In 2020, our understanding of the distributions of HIV risks in the most burdened settings, including eSwatini, remains limited. In part, this is driven by the limited availability of the size and burden of the populations at the greatest risk for HIV. Given pervasive social and healthcare stigmas, the size estimations of these populations often rely on the multiplier method—a variant of the capture-recapture approach where the first survey is replaced by an enumeration of population members who used some service or attended an event. To characterize the distributions of marginalized communities in eSwatini, multiple data sources are available at each region for the multiplier method. Current practices in such circumstances produce multiple population size estimates at each region ignoring the correlation among these estimates. We recast the multiple multiplier method as a special case of capture-recapture problem with incomplete data and propose a fully model based approach for size estimation using multiple capture-recapture data with arbitrary pattern of incompleteness. We use a data augmentation scheme that allows us to model the correlations in the data and produce a unified estimate of population size per region. A hierarchical model ties together the models for multiple regions, allowing us to borrow strength across the regions and enabling extrapolation to areas without data. In eSwatini we also encounter data misalignment where counts from some of the data sources are not available for each region but as an aggregate over few regions. We propose a solution to the general misalignment problem which considers data-source-specific patterns of misalignment. We use simulation studies to demonstrate the accurate inferential capabilities of our Bayesian multiplier method. This approach is then used to produce uncertainty-quantified population size estimates of key populations in eSwatini. Lastly, we propose a Bayesian nonparametric extension for incomplete capture-recapture that allows nonindependent data sources.

中文翻译：

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使用不完整和未对齐的捕获-捕获数据估算eSwatini中HIV流行病关键人群的规模

到2020年，我们对包括eSwatini在内的最繁重环境中的HIV风险分布的了解仍然有限。在一定程度上，这是由于受艾滋病毒最大威胁的人口规模和负担有限。考虑到普遍存在的社会和医疗耻辱感，这些人群的规模估计通常依赖于乘数法-捕获-捕获方法的一种变体，其中第一次调查被使用某些服务或参加活动的人口成员的列举所代替。为了表征eSwatini中边缘化社区的分布，每个区域都有多个数据源可用于乘数法。在这种情况下，当前的实践忽略了这些估计之间的相关性，在每个区域产生了多个人口规模估计。我们将多乘子方法重塑为具有不完整数据的捕获-捕获问题的特例，并提出了一种基于全模型的方法，用于使用具有任意不完整模式的多个捕获-捕获数据的大小估计。我们使用一种数据增强方案，该方案允许我们对数据中的相关性进行建模并产生每个区域的人口规模的统一估计。分层模型将多个区域的模型联系在一起，从而使我们能够在各个区域之间借用强度，并能够外推到没有数据的区域。在eSwatini中，我们还会遇到数据未对齐的情况，其中某些数据源的计数不适用于每个区域，但汇总为几个区域。我们提出了一种解决一般错位问题的解决方案，该问题考虑了数据源特定的错位模式。我们使用模拟研究来证明我们的贝叶斯乘法器方法的准确推断能力。然后，该方法用于对eSwatini中的关键人群进行不确定性量化的人群规模估计。最后，我们针对允许不独立数据源的不完全捕获-重新捕获提出了贝叶斯非参数扩展。