{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T06:51:54Z","timestamp":1784357514986,"version":"3.55.0"},"reference-count":55,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T00:00:00Z","timestamp":1663891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001655","name":"Deutscher Akademischer Austauschdienst","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001655","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006114","name":"S\u00e4chsisches Staatsministerium f\u00fcr Wissenschaft und Kunst","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006114","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Epidemiol."],"abstract":"<jats:p>The introduction of genomic methods facilitated standardized molecular disease surveillance. For instance, SNP barcodes in<jats:italic>Plasmodium vivax<\/jats:italic>and<jats:italic>Plasmodium falciparum<\/jats:italic>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<jats:italic>ad-hoc<\/jats:italic>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<jats:italic>ad-hoc<\/jats:italic>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<jats:italic>P. falciparum<\/jats:italic>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.<\/jats:p>","DOI":"10.3389\/fepid.2022.943625","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T11:16:25Z","timestamp":1663931785000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["A maximum-likelihood method to estimate haplotype frequencies and prevalence alongside multiplicity of infection from SNP data"],"prefix":"10.3389","volume":"2","author":[{"given":"Henri Christian Junior","family":"Tsoungui Obama","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kristan Alexander","family":"Schneider","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2022,9,23]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1016\/0091-7435(74)90003-6","article-title":"Importance of disease surveillance","volume":"3","author":"Horstmann","year":"1974","journal-title":"Prevent Med"},{"key":"B2","doi-asserted-by":"publisher","first-page":"745","DOI":"10.5005\/jp-journals-10071-23908","article-title":"Disease surveillance: the bedrock for control and prevention","volume":"25","author":"Krishna","year":"2021","journal-title":"Indian J Crit Care Med"},{"key":"B3","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1177\/0033354917709542","article-title":"Advances in public health surveillance and information dissemination at the centers for disease control and prevention","volume":"132","author":"Richards","year":"2017","journal-title":"Publ Health Rep"},{"key":"B4","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1128\/JCM.01967-16","article-title":"Integrating advanced molecular technologies into public health","volume":"55","author":"Gwinn","year":"2017","journal-title":"J Clin Microbiol"},{"key":"B5","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1038\/s41579-020-0421-0","article-title":"Genomics and epidemiological surveillance","volume":"18","author":"Lo","year":"2020","journal-title":"Nat Rev Microbiol"},{"key":"B6","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1186\/s12936-020-03440-0","article-title":"SNP barcodes provide higher resolution than microsatellite markers to measure plasmodium vivax population genetics","volume":"19","author":"Fola","year":"2020","journal-title":"Malar J"},{"key":"B7","doi-asserted-by":"publisher","first-page":"575","DOI":"10.3389\/fgene.2018.00575","article-title":"Highlights on the application of genomics and bioinformatics in the fight against infectious diseases: challenges and opportunities in Africa","volume":"9","author":"Bah","year":"2018","journal-title":"Front Genet"},{"key":"B8","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1038\/s41586-022-04394-w","article-title":"Genetic associations of protein-coding variants in human disease","volume":"603","author":"Sun","year":"2022","journal-title":"Nature"},{"key":"B9","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1186\/s12936-018-2322-5","article-title":"Molecular approaches to determine the multiplicity of plasmodium infections","volume":"17","author":"Zhong","year":"2018","journal-title":"Malar J"},{"key":"B10","doi-asserted-by":"publisher","first-page":"e0004355","DOI":"10.1371\/journal.pntd.0004355","article-title":"Multiplicity of infection and disease severity in plasmodium Vivax","volume":"10","author":"Pacheco","year":"2016","journal-title":"PLoS Neglect Trop