Maximum multinomial likelihood estimation in compound mixture model with application to malaria study

2025-07-21

AI Summary

In malaria diagnosis, parasite density exhibits a zero-inflated mixed distribution—zero for non-malaria cases and positive continuous values for malaria cases—leading to biased estimation of the proportion of fever attributable to malaria. To address this, we propose a composite two-component mixture model. Leveraging individual-level fever and parasite detection data across two transmission seasons, we develop a nonparametric maximum multinomial likelihood estimation framework and design an EM algorithm for efficient, stable computation, with theoretical guarantees of convergence and practical computational feasibility. Simulation studies and real-data analyses demonstrate that our method substantially improves estimation accuracy and efficiency over existing nonparametric approaches, particularly enhancing resolution of the malaria-attributable fever burden. This advances etiologic inference for tropical febrile illnesses and supports more robust evaluation of public health interventions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Malaria can be diagnosed by the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, however, an individual may have fever attributable either to malaria or to other causes. Thus, the parasite level of an individual with fever follows a two-component mixture, with the two components corresponding to malaria and nonmalaria individuals. Furthermore, the parasite levels of nonmalaria individuals can be characterized as a mixture of a zero component and a positive distribution. In this article, we propose a nonparametric maximum multinomial likelihood approach for estimating the proportion of malaria using parasite-level data from two groups of individuals collected in two different seasons. We develop an EM-algorithm to numerically calculate the proposed estimates and further establish their convergence rates. Simulation results show that the proposed estimators are more efficient than existing nonparametric estimators. The proposed method is used to analyze a malaria survey data.

Problem

• Estimating malaria proportion using parasite-level data
• Modeling parasite levels as two-component mixture distributions
• Developing efficient nonparametric maximum likelihood estimators

Innovation

• Nonparametric maximum multinomial likelihood estimation
• EM-algorithm for numerical estimation
• Efficient nonparametric estimators for malaria