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

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 characterised 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 analyse malaria survey data.

Keywords:

• Binomial likelihood
• clinical malaria
• EM-algorithm
• empirical likelihood
• parasite level

AMS 2000 Subject Classifications:

• Primary: 62G05
• Secondary: 62G20

Acknowledgments

We thank the editor, the Editorial Board member, and two anonymous referees for their constructive suggestions that significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of Liang and Li is partially supported by the Natural Sciences and Engineering Research Council of Canada [grant numbers RGPIN-2020-04739, RGPIN-2020-04964].