A Method to Estimate the Size and Characteristics of HIV-positive Populations Using an Individual-based Stochastic Simulation Model

Abstract

It is important not only to collect epidemiologic data on HIV but to also fully utilize such information to understand the epidemic over time and to help inform and monitor the impact of policies and interventions. We describe and apply a novel method to estimate the size and characteristics of HIV-positive populations. The method was applied to data on men who have sex with men living in the UK and to a pseudo dataset to assess performance for different data availability. The individual-based simulation model was calibrated using an approximate Bayesian computation-based approach. In 2013, 48,310 (90% plausibility range: 39,900-45,560) men who have sex with men were estimated to be living with HIV in the UK, of whom 10,400 (6,160-17,350) were undiagnosed. There were an estimated 3,210 (1,730-5,350) infections per year on average between 2010 and 2013. Sixty-two percent of the total HIV-positive population are thought to have viral load <500 copies/ml. In the pseudo-epidemic example, HIV estimates have narrower plausibility ranges and are closer to the true number, the greater the data availability to calibrate the model. We demonstrate that our method can be applied to settings with less data, however plausibility ranges for estimates will be wider to reflect greater uncertainty of the data used to fit the model.

FIGURE 1.

Calibrating the model to data on MSM in the UK. A, Number of HIV diagnoses, (B) number of AIDS diagnoses, (C) number of deaths, (D) proportion of diagnoses which were recent infections (defined here as an infection which took place within six months of an HIV diagnosis), (E) total number seen for care, (F) Median CD4 count at diagnosis. Diamonds represent surveillance data until 2012 supplied by Public Health England (PHE). Filled diamonds show data used to calibrate the model; open diamonds show data not used to calibrate the model. Model median (solid line), model 90% plausibility range (dotted lines) and model range (light grey band) also shown. RITA indicates recent infection testing algorithm; SOPHID, survey of prevalent HIV infections diagnosed; CD4 SS, CD4 surveillance scheme.

FIGURE 2.

A, Estimated incidence (number of new HIV infections in a year) and the (B) estimated diagnosis rate (probability of being diagnosed in any given 3-month period) among MSM in the UK.

FIGURE 3.

Estimates of the (A) total number of MSM living with HIV in the UK and (B) total number of MSM living with undiagnosed HIV, by calendar year. Columns and error bars: Modeled median and 90% plausibility range.

FIGURE 4.

Estimated (A) treatment cascade and (B) population characteristics of all MSM living with HIV in the UK in 2013. Columns and error bars: Modeled median and 90% plausibility range. ART indicates antiretroviral therapy. “Resistance” is defined as at least one resistance mutation in majority virus. “In need of ART” includes people who are on ART and those who are ART-naïve with CD4 count <500 cells/mm³. ART indicates antiretroviral therapy.

FIGURE 5.

Estimate of the (A) number of people living with HIV and (B) number of people living with undiagnosed HIV in a hypothetical epidemic by data availability (high, medium, and low; see Table). Columns and error bars: modeled median and 90% plausibility range. “Based on prior distributions” refers to the outputs when all parameter sets are considered (none excluded by calibration-score criteria). The reference line (dotted) refers to the actual number of people living with HIV in the hypothetical epidemic.

FIGURE 6.

The resulting incidence curves and diagnosis rate curves as determined using our calibration method to the (A) and (B) high, (C) and (D) medium, and (E) and (F) low data availability scenario, respectively, with the “true” values as in the hypothetical epidemic represented by diamonds.