A flexible class of latent variable models for the analysis of antibody response data

TL;DR

This paper introduces a flexible latent variable model for antibody data that captures immune status on a continuum, improving over traditional dichotomous models and enabling comprehensive age-related analysis.

Contribution

It proposes a novel continuum-based latent variable framework that generalizes finite mixture models and includes an efficient estimator with proven consistency.

Findings

The model captures age-related antibody distribution changes effectively.

The $L_2$ estimator reduces computational cost significantly.

Application to malaria serology demonstrates joint age analysis capabilities.

Abstract

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.