{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T04:58:05Z","timestamp":1772773085727,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T00:00:00Z","timestamp":1559779200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T00:00:00Z","timestamp":1559779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000865","name":"Bill and Melinda Gates Foundation","doi-asserted-by":"publisher","award":["OPP1131404"],"award-info":[{"award-number":["OPP1131404"]}],"id":[{"id":"10.13039\/100000865","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Commun"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Global stakeholders including the World Health Organization rely on predictive models for developing strategies and setting targets for tuberculosis care and control programs. Failure to account for variation in individual risk leads to substantial biases that impair data interpretation and policy decisions. Anticipated impediments to estimating heterogeneity for each parameter are discouraging despite considerable technical progress in recent years. Here we identify acquisition of infection as the single process where heterogeneity most fundamentally impacts model outputs, due to selection imposed by dynamic forces of infection. We introduce concrete metrics of risk inequality, demonstrate their utility in mathematical models, and pack the information into a risk inequality coefficient (RIC) which can be calculated and reported by national tuberculosis programs for use in policy development and modeling.<\/jats:p>","DOI":"10.1038\/s41467-019-10447-y","type":"journal-article","created":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T06:03:09Z","timestamp":1559800989000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Introducing risk inequality metrics in tuberculosis policy development"],"prefix":"10.1038","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1454-4979","authenticated-orcid":false,"given":"M. Gabriela M.","family":"Gomes","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7167-8754","authenticated-orcid":false,"given":"Juliane F.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Adelmo","family":"Bertolde","sequence":"additional","affiliation":[]},{"given":"Diepreye","family":"Ayabina","sequence":"additional","affiliation":[]},{"given":"Tuan Anh","family":"Nguyen","sequence":"additional","affiliation":[]},{"given":"Ethel L.","family":"Maciel","sequence":"additional","affiliation":[]},{"given":"Raquel","family":"Duarte","sequence":"additional","affiliation":[]},{"given":"Binh Hoa","family":"Nguyen","sequence":"additional","affiliation":[]},{"given":"Priya B.","family":"Shete","sequence":"additional","affiliation":[]},{"given":"Christian","family":"Lienhardt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,6]]},"reference":[{"key":"10447_CR1","unstructured":"World Health Organization. Global tuberculosis report 2017. (World Health Organization, Geneva, 2017)."},{"key":"10447_CR2","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1093\/oxfordjournals.epirev.a000807","volume":"23","author":"C Lienhardt","year":"2001","unstructured":"Lienhardt, C. From exposure to disease: the role of environmental factors in susceptibility to and development of tuberculosis. Epidemiol. Rev. 23, 288\u2013301 (2001).","journal-title":"Epidemiol. Rev."},{"issue":"9728","key":"10447_CR3","doi-asserted-by":"publisher","first-page":"1814","DOI":"10.1016\/S0140-6736(10)60483-7","volume":"375","author":"Knut L\u00f6nnroth","year":"2010","unstructured":"L\u00f6nnroth, K. et al. Tuberculosis control and elimination 2010\u201350: cure, care, and social development. Lancet 375, 1814\u20131829 (2010).","journal-title":"The Lancet"},{"key":"10447_CR4","unstructured":"United Nations General Assembly. Transforming our world: the 2030 Agenda for Sustainable Development New York: United Nations. Resolution adopted by the General Assembly on 25 September 2015 (2015)."