Estimating and testing haplotype-trait associations in non-diploid populations

Measuring changes in Plasmodium falciparum transmission: precision, accuracy and costs of metrics

As malaria declines in parts of Africa and elsewhere, and as more countries move towards elimination, it is necessary to robustly evaluate the effect of interventions and control programmes on malaria transmission. To help guide the appropriate design of trials to evaluate transmission-reducing interventions, we review 11 metrics of malaria transmission, discussing their accuracy, precision, collection methods and costs and presenting an overall critique. We also review the nonlinear scaling relationships between five metrics of malaria transmission: the entomological inoculation rate, force of infection, sporozoite rate, parasite rate and the basic reproductive number, R0. Our chapter highlights that while the entomological inoculation rate is widely considered the gold standard metric of malaria transmission and may be necessary for measuring changes in transmission in highly endemic areas, it has limited precision and accuracy and more standardised methods for its collection are required. In areas of low transmission, parasite rate, seroconversion rates and molecular metrics including MOI and mFOI may be most appropriate. When assessing a specific intervention, the most relevant effects will be detected by examining the metrics most directly affected by that intervention. Future work should aim to better quantify the precision and accuracy of malaria metrics and to improve methods for their collection.

Malaria haplotype frequency estimation

We present a Bayesian approach for estimating the relative frequencies of multi-single nucleotide polymorphism (SNP) haplotypes in populations of the malaria parasite Plasmodium falciparum by using microarray SNP data from human blood samples. Each sample comes from a malaria patient and contains one or several parasite clones that may genetically differ. Samples containing multiple parasite clones with different genetic markers pose a special challenge. The situation is comparable with a polyploid organism. The data from each blood sample indicates whether the parasites in the blood carry a mutant or a wildtype allele at various selected genomic positions. If both mutant and wildtype alleles are detected at a given position in a multiply infected sample, the data indicates the presence of both alleles, but the ratio is unknown. Thus, the data only partially reveals which specific combinations of genetic markers (i.e. haplotypes across the examined SNPs) occur in distinct parasite clones. In addition, SNP data may contain errors at non-negligible rates. We use a multinomial mixture model with partially missing observations to represent this data and a Markov chain Monte Carlo method to estimate the haplotype frequencies in a population. Our approach addresses both challenges, multiple infections and data errors.

Estimating the numbers of malaria infections in blood samples using high-resolution genotyping data

People living in endemic areas often habour several malaria infections at once. High-resolution genotyping can distinguish between infections by detecting the presence of different alleles at a polymorphic locus. However the number of infections may not be accurately counted since parasites from multiple infections may carry the same allele. We use simulation to determine the circumstances under which the number of observed genotypes are likely to be substantially less than the number of infections present and investigate the performance of two methods for estimating the numbers of infections from high-resolution genotyping data. The simulations suggest that the problem is not substantial in most datasets: the disparity between the mean numbers of infections and of observed genotypes was small when there was 20 or more alleles, 20 or more blood samples, a mean number of infections of 6 or less and where the frequency of the most common allele was no greater than 20%. The issue of multiple infections carrying the same allele is unlikely to be a major component of the errors in PCR-based genotyping. Simulations also showed that, with heterogeneity in allele frequencies, the observed frequencies are not a good approximation of the true allele frequencies. The first method that we proposed to estimate the numbers of infections assumes that they are a good approximation and hence did poorly in the presence of heterogeneity. In contrast, the second method by Li et al estimates both the numbers of infections and the true allele frequencies simultaneously and produced accurate estimates of the mean number of infections.