AI 中文总结
本文提出双变量地质统计潜变量模型，用于分析抗体密度数据，可捕捉抗体反应的环境与宿主内相关性，经肯尼亚疟疾血清数据验证，忽略相关性会降低推断效果。
AI 中文摘要
可测量多种抗原抗体反应的血清流行病学调查日益普及，这需要开发能够充分利用此类数据中生物和空间全部信息内容的方法。然而，抗体反应的非高斯性和潜在多峰分布特性使得这类方法的开发在多变量场景下固有复杂。本文扩展了Giorgi和Wallin（2026）提出的潜变量框架，该框架通过个体水平的潜血清反应性过程对连续抗体浓度进行建模，该过程代表针对给定抗原的免疫激活水平。我们主要关注双变量场景，并提出一系列指导原则以证明所得联合建模结构的合理性。所提模型捕捉抗体反应之间不同的相关性来源，这些来源既包括来自同一环境的共同暴露，也包括同一宿主内发生的生物过程。我们通过一种新型双变量Matérn随机场引入空间依赖性，并用其构建抗原特异性空间过程之间简约的互协方差函数类。我们将该框架应用于分析肯尼亚高地疟疾血清流行病学调查中的双变量抗体测量数据。应用结果和模拟研究表明，忽略此类相关性会显著降低对抗体分布联合属性及个体水平血清反应性的推断效果，但当仅关注每种抗体的边缘分布时，影响较小。最后，我们讨论该框架如何扩展至两种以上抗原的场景，并强调随着抗原数量增加出现的建模挑战。
英文摘要
The increasing availability of serosurveys that measure antibody responses to multiple antigens requires the development of methods that can exploit the full information content of such data, both biological and spatial. However, the non-Gaussian and potentially multimodal distributional behaviour of antibody responses makes the development of such methods inherently complex, especially in a multivariate setting. Here, we extend the latent variable framework of Giorgi and Wallin (2026), in which continuous antibody concentrations are modelled through an individual-level latent seroreactivity process that represents the level of immune activation to a given antigen. We focus primarily on the bivariate setting and set out a series of guiding principles that justify the resulting joint modelling structure. The proposed model captures distinct sources of correlation between antibody responses, arising both from shared exposure to the same environment and from biological processes occurring within the same host. Spatial dependence is introduced through a novel bivariate Matérn random field, which we use to construct a parsimonious class of cross-covariance functions between antigen-specific spatial processes. We illustrate the application of the framework to analyse data on bivariate antibody measurements from a malaria serosurvey in the Kenyan highlands. Results from the application and a simulation study show that ignoring this correlation substantially degrades inference on joint properties of the antibody distributions and on individual-level seroreactivity, but matters less when interest lies exclusively in each antibody's marginal distribution. Finally, we discuss how the framework could be extended to settings with more than two antigens, and highlight the modelling challenges that arise as the number of antigens grows.
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