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

TL;DR

This paper introduces a nonparametric maximum likelihood estimation method using an EM-algorithm to accurately estimate malaria prevalence from parasite-level data, accounting for mixture components in endemic areas.

Contribution

It develops a novel nonparametric maximum multinomial likelihood approach with an EM-algorithm for malaria prevalence estimation, including convergence analysis.

Findings

Proposed estimators outperform existing methods in simulations.

Method successfully applied to real malaria survey data.

Establishment of convergence rates for the estimators.

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.