Markov chain Monte Carlo and expectation maximization approaches for estimation of haplotype frequencies for multiply infected human blood samples

Abstract

BackgroundHaplotypes are important in anti-malarial drug resistance because genes encoding drug resistance may accumulate mutations at several codons in the same gene, each mutation increasing the level of drug resistance and, possibly, reducing the metabolic costs of previous mutation. Patients often have two or more haplotypes in their blood sample which may make it impossible to identify exactly which haplotypes they carry, and hence to measure the type and frequency of resistant haplotypes in the malaria population.ResultsThis study presents two novel statistical methods expectation–maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms to investigate this issue. The performance of the algorithms is evaluated on simulated datasets consisting of patient blood characterized by their multiplicity of infection (MOI) and malaria genotype. The datasets are generated using different resistance allele frequencies (RAF) at each single nucleotide polymorphisms (SNPs) and different limit of detection (LoD) of the SNPs and the MOI. The EM and the MCMC algorithm are validated and appear more accurate, faster and slightly less affected by LoD of the SNPs and the MOI compared to previous related statistical approaches.ConclusionsThe EM and the MCMC algorithms perform well when analysing malaria genetic data obtained from infected human blood samples. The results are robust to genotyping errors caused by LoDs and function well even in the absence of MOI data on individual patients.Electronic supplementary materialThe online version of this article (doi:10.1186/s12936-016-1473-5) contains supplementary material, which is available to authorized users.

Mapping sulphadoxine-pyrimethamine-resistant Plasmodium falciparum malaria in infected humans and in parasite populations in Africa

“…Assuming a negative binomial distribution for MOI instead of a Poisson distribution (Method 6), or allowing the mean MOI to vary during fitting (Method 7) or also produced negligible difference in frequency estimates (Table 1 ). Together, the comparison of methods 2–7 indicate that the estimated frequencies are not highly sensitive to the assumed MOI distribution, confirming previous results 31 , 35 . This shows that good frequency estimates can be obtained without needing MOI data for each survey.…”

“…In the systematic review surveys, the prevalence of mixed resistant-wild type infections among infected individuals varied from 0 to 82%, indicating that the frequency of resistance in the parasite population might be different from the prevalence of resistance in humans in some areas. We sought to estimate frequencies in the parasite populations in each survey from the systematic review data by applying and developing existing methods 19 , 31 , 32 , 35 . The main challenge was that the systematic review data mainly provide only summary measures on the prevalence of dhps mutations in humans in each survey, and no information on how many parasite clones were observed per person, whereas most of the existing methods for estimating frequency require detailed data for each individual on mutations and their MOI.…”

“… 19 , that resistant or wild type clones in an infection are not detected if they constitute less than a given proportion (the ‘genotyping sensitivity limit’) of the total clones or (C) that the probability of missing any clone is constant regardless of the MOI of an infection (similarly to Ken-Dror et al . 35 ). We use these letters A, B and C to denote these different detectability assumptions.…”

“…Several previous studies have developed other methods for estimating the frequency of resistance. When detailed data are available on the MOI together with presence of resistant and wild type parasites in individual infections, the frequency can be estimated by maximum likelihood 32 – 35 . These methods are ideal where such detailed data are available, however this is often not the case with routine surveillance data of molecular markers.…”

A Computer Modelling Approach To Evaluate the Accuracy of Microsatellite Markers for Classification of Recurrent Infections during Routine Monitoring of Antimalarial Drug Efficacy

“…We could describe parasite dynamics using other methods (for example, pre-determining a number of clones at a given time and randomly drawing their densities, e.g. (38)) but chose to use a PK/PD model for increased realism, relative simplicity, and to provide the ability for ourselves or other users to calibrate the model to their liking. The crucial part of our methodology is how we calculate detection of microsatellites in blood samples; specifically that it is based on the relative density of alleles in the parasitaemia (and thus dependant on relative clone numbers) and accounts for a "sampling limit" and inherent errors in reading microsatellite lengths.…”