## Key advances in incidence surveillance: General and robust methodologies to estimate HIV incidence using tests for recent infection or prevalence surveys

Traditionally, epidemiologists have referred to counting infection events in cohorts of subjects as the ‘gold standard’ for incidence estimation. However, for population-level surveillance, this approach is often impractical and prone to bias. Numerous alternatives to cohort studies have attracted wide interest in recent years, with active discourse around:

- Inferring incidence from cross-sectional surveys testing for biomarkers of ‘recent infection’
- Inferring incidence from population renewal equations, given suitable age-stratified prevalence and mortality

However, the widespread implementation of these approaches has been hindered by a lack of consensus. In particular, methodologies have often been derived under particular assumptions (about demographic and epidemiological context and the biomarker dynamics) which are known to be violated in reality.

SACEMA has recently developed very general theoretical frameworks for each of these two approaches, which may support the emergence of consensus in the field. The references, with abstracts, are provided below. Tools, designed to perform various analyses related to the incidence estimation methodologies presented, are available online.

Incidence estimation from prevalence surveys, using **age- and time- dependent prevalence and mortality** data.

Mahiane GS, Ouifki R, Brand H, Delva W, Welte A. A general HIV incidence inference scheme based on likelihood of individual level data and a population renewal equation. *PLoS One* 2012; 7(9):e44377.

We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.

Incidence estimation from cross-sectional surveys testing for biomarkers of 'recent infection'

Kassanjee R, McWalter TA, Bärnighausen T, Welte A. A new general biomarker-based incidence estimator. *Epidemiology* 2012; 23(5): 721-28.

Background: Estimating disease incidence from cross-sectional surveys, using biomarkers for “recent” infection, has attracted much interest. Despite widespread applications to HIV, there is currently no consensus on the correct handling of biomarker results classifying persons as “recently” infected long after the infections occurred.

Methods: We derive a general expression for a weighted average of recent incidence that—unlike previous estimators—requires no particular assumption about recent infection biomarker dynamics or about the demographic and epidemiologic context. This is possible through the introduction of an explicit timescale T that truncates the period of averaging implied by the estimator.

Results: The recent infection test dynamics can be summarized into 2 parameters, similar to those appearing in previous estimators: a mean duration of recent infection and a false-recent rate. We identify a number of dimensionless parameters that capture the bias that arises from working with tractable forms of the resulting estimator and elucidate the utility of the incidence estimator in terms of the performance of the recency test and the population state. Estimation of test characteristics and incidence is demonstrated using simulated data. The observed confidence interval coverage of the test characteristics and incidence is within 1% of intended coverage.

Conclusions: Biomarker-based incidence estimation can be consistently adapted to a general context without the strong assumptions of previous work about biomarker dynamics and epidemiologic and demographic history.