estimated the parameters of the logistic model through maximum likelihood. We assessed goodness-of-fit for each model by ranking the observations in order of estimated time from infection, splitting the data into 5 consecutive groups of 35 observations each, establishing expected frequencies for each of these groups based on the estimated logistic model, and then applying the ² goodness-of-fit test. The average time that percentage CD4 remains above the cutoff () and the incidence time lag () were computed from the estimated logistic model for each cutoff.

To determine the current status of percentage CD4 levels in the population of infected Ethiopian immigrants, the most recent percentage CD4 levels were recorded for 145 HIV-positive individuals at the Rambam Medical Center; all these measurements were obtained between December 1996 and May 1997. For each of the percentage CD4 cutoffs considered, we set equal to the fraction of these 145 percentage CD4 measurements that exceeded the cutoff.

To keep our study specific to adult immigrants who have arrived since 1991, we first set HIV prevalence equal to 3.5% as already described. We then employed Equation 1 to produce recent incidence estimates using percentage CD4 cutoffs ranging from 25% to 35%, along with 95% confidence intervals following the methods used by Kaplan and Brookmeyer (19). To allow for errors in our HIV-prevalence estimate, we also used Equation 1 with prevalence estimates of 2% and 5% to place bounds on the expected incidence rate.

The HIV incidence experienced by recent immigrants prior to immigration was estimated using the following epidemic model: Equation [3] where p´(t) is the instantaneous rate of change (the derivative) of HIV prevalence at time t, p(t) is the HIV prevalence at time t, r is the incidence rate, and is the rate with which HIV-positive persons leave the population. Equation 3 implies that the change in the number of infected persons equals the difference between the number of new infections and the number of infected persons departing the population and is appropriate in situations in which the incidence rate remains roughly constant over the time period of interest (13). As is conventional in HIV/AIDS epidemic models, we initially set equal to the reciprocal of the 10-year mean incubation time from HIV to AIDS (therefore = 0.1 y^-1) (20,21), but then varied from 0 (in which case observed HIV prevalence would correspond with cumulative HIV incidence) to 0.3 y^-1 (corresponding with a rapid average progression of only 3.3 years until removal from the population). We then estimated the prior incidence rate r via maximum likelihood by applying the model to HIV prevalence data derived from tests administered to newly arriving adult Ethiopian immigrants observed at the Rambam clinic from mid-1991 to the end of 1996 and assessed the fit of the model to the data using the ² goodness-of-fit test. Note the distinction between the fraction of new arrivals who are infected over time, and the fraction of the resident population that is currently infected. The former prevalence figure only conveys information regarding incidence experienced in Ethiopia, whereas the latter figure also depends on the ongoing incidence of infection in Israel.

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Equation 3

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Figure 1 displays the results of three quadratic logistic models for percentage CD4 progression using cutoffs of 25%, 30%, and 35% respectively. In these three cases, as well as all other cutoffs considered, the pattern is the same: the likelihood of percentage CD4 exceeding the threshold initially grows and then falls over time. The same phenomenon was observed when percentage CD4 measurements were taken from injecting drug users in Baltimore, Maryland and the Bronx, New York, U. S. A. (19). Table 1 reports the estimated mean time spent by percentage CD4 counts above the cutoff since the estimated time of infection (), the time lag (), and the ² goodness-of-fit statistic associated with each of the cutoffs considered. The ² statistics reveal that at = 0.10, the logistic models provide adequate descriptions of the data for percentage CD4 cutoffs between 25 and 31 inclusive, so we will focus our attention on these cutoffs. Note that the time lag associated with these models ranges from 19.2 to 20.8 months. Given that the percentage CD4 samples from the current population of adult Ethiopian immigrants were obtained between December 1996 and May 1997, we should obtain similar estimates of HIV incidence around May 1995 from these different cutoffs.

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FIG. 1. Probability that %CD4 exceeds the cutoff over estimated time from infection (Eq. 2) for cutoffs of 25%, 30%, and 35%.

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TABLE 1. Characteristics and statistical fit of alternative %CD4 progression models by %CD4 cutoff

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Table 2 reports the fraction of the 145 currently infected persons sampled with percentage CD4 in excess of the percentage CD4 cutoffs, along with the implied snapshot incidence estimates and 95% confidence intervals; these estimates are also shown graphically in Figure 2. The results employing the different cutoffs are consistent. Taken together, they suggest that as of May 1995, HIV incidence in adult Ethiopians who immigrated to Israel since 1991 equals 7 ± 4 new infections/1000 uninfected persons/year (where throughout this paper, "± estimates" are derived from 95% confidence intervals). Considering the estimated population of 17,500 recent adult immigrants (for an estimated 70% of the 25,000 recent immigrants who are >15 years of age) and the corresponding prevalence estimate of 3.5%, these results suggest that about 120 ± 70 new infections have occurred annually in this population.

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TABLE 2. Observed number of infected persons with %CD4 exceeding the cutoff, estimated HIV incidence, and 95% confidence intervals by %CD4 cutoff

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FIG. 2. Snapshot HIV incidence estimates (Eq. 1) and 95% confidence intervals by %CD4 cutoff.

