A Non-Parametric Approach To Estimate Multiplicity of Infection (MOI) and Pathogen Haplotype Frequencies Provisionally Accepted

Loyce Kayanula^1* Kristan A. Schneider¹

• ¹Faculty of Applied Computer and Life Sciences, University of Applied Sciences Mittweida, Germany

The presence of multiple genetically distinct variants (lineages) within an infection (multiplicity of infection - MOI) is common in infectious diseases such as malaria. There, MOI is considered an epidemiologically and clinically relevant quantity that scales with transmission intensity and potentially impacts the clinical pathogenesis of the disease. Several statistical methods to estimate MOI assume that the number of infectious events per person follows a Poisson distribution. However, this has been criticized since empirical evidence suggests that the number of mosquito bites per person is over-dispersed compared to the Poisson distribution. We introduce a statistical model that does not assume that MOI follows a parametric distribution, i.e., the most flexible possible approach. The method is designed to estimate the distribution of MOI and allele frequency distributions from a single molecular marker. We derive the likelihood function and propose a maximum-likelihood approach to estimate the desired parameters. The expectation-maximization algorithm (EM algorithm) is used to numerically calculate the maximum likelihood estimate. By numerical simulations, we evaluate the performance of the proposed method in comparison to an established method that assumes a Poisson distribution for MOI. Our results suggest that the Poisson model performs sufficiently well if MOI is not highly over-dispersed. Hence, any model extension will not greatly improve the estimation of MOI. However, if MOI is highly over-dispersed, the method is less biased. We exemplify the method by analyzing three empirical in P. falciparum data sets from drug-resistance studies in Venezuela, Cameroon, and Kenya. Based on the allele-frequency estimates, we estimate heterozygosity and the average MOI for the respective microsatellite markers. In conclusion, the proposed non-parametric method to estimate the distribution of MOI is appropriate when transmission intensities in the population are heterogeneous, yielding an over-dispersed distribution. If MOI is not highly over-dispersed, the Poisson model is sufficiently accurate and cannot be improved by other methods. The EM algorithm provides a numerically stable method to derive MOI estimates and is made available as an R script.