Estimating incidence from prevalence in generalised HIV epidemics: methods and validation

Abstract

Background: HIV surveillance of generalised epidemics in Africa primarily relies on prevalence at antenatal clinics, but estimates of incidence in the general population would be more useful. Repeated cross-sectional measures of HIV prevalence are now becoming available for general populations in many countries, and we aim to develop and validate methods that use these data to estimate HIV incidence.

Methods and findings: Two methods were developed that decompose observed changes in prevalence between two serosurveys into the contributions of new infections and mortality. Method 1 uses cohort mortality rates, and method 2 uses information on survival after infection. The performance of these two methods was assessed using simulated data from a mathematical model and actual data from three community-based cohort studies in Africa. Comparison with simulated data indicated that these methods can accurately estimates incidence rates and changes in incidence in a variety of epidemic conditions. Method 1 is simple to implement but relies on locally appropriate mortality data, whilst method 2 can make use of the same survival distribution in a wide range of scenarios. The estimates from both methods are within the 95% confidence intervals of almost all actual measurements of HIV incidence in adults and young people, and the patterns of incidence over age are correctly captured.

Conclusions: It is possible to estimate incidence from cross-sectional prevalence data with sufficient accuracy to monitor the HIV epidemic. Although these methods will theoretically work in any context, we have able to test them only in southern and eastern Africa, where HIV epidemics are mature and generalised. The choice of method will depend on the local availability of HIV mortality data.

Figure 1. Lexis Diagrams Showing Values Used in the Methods

Two serosurveys T years apart quantify prevalence in age groups of width r. One age group (i) is shown. (A) At time j, N_i,j is the total number in survey; H_i,j is the number infected; p_i,j is HIV; is the fraction of infected individuals that survive between surveys; is mortality rate of infected individuals in the cohort; is the rate of HIV incidence in the cohort. N and H are not used required to use the methods but do appear in the mathematical derivation. (B) Cross-sectional incidence ( ). (C) Contributions to cross-sectional incidence estimate from incidence in two cohorts ( and ). For details see main text and Text S1.

Figure 2. Lexis Diagram Showing How Cohort Mortality Rates Can Be Estimated Using Data on Survival after Infection

In order to estimate expected mortality in one cohort (here ) using data on survival after infection, it is necessary to approximate the composition of the infected population in that cohort with respect to time since infection. Thus, it is necessary to consider the previous exposure of that cohort to incidence (indicated by the grey lines and text). When the intersurvey period is the same as the width of the age groups (T = r), and the pattern of incidence is constant, the previous experience of the cohorts will be reflected in the experience of younger cohorts (i.e., cohorts 0, 1, and 2).

Figure 3. Comparison of True Simulated Incidence Rate (Grey Lines) and Estimates Using Either Method (Black Lines; Both Give Same Results) when True Incidence Increases Steadily (A), Decreases Steadily (B), or Decreases Suddenly (C)

Vertical lines indicate when five-yearly serosurveys are done. Estimates of incidence are made at the time of the serosurvey (open circles) but relate to the preceding 5-y period.

Figure 4. Comparison of Method Estimates With Simulated Data Under Range of Conditions Violating Underlying Method Assumptions.

(A) The age-specific mortality rates for HIV-infected individuals when incidence is highest at young ages (dark line with crosses) or middle ages (grey line with triangles). (B) Estimates of incidence using method 1 when the “wrong” pattern age-specific mortality rates are used (i.e., from the alternative scenario in [A]: dashed lines) and when the correct rates or method 2 is used (solid lines). Bars show simulated incidence rates. (C) Estimates of incidence using method 2 when the age pattern of incidence changes (instantaneously between the two scenarios shown in [B]), 5 y (thick line), 10 y (dash-dot line), or 15 y (thin line) before the first survey. The dotted lines show the estimate if the age pattern of incidence does not change; the line with circles shows the estimates if the age pattern changes in the interval between the two surveys. The bars show the average incidence rate in the intersurvey period.

Figure 5. Incidence Estimates Using Method 2 Assuming that Provision of Antiretroviral Therapy is Scaled Up from 0% to 30% over Five Years

The grey line with circles shows the estimate of incidence based on surveys before and after the 5-y scale-up; the grey line with triangles shows the estimate of incidence based on surveys after scale-up, while provision is maintained at 30%. The black line shows the estimates if ART is not provided. Graphs show the simulations assuming that the incidence rate is highest at (A) older ages and (B) young ages. Similar results are obtained using method 1.

Figure 6. Result from the Cohort Studies Analysis

For each graph, the bars show incidence measured in the closed cohort with 95% confidence intervals and the lines show derived incidence estimates using method 1 (dark grey line) and method 2 (light grey line). (A) Manicaland; (B) Masaka, period 1; (C) Masaka, period 2; (D) Masaka, period 3; (E) Kisesa, period 1; (F) Kisesa, period 2; (G) Kisesa, period 3.