Existing approaches to modelling antibody concentration data are mostly based on finite mixture models that rely on the assumption that individuals can be divided into two distinct groups: seronegative and seropositive. Here, we challenge this dichotomous modelling assumption and propose a latent variable modelling framework in which the immune status of each individual is represented along a continuum of latent seroreactivity, ranging from minimal to strong immune activation. This formulation provides greater flexibility in capturing age-related changes in antibody distributions while preserving the full information content of quantitative measurements. We show that the proposed class of models can accommodate a large variety of model formulations, both mechanistic and regression-based, and also includes finite mixture models as a special case. We also propose a computationally efficient $L_2$-based estimator as an alternative to maximum likelihood estimation, which substantially reduces computational cost, and we establish its consistency. Through a case study on malaria serology, we demonstrate how the flexibility of the novel framework enables joint analyses across all ages while accounting for changes in transmission patterns. We conclude by outlining extensions of the proposed modelling framework and its relevance to other omics applications.

翻译：现有的抗体浓度数据建模方法主要基于有限混合模型，这些模型依赖于个体可被划分为两个不同组别的假设：血清阴性组和血清阳性组。本文挑战这种二分法建模假设，提出一种潜变量建模框架，其中每个个体的免疫状态通过一个从最小到强免疫激活的潜血清反应性连续谱来表示。该公式在保留定量测量完整信息内容的同时，为捕捉抗体分布中与年龄相关的变化提供了更大的灵活性。我们证明所提出的模型类别能够容纳多种模型公式，包括基于机理和回归的方法，并将有限混合模型作为特例包含在内。我们还提出一种计算高效的基于$L_2$范数的估计量作为最大似然估计的替代方案，该估计量显著降低了计算成本，并证明了其一致性。通过疟疾血清学的案例研究，我们展示了新框架的灵活性如何实现在考虑传播模式变化的同时对所有年龄段进行联合分析。最后，我们概述了所提建模框架的扩展方向及其在其他组学应用中的相关性。