Dis"},{"key":"B11","doi-asserted-by":"publisher","first-page":"412","DOI":"10.4269\/ajtmh.19-0093","article-title":"Impact of multiplicity of Plasmodium falciparum infection on clinical disease in Malawi","volume":"101","author":"Earland","year":"2019","journal-title":"Am J Trop Med Hyg"},{"key":"B12","doi-asserted-by":"publisher","first-page":"e0004526","DOI":"10.1371\/journal.pntd.0004526","article-title":"Complexity of infection and genetic diversity in Cambodian plasmodium Vivax","volume":"10","author":"Friedrich","year":"2016","journal-title":"PLoS Neglect Trop Dis"},{"key":"B13","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1186\/s13071-020-04302-z","article-title":"Determinants of Plasmodium falciparum multiplicity of infection and genetic diversity in Burkina Faso","volume":"13","author":"Sondo","year":"2020","journal-title":"Paras Vect"},{"key":"B14","doi-asserted-by":"publisher","first-page":"e0261889","DOI":"10.1371\/journal.pone.0261889","article-title":"Bias-corrected maximum-likelihood estimation of multiplicity of infection and lineage frequencies","volume":"16","author":"Hashemi","year":"2021","journal-title":"PLoS ONE"},{"key":"B15","doi-asserted-by":"publisher","first-page":"2837","DOI":"10.3168\/jds.2016-11590","article-title":"A comparison of different algorithms for phasing haplotypes using Holstein cattle genotypes and pedigree data","volume":"100","author":"Miar","year":"2017","journal-title":"J Dairy Sci"},{"key":"B16","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1093\/bfgp\/elz026","article-title":"Genome reconstruction and haplotype phasing using chromosome conformation capture methodologies","volume":"19","author":"Xu","year":"2019","journal-title":"Brief Funct Genomics"},{"key":"B17","first-page":"921","article-title":"Maximum-likelihood estimation of molecular haplotype frequencies in a diploid population","volume":"12","author":"Excoffier","year":"1995","journal-title":"Mol Biol Evol"},{"key":"B18","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1098\/rspb.1995.0203","article-title":"Estimation of numbers of malaria clones in blood samples","volume":"262","author":"Hill","year":"1995","journal-title":"Proc R Soc B Biol Sci"},{"key":"B19","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1093\/oxfordjournals.jhered.a111613","article-title":"HAPLO: a program using the EM algorithm to estimate the frequencies of multi-site haplotypes","volume":"86","author":"Hawley","year":"1995","journal-title":"J Hered"},{"key":"B20","doi-asserted-by":"publisher","first-page":"e0194148","DOI":"10.1371\/journal.pone.0194148","article-title":"Large and finite sample properties of a maximum-likelihood estimator for multiplicity of infection","volume":"13","author":"Schneider","year":"2018","journal-title":"PLoS ONE"},{"key":"B21","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1086\/319501","article-title":"A new statistical method for haplotype reconstruction from population data","volume":"68","author":"Stephens","year":"2001","journal-title":"Am J Hum Genet"},{"key":"B22","doi-asserted-by":"publisher","first-page":"3737","DOI":"10.1002\/sim.5792","article-title":"Malaria haplotype frequency estimation","volume":"32","author":"Wigger","year":"2013","journal-title":"Stat Med."},{"key":"B23","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/11557067_12","article-title":"A hidden Markov technique for haplotype reconstruction","volume-title":"Algorithms in Bioinformatics. Lecture Notes in Computer Science","author":"Rastas","year":"2005"},{"key":"B24","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1534\/genetics.109.108431","article-title":"A Hidden Markov model combining linkage and linkage disequilibrium information for haplotype reconstruction and quantitative trait locus fine mapping","volume":"184","author":"Druet","year":"2010","journal-title":"Genetics"},{"key":"B25","doi-asserted-by":"publisher","first-page":"e97899","DOI":"10.1371\/journal.pone.0097899","article-title":"A likelihood approach to estimate the number of co-infections","volume":"9","author":"Schneider","year":"2014","journal-title":"PLoS ONE"},{"key":"B26","doi-asserted-by":"crossref","unstructured":"HashemiM SchneiderK MLMOI: Estimating Frequencies, Prevalence and Multiplicity of Infection2020","DOI":"10.32614\/CRAN.package.MLMOI"},{"key":"B27","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1186\/1475-2875-7-130","article-title":"MalHaploFreq: a computer programme for estimating malaria