Households represent a key unit of interest in infectious disease epidemiology, in both empirical studies and mathematical modelling. The within-household transmission potential of a disease is often summarised by a secondary attack ratio (SAR). Despite its widespread use, the SAR depends on the household size distribution (HHSD) seen during the study period, making it difficult to generalise to new contexts. Extending estimates of transmission potential to new populations instead requires estimates of person-to-person transmission rates which can be convoluted with data on population structure to parametrise mechanistic transmission models. In this study we present a new Bayesian inference method which uses an MCMC algorithm to infer the transmission intensity by imputing the unreported household structure underlying the epidemic. This method can be run on household epidemiological data reported at varying levels of resolution. For synthetic data from a realistic underlying HHSD, we were able to achieve over 95% coverage in our estimates of transmission rate consistently. We were also able to consistently achieve over 95% coverage for data generated with a pathological underlying HHSD, given strong information about the HHSD. Using an existing dataset which recorded micro-scale household epidemiological outcomes during the COVID-19 pandemic, we show that stratifying observed SARs by household size substantially reduces the uncertainty in estimates. Our findings suggest that researchers conducting household epidemiological studies can improve the utility of results for infectious disease modellers by reporting household-stratified estimates. These results aim to encourage the reporting of higher resolution outputs in epidemiological field work as, in the absence of strong priors, transmission parameters were not easily identifiable from low resolution datasets, which are often reported.

翻译：家庭在传染病流行病学中既是实证研究也是数学模型的关键分析单元。疾病的家庭内传播潜力通常通过续发感染率（SAR）进行总结。尽管SAR被广泛使用，但其数值依赖于研究期间观察到的家庭规模分布（HHSD），难以推广至新情境。将传播潜力估计扩展到新人群需要估算个体间传播率，该指标可结合人口结构数据对机制性传播模型进行参数化。本研究提出一种新的贝叶斯推断方法，通过马尔可夫链蒙特卡洛算法对疫情背后未报告的家庭结构进行插补，从而推断传播强度。该方法可处理不同分辨率报告的流行病家庭数据。基于符合现实家庭规模分布的合成数据，我们能在传播率估计中持续实现超过95%的覆盖率。在已知家庭规模分布强先验信息条件下，对于由病理性家庭规模分布生成的数据，同样能稳定达到95%以上的覆盖率。利用新冠疫情期间记录微观家庭流行病学结果的现有数据集，我们证明按家庭规模分层观察续发感染率可显著降低估计的不确定性。研究结果表明，通过报告家庭分层估计值，开展家庭流行病学研究的研究者能提升结果对传染病建模工作者的实用价值。本研究旨在鼓励流行病学现场工作中报告更高分辨率的数据输出，因为在缺乏强先验信息时，从常被报告的低分辨率数据集中难以有效识别传播参数。