Severe Acute Malnutrition Burden Estimation under Data Scarcity: A Queueing-Based Bayesian Framework

Abstract

Humanitarian organizations need local estimates of severe acute malnutrition (SAM) burden to plan treatment capacity and allocate scarce supplies, yet typically observe only cross-sectional prevalence. The conventional approach applies a universal incidence-correction factor, imposing the same relationship among prevalence, incidence, and disease duration across locations. We develop a queueing-based Bayesian framework that estimates district-specific incidence, duration, arrival variability, and burden from short series of repeated prevalence observations. We consider two specifications: a partially pooled model that shares information across districts and a no-pooling model with district-specific priors elicited by a large language model (LLM) from narrative contextual evidence. We apply the framework to nine biannual observations from 74 districts in Somalia. Both specifications produce geographically differentiated estimates broadly consistent with documented regional conditions. The LLM-informed specification permits greater local differentiation, while the prevalence data materially update the elicited priors. Average aggregate burden is 14% higher under the LLM-informed specification and 56% higher under partial pooling than under the conventional K=1.6 calculation. The framework offers a flexible and transparent way to combine theoretical structure, contextual knowledge, and limited observed data for local burden estimation.