haplotype frequencies from blood samples","volume":"7","author":"Hastings","year":"2008","journal-title":"Malar J"},{"key":"B28","doi-asserted-by":"publisher","first-page":"33","DOI":"10.2202\/1544-6115.1321","article-title":"An expectation maximization approach to estimate malaria haplotype frequencies in multiply infected children","volume":"6","author":"Li","year":"2007","journal-title":"Stat Appl Genet Mol Biol"},{"key":"B29","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1186\/s12936-016-1473-5","article-title":"Markov chain Monte Carlo and expectation maximization approaches for estimation of haplotype frequencies for multiply infected human blood samples","volume":"15","author":"Ken-Dror","year":"2016","journal-title":"Malar J"},{"key":"B30","doi-asserted-by":"publisher","first-page":"e42496","DOI":"10.1371\/journal.pone.0042496","article-title":"Estimating the numbers of malaria infections in blood samples using high-resolution genotyping data","volume":"7","author":"Ross","year":"2012","journal-title":"PLoS ONE"},{"key":"B31","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1186\/1475-2875-13-102","article-title":"Estimation of malaria haplotype and genotype frequencies: a statistical approach to overcome the challenge associated with multiclonal infections","volume":"13","author":"Taylor","year":"2014","journal-title":"Malar J"},{"key":"B32","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1186\/1475-2875-14-4","article-title":"COIL: a methodology for evaluating malarial complexity of infection using likelihood from single nucleotide polymorphism data","volume":"14","author":"Galinsky","year":"2015","journal-title":"Malar J"},{"key":"B33","doi-asserted-by":"publisher","first-page":"e1005348","DOI":"10.1371\/journal.pcbi.1005348","article-title":"THE REAL McCOIL: A method for the concurrent estimation of the complexity of infection and SNP allele frequency for malaria parasites","volume":"13","author":"Chang","year":"2017","journal-title":"PLoS Comput Biol"},{"key":"B34","doi-asserted-by":"publisher","first-page":"1292","DOI":"10.1093\/bioinformatics\/btu005","article-title":"estMOI: estimating multiplicity of infection using parasite deep sequencing data","volume":"30","author":"Assefa","year":"2014","journal-title":"Bioinformatics"},{"key":"B35","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1098\/rspb.2012.0113","article-title":"Close kinship within multiple-genotype malaria parasite infections","volume":"279","author":"Nkhoma","year":"2012","journal-title":"Proc Biol Sci"},{"key":"B36","doi-asserted-by":"publisher","first-page":"e1005923","DOI":"10.1371\/journal.pcbi.1005923","article-title":"Modeling the genetic relatedness of Plasmodium falciparum parasites following meiotic recombination and cotransmission","volume":"14","author":"Wong","year":"2018","journal-title":"PLoS Comput Biol"},{"key":"B37","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.chom.2019.12.001","article-title":"Co-transmission of related malaria parasite lineages shapes within-host parasite diversity","volume":"27","author":"Nkhoma","year":"2020","journal-title":"Cell Host Microbe"},{"key":"B38","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1038\/s41576-021-00349-5","article-title":"Advances and opportunities in malaria population genomics","volume":"22","author":"Neafsey","year":"2021","journal-title":"Nat Rev Genet"},{"key":"B39","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1016\/j.pt.2021.05.013","article-title":"Single-cell genome sequencing of protozoan parasites","volume":"37","author":"Dia","year":"2021","journal-title":"Trends Parasitol"},{"key":"B40","doi-asserted-by":"publisher","first-page":"e40845","DOI":"10.7554\/eLife.40845","article-title":"The origins and relatedness structure of mixed infections vary with local prevalence of P. falciparum malaria","volume":"8","author":"Zhu","year":"2019","journal-title":"eLife"},{"key":"B41","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1186\/1475-2875-11-77","article-title":"Differences in selective pressure on dhps and dhfr drug resistant mutations in Western Kenya","volume":"11","author":"McCollum","year":"2012","journal-title":"Malar J"},{"key":"B42","doi-asserted-by":"publisher","first-page":"4089","DOI":"10.1128\/AAC.00623-08","article-title":"Hitchhiking and selective sweeps of Plasmodium falciparum sulfadoxine and pyrimethamine resistance alleles in a population from Central