Molecular surveillance of multiplicity of infection, haplotype frequencies, and prevalence in infectious diseases
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Background
The presence of multiple different pathogen variants within the same infection, referred to as multiplicity of infection (MOI), confounds molecular disease surveillance in diseases such as malaria. Specifically, if molecular/genetic assays yield unphased data, MOI causes ambiguity concerning pathogen haplotypes. Hence, statistical models are required to infer haplotype frequencies and MOI from ambiguous data. Such methods must apply to a general genetic architecture, when aiming to condition secondary analyses, e.g., population genetic measures such as heterozygosity or linkage disequilibrium, on the background of variants of interest, e.g., drug-resistance associated haplotypes.
Methods and Findings
Here, a statistical method to estimate MOI and pathogen haplotype frequencies, assuming a general genetic architecture, is introduced. The statistical model is formulated and the relation between haplotype frequency, prevalence and MOI is explained. Because no closed solution exists for the maximum-likelihood estimate, the expectation-maximization (EM) algorithm is used to derive the maximum-likelihood estimate. The asymptotic variance of the estimator (inverse Fisher information) is derived. This yields a lower bound for the variance of the estimated model parameters (Cramér-Rao lower bound; CRLB). By numerical simulations, it is shown that the bias of the estimator decrease with sample size, and that its covariance is well approximated by the inverse Fisher information, suggesting that the estimator is asymptotically unbiased and efficient. Application of the method is exemplified by analyzing an empirical dataset from Cameroon concerning anti-malarial drug resistance. It is shown how the method can be utilized to derive population genetic measures associated with haplotypes of interest.
Conclusion
The proposed method has desirable statistical properties and is adequate for handling molecular consisting of moderate number of multiallelic molecular markers. The EM-algorithm provides a stable iteration to numerically calculate the maximum-likelihood estimates. An efficient implementation of the algorithm alongside a detailed documentation is provided as supplementary material.
Author summary
Malaria annually causes 263 million infections and 596,000 deaths. Control efforts are challenged by factors like spreading drug resistance. Monitoring pathogen variants at the genetic level (molecular surveillance), especially those linked to drug resistance, is a public health priority. A major challenge is the presence of multiple, genetically distinct pathogen variants (characterized by several genetic markers) within infections (multiplicity of infection). Because genetic assays do not provide phased information in this context, ambiguity in reconstructing the actual variants present in an infection arises. This challenge is not limited to malaria. Probabilistic methods are required to phase genetic data, i.e., to reconstruct the pathogen variants present in infections. As such, we introduce a statistical method to estimate the distribution of pathogen variants at the population level from unphased molecular data obtained from disease-positive specimens. This is a combinatorially difficult task, as the number of possible genetic variants grows exponentially with the amount of genetic information included. Although the method applies to data with an arbitrary genetic architecture, its application is constrained by computational limitations. The method’s adequacy is explored and used to analyze a malaria dataset from Cameroon to guide applications. A stable numerical implementation is provided.
