A Bayesian evidence synthesis approach to estimate disease prevalence in hard-to-reach populations: hepatitis C in New York City

Abstract

Existing methods to estimate the prevalence of chronic hepatitis C (HCV) in New York City (NYC) are limited in scope and fail to assess hard-to-reach subpopulations with highest risk such as injecting drug users (IDUs). To address these limitations, we employ a Bayesian multi-parameter evidence synthesis model to systematically combine multiple sources of data, account for bias in certain data sources, and provide unbiased HCV prevalence estimates with associated uncertainty. Our approach improves on previous estimates by explicitly accounting for injecting drug use and including data from high-risk subpopulations such as the incarcerated, and is more inclusive, utilizing ten NYC data sources. In addition, we derive two new equations to allow age at first injecting drug use data for former and current IDUs to be incorporated into the Bayesian evidence synthesis, a first for this type of model. Our estimated overall HCV prevalence as of 2012 among NYC adults aged 20-59 years is 2.78% (95% CI 2.61-2.94%), which represents between 124,900 and 140,000 chronic HCV cases. These estimates suggest that HCV prevalence in NYC is higher than previously indicated from household surveys (2.2%) and the surveillance system (2.37%), and that HCV transmission is increasing among young injecting adults in NYC. An ancillary benefit from our results is an estimate of current IDUs aged 20-59 in NYC: 0.58% or 27,600 individuals.

Correcting prevalence estimation for biased sampling with testing errors

“…9 Such given information corresponds to the overrepresentation of symptomatic individuals (11) and the random sampling of infected and non-infected individuals inside each category of symptoms (12). The next theorem shows that (11) provides an upper bound to 𝑝 1 and 𝑝 (1) 1 . Theorem 1.…”

“…The population total 𝑁 is known, whereas 𝑁 (1) 1 , 𝑁 (1) 0 , 𝑁 (0) 1 , and 𝑁 (0) 0 are unknown, though their sum is 𝑁. The group of individuals with symptoms 𝑠 in the population will be denoted by 𝐼 𝑠 = 𝐼 (0) 𝑠 ∪𝐼 (1) 𝑠 , and its total by 𝑁 𝑠 = 𝑁 (0) 𝑠 +𝑁 (1) 𝑠 , for 𝑠 = 0, 1. Analogously, the group of individuals with infection status 𝑖 in the population will be denoted by 𝐼 (𝑖) = 𝐼 (𝑖) 0 ∪ 𝐼 (𝑖) 1 , and its total by 𝑁 (𝑖) = 𝑁 (𝑖) 0 + 𝑁 (𝑖) 1 , for 𝑖 = 0, 1.…”

“…where the logarithm is taken to be in base 𝑒, so that information is measured in nats. Thus defined, active information measures the amount of Shannon information of the estimator p to the true proportion 𝑝 (1) , and it is the quantity that is averaged in the Kullback-Leibler divergence 21 . That is, if the true proportion is overestimated, the active information will be positive and large; if the true proportion is underestimated, the active information will be negative; and if the true proportion is accurately estimated, the active information will be around zero.…”

“…Consider a population  of size 𝑁 that is divided into four categories: asymptomatic and non-infected individuals, 𝐼 (0) 0 , with size 𝑁 (0) 0 ; asymptomatic and infected individuals, 𝐼 (1) 0 , with size 𝑁 (1) 0 ; symptomatic and infected individuals, 𝐼 (1) 1 , with size 𝑁 (1) 1 ; and symptomatic and non-infected individuals, 𝐼 (0) 1 , with size 𝑁 (0) 1 . The population total 𝑁 is known, whereas 𝑁 (1) 1 , 𝑁 (1) 0 , 𝑁 (0) 1 , and 𝑁 (0) 0 are unknown, though their sum is 𝑁. The group of individuals with symptoms 𝑠 in the population will be denoted by 𝐼 𝑠 = 𝐼 (0) 𝑠 ∪𝐼 (1) 𝑠 , and its total by 𝑁 𝑠 = 𝑁 (0) 𝑠 +𝑁 (1) 𝑠 , for 𝑠 = 0, 1.…”

“…An example is estimating the general population prevalence of chronic hepatitis C (HCV) because of the challenges of sampling from subpopulations of former and current injecting drug users, the homeless or incarcerated. 1 Other examples include the over-representation of symptomatic individuals in a sample since these individuals are more likely to get tested than asymptomatic ones, with which the final estimates of prevalence inflates, since symptomatic individuals are also more likely to be truly infected than asymptomatic ones.…”