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If we erred by 1.5 percentage points in either direction in our estimate of HIV prevalence in recent adult Ethiopian immigrants, then our incidence estimates would range from 4/1000/year if HIV prevalence was only 2%, to 10/1000/year if HIV prevalence was as high as 5%. In addition, if we erred by as much as 10 percentage points in estimating the proportion of recent immigrants who are >15 years of age, then the size of the adult recent immigrant population would fall between 15,000 and 20,000 persons. Combining this with our estimated ranges for HIV prevalence and incidence stated earlier in this paragraph, the expected annual number of new infections in adult Ethiopian immigrants in Israel would run from 60 through 190 in aggregate, in contrast to our base estimate of 120.

Table 3 reports the prevalence of infection in newly arrived Ethiopian immigrants over time tested at the Rambam clinic along with the numbers tested. These prevalence data are graphed in Figure 3 along with the estimated epidemic model. As evident from Figure 3 and the corresponding ² value of 0.75; 0.70, the epidemic model provides an excellent fit to the data. The resulting incidence estimate from this model equals 17 ± 5 new infections/1000 uninfected persons/year.

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TABLE 3. HIV prevalence among newly arrived Ethiopian immigrants tested at the Rambam Medical Center over time

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FIG. 3. HIV prevalence observed in newly arriving Ethiopian immigrants tested at Rambam Medical Center over time, and the fitted constant incidence epidemic model (Eq. 3).

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From Table 4, if there was no HIV progression in the population of immigrants from July 1991 through December 1996, then the observed HIV prevalence would correspond with cumulative incidence in this group, and the annual incidence rate would roughly equal 12/1000/year. Alternatively, if rapid HIV progression resulted in an average of only 3.3 years until removal from the population, then the annual incidence rate would equal 28 infections/1000/year.

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TABLE 4. Estimated HIV incidence among newly arrived Ethiopian immigrants r as a function of the HIV progression rate

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Using indirect statistical methods, we have estimated recent HIV incidence in Ethiopian immigrants to Israel. Based on the progression of percentage CD4 in infected persons, we estimate 120 ± 70 new infections have occurred annually in Ethiopian immigrants to Israel around May 1995. In an earlier study, the annual rate of new infections in Israelis excluding Ethiopian immigrants was estimated as 60 ± 25 new infections annually using back calculation from reporting delay-corrected AIDS data (22). This comparison strongly suggests that the majority of new infections in Israel are occurring in Ethiopian immigrants. Note that in the aggregate we are estimating that approximately 180 new HIV infections occur annually in Israel, which is somewhat higher than the reported annual rate of 140 new infections (2).

However, our results also contain good news. Our epidemic model based on prevalence estimates in newly arriving Ethiopian immigrants over time suggests that this community was experiencing an HIV incidence rate prior to immigration of 17 ± 5 new infections/1000 uninfected persons/year. Even if no HIV progression in these immigrants led to removal from the population, the resulting incidence rate would have equaled 12/1000/year. The current incidence estimate produced through percentage CD4 progression is 7 ± 4 new infections/1000 uninfected persons/year, which is lower. This suggests that the HIV incidence rate in Ethiopian immigrants has dropped after arrival in Israel, a situation supported by the paucity of reported infections in Ethiopian immigrants in years other than those of their immigration.

Some readers may be skeptical that our recent incidence estimates based on percentage CD4 are in error because of underestimation of the HIV prevalence in Ethiopian immigrants. Not all infected persons know they are infected, and consequently not all infections are known to the authorities. Indeed, we showed that if HIV prevalence in recent adult immigrants equals 5%, then our estimated incidence rate climbs to 10/1000/year. However, for the HIV incidence in adult Ethiopian immigrants postimmigration to equal the estimated preimmigration rate of 17/1000 uninfected persons/year, current HIV prevalence in adult Ethiopian immigrants would have to equal 8%. It is difficult to believe that there are 1400 infected adult Ethiopian immigrants in Israel, more than twice the number of known infections, when all such immigrants were tested on arrival in Israel.

The estimated recent incidence rate in adult Ethiopian immigrants in Israel is high relative to the rest of the Israeli population. With reference to HIV prevention, that approximately 120 new infections are estimated to occur annually in this population remains cause for concern. Even a program that was only 10% effective in reducing transmission could prevent 12 infections annually by our estimates.

However, our analysis also suggests an opportunity lost. Given the estimated HIV incidence rate experienced by the Ethiopian immigrant community before their arrival in Israel, perhaps the appropriate location to focus HIV prevention efforts was in Ethiopia itself. Had a prevention program been implemented there in the early 1990s, perhaps the incidence that gave rise to the increasing prevalence of infection in new immigrants could have been stemmed, which, in turn, would have lowered the ongoing rate of new infections in Ethiopian immigrants in Israel at the present time.

Acknowledgments: Prof. Kaplan's research was supported in part by the Societal Institute for the Mathematical Sciences through grant no. DA09531 from the National Institute on Drug Abuse and the Lady Davis Fellowship Trust, Jerusalem. We thank the staff of the AIDS Clinic and the Virology Laboratory at Rambam Medical Center, Haifa, Israel.