A maximum-likelihood method to estimate haplotype frequencies and prevalence alongside multiplicity of infection from SNP data

Abstract

The introduction of genomic methods facilitated standardized molecular disease surveillance. For instance, SNP barcodes in Plasmodium vivax and Plasmodium falciparum malaria allows the characterization of haplotypes, their frequencies and prevalence to reveal temporal and spatial transmission patterns. A confounding factor is the presence of multiple genetically distinct pathogen variants within the same infection, known as multiplicity of infection (MOI). Disregarding ambiguous information, as usually done in ad-hoc approaches, leads to less confident and biased estimates. We introduce a statistical framework to obtain maximum-likelihood estimates (MLE) of haplotype frequencies and prevalence alongside MOI from malaria SNP data, i.e., multiple biallelic marker loci. The number of model parameters increases geometrically with the number of genetic markers considered and no closed-form solution exists for the MLE. Therefore, the MLE needs to be derived numerically. We use the Expectation-Maximization (EM) algorithm to derive the maximum-likelihood estimates, an efficient and easy-to-implement algorithm that yields a numerically stable solution. We also derive expressions for haplotype prevalence based on either all or just the unambiguous genetic information and compare both approaches. The latter corresponds to a biased ad-hoc estimate of prevalence. We assess the performance of our estimator by systematic numerical simulations assuming realistic sample sizes and various scenarios of transmission intensity. For reasonable sample sizes, and number of loci, the method has little bias. As an example, we apply the method to a dataset from Cameroon on sulfadoxine-pyrimethamine resistance in P. falciparum malaria. The method is not confined to malaria and can be applied to any infectious disease with similar transmission behavior. An easy-to-use implementation of the method as an R-script is provided.