},{"key":"10447_CR5","unstructured":"Gomes, M. G. M. On the mathematics of populations. CIM Bulletin. Preprint at, http:\/\/biorxiv.org\/cgi\/content\/short\/612366v1"},{"key":"10447_CR6","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1073\/pnas.94.1.338","volume":"94","author":"MEJ Woolhouse","year":"1997","unstructured":"Woolhouse, M. E. J. et al. Heterogeneities in the transmission of infectious agents: implications for the design of control programs. Proc. Natl Acad. Sci. USA 94, 338\u2013342 (1997).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"10447_CR7","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/nature04153","volume":"438","author":"JO Lloyd-Smith","year":"2005","unstructured":"Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E. & Getz, W. M. Superspreading and the effect of individual variation on disease emergence. Nature 438, 355\u2013359 (2005).","journal-title":"Nature"},{"key":"10447_CR8","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1016\/j.jtbi.2007.04.015","volume":"247","author":"C Colijn","year":"2007","unstructured":"Colijn, C., Cohen, T. & Murray, M. Emergent heterogeneity in declining tuberculosis epidemics. J. Theor. Biol. 247, 765\u2013774 (2007).","journal-title":"J. Theor. Biol."},{"key":"10447_CR9","doi-asserted-by":"publisher","first-page":"375","DOI":"10.5588\/ijtld.14.0423","volume":"19","author":"JR Andrews","year":"2015","unstructured":"Andrews, J. R., Basu, S., Dowdy, D. W. & Murray, M. B. The epidemiological advantage of preferential targeting of tuberculosis control at the poor. Int. J. Tuberc. Lung Dis. 19, 375\u2013380 (2015).","journal-title":"Int. J. Tuberc. Lung Dis."},{"key":"10447_CR10","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1098\/rsif.2005.0051","volume":"2","author":"MJ Keeling","year":"2005","unstructured":"Keeling, M. J. & Eames, K. T. D. Networks and epidemic models. J. R. Soc. Interface 2, 295\u2013307 (2005).","journal-title":"J. R. Soc. Interface"},{"key":"10447_CR11","doi-asserted-by":"publisher","first-page":"1408","DOI":"10.1093\/ije\/dyu192","volume":"44","author":"OO Aalen","year":"2015","unstructured":"Aalen, O. O., Valberg, M., Grotmol, T. & Tretli, S. Understanding variation in disease risk: the elusive concept of frailty. Int. J. Epidemiol. 44, 1408\u20131421 (2015).","journal-title":"Int. J. Epidemiol."},{"key":"10447_CR12","doi-asserted-by":"publisher","DOI":"10.1186\/s12879-016-1464-8","volume":"16","author":"MGM Gomes","year":"2016","unstructured":"Gomes, M. G. M. et al. End TB strategy: the need to reduce risk inequalities. BMC Infect. Dis. 16, 132 (2016).","journal-title":"BMC Infect. Dis."},{"key":"10447_CR13","unstructured":"Trauer, J. M. et al. The importance of heterogeneity to the epidemiology of tuberculosis. Clin. Infect. Dis."},{"key":"10447_CR14","first-page":"209","volume":"9","author":"MO Lorenz","year":"1905","unstructured":"Lorenz, M. O. Methods for measuring the concentration of wealth. Am. Stat. Assoc. 9, 209\u2013219 (1905).","journal-title":"Am. Stat. Assoc."},{"key":"10447_CR15","unstructured":"Gini, C. Variabilit\u00e0 e Mutuabilit\u00e0: Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. (C. Cuppini, Bologna, 1912)."},{"key":"10447_CR16","doi-asserted-by":"publisher","first-page":"1799","DOI":"10.1016\/S0140-6736(15)60570-0","volume":"385","author":"M Uplekar","year":"2015","unstructured":"Uplekar, M. et al. WHO\u2019s new End TB Strategy. Lancet 385, 1799\u20131801 (2015).","journal-title":"Lancet"},{"key":"10447_CR17","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1098\/rspb.2011.2712","volume":"279","author":"MGM Gomes","year":"2012","unstructured":"Gomes, M. G. M. et al. How host selection governs tuberculosis reinfection. Proc. R. Soc. Lond. B Biol. Sci. 279, 2473\u20132478 (2012).","journal-title":"Proc. R. Soc. Lond. B Biol. Sci."},{"key":"10447_CR18","doi-asserted-by":"publisher","first-page":"9557","DOI":"10.1073\/pnas.1203517109","volume":"109","author":"DW Dowdy","year":"2012","unstructured":"Dowdy, D. W., Golub, J. E., Chaisson, R. E. & Saraceni, V. Heterogeneity in tuberculosis transmission and the role of geographic hotspots in propagating epidemics. Proc. Natl Acad. Sci. USA 109, 9557\u20139562 (2012).