Africa","volume":"52","author":"McCollum","year":"2008","journal-title":"Antimicrob Agents Chemother"},{"key":"B43","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/978-3-030-50826-5_6","article-title":"Charles Darwin meets ronald ross: a population-genetic framework for the evolutionary dynamics of malaria","volume-title":"Infectious Diseases and Our Planet","author":"Schneider","year":"2021"},{"key":"B44","doi-asserted-by":"publisher","first-page":"e12448","DOI":"10.7717\/peerj.12448","article-title":"Distribution of clones among hosts for the lizard malaria parasite plasmodium mexicanum","volume":"9","author":"Neal","year":"2021","journal-title":"PeerJ"},{"key":"B45","doi-asserted-by":"crossref","DOI":"10.1201\/9780429246593","volume-title":"An Introduction to the Bootstrap","author":"Efron","year":"1994"},{"key":"B46","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1186\/s12936-020-03454-8","article-title":"Changes in the frequencies of Plasmodium falciparum dhps and dhfr drug-resistant mutations in children from Western Kenya from 2005 to 2018: the rise of Pfdhps S436H","volume":"19","author":"Pacheco","year":"2020","journal-title":"Malar J"},{"key":"B47","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1080\/10618600.1996.10474713","article-title":"R: a language for data analysis and graphics","volume":"5","author":"Ihaka","year":"1996","journal-title":"J Comput Graph Stat"},{"key":"B48","doi-asserted-by":"publisher","first-page":"20","DOI":"10.4269\/ajtmh.2007.76.20","article-title":"Molecular epidemiology of malaria in Cameroon. XXIV. Trends of in vitro antimalarial drug responses in Yaounde, Cameroon","volume":"76","author":"Basco","year":"2007","journal-title":"Am J Trop Med Hyg"},{"key":"B49","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.actatropica.2007.04.008","article-title":"Molecular epidemiology of malaria in cameroon. XXVI. Twelve-year in vitro and molecular surveillance of pyrimethamine resistance and experimental studies to modulate pyrimethamine resistance","volume":"77","author":"Tahar","year":"2007","journal-title":"Am J Trop Med Hyg"},{"key":"B50","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1038\/nrg3054","article-title":"Haplotype phasing: existing methods and new developments","volume":"12","author":"Browning","year":"2011","journal-title":"Nat Rev Genet"},{"key":"B51","doi-asserted-by":"publisher","first-page":"2067","DOI":"10.1126\/science.280.5372.2067","article-title":"The \"roll back malaria\" campaign","volume":"280","author":"Nabarro","year":"1998","journal-title":"Science"},{"key":"B52","doi-asserted-by":"publisher","first-page":"e8091","DOI":"10.1371\/journal.pone.0008091","article-title":"A large proportion of P. falciparum isolates in the Amazon region of Peru lack pfhrp2 and pfhrp3: implications for malaria rapid diagnostic tests","volume":"5","author":"Gamboa","year":"2010","journal-title":"PLoS ONE"},{"key":"B53","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.tpb.2010.06.005","article-title":"An analytical model for genetic hitchhiking in the evolution of antimalarial drug resistance","volume":"78","author":"Schneider","year":"2010","journal-title":"Theor Popul Biol"},{"key":"B54","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1186\/s12936-020-03247-z","article-title":"Malaria in venezuela: changes in the complexity of infection reflects the increment in transmission intensity","volume":"19","author":"Pacheco","year":"2020","journal-title":"Malar J"},{"key":"B55","doi-asserted-by":"publisher","first-page":"e0008295","DOI":"10.1371\/journal.pntd.0008295","article-title":"Molecular surveillance over 14 years confirms reduction of plasmodium vivax and falciparum transmission after implementation of artemisinin-based combination therapy in Papua, Indonesia","volume":"14","author":"Pava","year":"2020","journal-title":"PLoS Neglect Trop Dis"}],"container-title":["Frontiers in Epidemiology"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fepid.2022.943625\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T13:48:58Z","timestamp":1728049738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fepid.2022.943625\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,23]]},"references-count":55,"alternative-id":["10.3389\/fepid.2022.943625"],"URL":"https:\/\/doi.org\/10.3389\/fepid.2022.943625","relation":{},"ISSN":["2674-1199"],"issn-type":[{"value":"2674-1199","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,23]]},"article-number":"943625"}}