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"10447_CR19","doi-asserted-by":"publisher","first-page":"e1001347","DOI":"10.1371\/journal.pmed.1001347","volume":"9","author":"NA Menzies","year":"2012","unstructured":"Menzies, N. A., Cohen, T., Lin, H. H., Murray, M. & Salomon, J. A. Population health impact and cost-effectiveness of tuberculosis diagnosis with Xpert MTB\/RIF: a dynamic simulation and economic evaluation. PLOS Med. 9, e1001347 (2012).","journal-title":"PLOS Med."},{"key":"10447_CR20","doi-asserted-by":"publisher","first-page":"e426","DOI":"10.1016\/S2214-109X(18)30022-6","volume":"6","author":"FM Marx","year":"2018","unstructured":"Marx, F. M. et al. Tuberculosis control interventions targeted to previously treated people in a high-incidence setting: a modelling study. Lancet Glob. Health 6, e426\u2013e435 (2018).","journal-title":"Lancet Glob. Health"},{"key":"10447_CR21","doi-asserted-by":"publisher","first-page":"790","DOI":"10.5588\/ijtld.16.0599","volume":"21","author":"JS Nery","year":"2017","unstructured":"Nery, J. S. et al. Effect of Brazil\u2019s conditional cash transfer programme on tuberculosis incidence. Int. J. Tuberc. Lung Dis. 21, 790\u2013796 (2017).","journal-title":"Int. J. Tuberc. Lung Dis."},{"key":"10447_CR22","doi-asserted-by":"publisher","first-page":"1300","DOI":"10.5588\/ijtld.17.0907","volume":"22","author":"RA De Souza","year":"2018","unstructured":"De Souza, R. A. et al. Family health and conditional cash transfer in Brazil and its effect on tuberculosis mortality. Int. J. Tuberc. Lung Dis. 22, 1300\u20131306 (2018).","journal-title":"Int. J. Tuberc. Lung Dis."},{"key":"10447_CR23","doi-asserted-by":"publisher","DOI":"10.1186\/s12889-018-5539-x","volume":"18","author":"D Boccia","year":"2018","unstructured":"Boccia, D. et al. Modelling the impact of social protection on tuberculosis: the S-PROTECT project. BMC Public Health 18, 786 (2018).","journal-title":"BMC Public Health"},{"key":"10447_CR24","doi-asserted-by":"publisher","first-page":"e001029","DOI":"10.1136\/bmjgh-2018-001029","volume":"4","author":"JC Carter","year":"2019","unstructured":"Carter, J. C. et al. The impact of a cash transfer programme on tuberculosis treatment success rate: a quasi-experimental study in Brazil. BMJ Glob. Health 4, e001029 (2019).","journal-title":"BMJ Glob. Health"},{"key":"10447_CR25","doi-asserted-by":"publisher","first-page":"e0212617","DOI":"10.1371\/journal.pone.0212617","volume":"14","author":"B Reis-Santos","year":"2019","unstructured":"Reis-Santos, B. et al. Tuberculosis in Brazil and cash transfer programs: a longitudinal database study of the effect of cash transfer on cure rates. PLOS One 14, e0212617 (2019).","journal-title":"PLOS One"},{"key":"10447_CR26","doi-asserted-by":"publisher","first-page":"e1001674","DOI":"10.1371\/journal.pmed.1001674","volume":"11","author":"H Salje","year":"2014","unstructured":"Salje, H. et al. The importance of implementation strategy in scaling up Xpert MTB\/RIF for diagnosis of tuberculosis in the Indian health-care system: a transmission model. PLOS Med. 11, e1001674 (2014).","journal-title":"PLOS Med."},{"key":"10447_CR27","doi-asserted-by":"publisher","first-page":"e1002152","DOI":"10.1371\/journal.pmed.1002152","volume":"13","author":"RMGJ Houben","year":"2016","unstructured":"Houben, R. M. G. J. & Dodd, P. J. The global burden of latent tuberculosis infection: A re-estimation using mathematical modelling. PLOS Med. 13, e1002152 (2016).","journal-title":"PLOS Med."},{"key":"10447_CR28","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1080\/00324728.1979.10410448","volume":"33","author":"N Keyfitz","year":"1979","unstructured":"Keyfitz, N. & Littman, G. Mortality in a heterogeneous population. Popul. Stud. 33, 333\u2013342 (1979).","journal-title":"Popul. Stud."},{"key":"10447_CR29","doi-asserted-by":"publisher","first-page":"439","DOI":"10.2307\/2061224","volume":"16","author":"JW Vaupel","year":"1979","unstructured":"Vaupel, J. W., Manton, K. G. & Stallard, E. Impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439\u2013454 (1979).","journal-title":"Demography"},{"key":"10447_CR30","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1080\/00031305.1985.10479424","volume":"39","author":"JW Vaupel","year":"1985","unstructured":"Vaupel, J. W. & Yashin, A. I. Heterogeneity ruses\u2014some surprising effects of selection on population dynamics. Am. Stat. 39, 176\u2013185 (1985).","journal-title":"Am. Stat."},{"key":"10447_CR31","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1137\/S0036144500371907","volume":"42","author":"HW Hethcote","year":"2000","unstructured":"Hethcote, H. W. The mathematics of infectious diseases. SIAM Rev. 42, 599\u2013653 (2000).","journal-title":"SIAM Rev."},{"key":"10447_CR32","doi-asserted-by":"publisher","first-page":"1985","DOI":"10.1890\/11-0079.1","volume":"92","author":"BE Kendall","year":"2011","unstructured":"Kendall, B. E., Fox, G. A., Fujiwara, M. & Nogeire, T. M. Demographic heterogeneity, cohort selection, and population growth. Ecology 92, 1985\u20131993 (2011).","journal-title":"Ecology"},{"key":"10447_CR33","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1097\/EDE.0000000000000499","volume":"27","author":"A Mauguen","year":"2016","unstructured":"Mauguen, A. & Begg, C. B. Using the Lorenz curve to characterize risk predictiveness and etiologic heterogeneity. Epidemiology 27, 531\u2013537 (2016).","journal-title":"Epidemiology"},{"key":"10447_CR34","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-01284-y","volume":"8","author":"MJ Stensrud","year":"2017","unstructured":"Stensrud, M. J. & Morten, V. Inequality in genetic cancer risk suggests bad genes rather than bad luck. Nat. Commun. 8, 1165 (2017).","journal-title":"Nat. Commun."},{"key":"10447_CR35","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1146\/annurev.publhealth.21.1.543","volume":"21","author":"A Wagstaff","year":"2000","unstructured":"Wagstaff, A. & van Doorslaer, E. Income inequality and health: what does the literature tell us? Ann. Rev. Public Health 21, 543\u2013567 (2000).","journal-title":"Ann. Rev. Public Health"},{"key":"10447_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jtbi.1996.0042","volume":"179","author":"AL Lloyd","year":"1996","unstructured":"Lloyd, A. L. & May, R. M. Spatial heterogeneity in epidemic models. J. Theor. Biol. 179, 1\u201311 (1996).","journal-title":"J. Theor. Biol."},{"key":"10447_CR37","doi-asserted-by":"publisher","DOI":"10.1186\/s12976-017-0049-6","volume":"14","author":"V Moreno","year":"2017","unstructured":"Moreno, V. et al. The role of mobility and health disparities on the transmission dynamics of tuberculosis. Theor. Biol. Med. Model 14, 3 (2017).","journal-title":"Theor. Biol. Med. Model"},{"key":"10447_CR38","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.epidem.2018.10.002","volume":"26","author":"SM Kissler","year":"2019","unstructured":"Kissler, S. M. et al. Geographic transmission hubs of the 2009 influenza pandemic in the United States. Epidemics 26, 86\u201394 (2019).","journal-title":"Epidemics"},{"key":"10447_CR39","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1037\/h0031322","volume":"76","author":"A Tversky","year":"1971","unstructured":"Tversky, A. & Kahneman, D. Belief in the law of small numbers. Psychol. Bull. 76, 105\u2013110 (1971).","journal-title":"Psychol. Bull."},{"key":"10447_CR40","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-03981-8","volume":"9","author":"JG King","year":"2018","unstructured":"King, J. G., Souto-Maior, C., Sartori, L., Maciel-de-Freitas, R. & Gomes, M. G. M. Variation in Wolbachia effects on Aedes mosquitoes as a determinant of invasiveness and vectorial capacity. Nat. Commun. 9, 1483 (2018).","journal-title":"Nat. Commun."},{"key":"10447_CR41","doi-asserted-by":"publisher","first-page":"e00796","DOI":"10.1128\/mBio.00796-17","volume":"8","author":"KE Langwig","year":"2017","unstructured":"Langwig, K. E. et al. Vaccine effects on heterogeneity in susceptibility and implications for population health management. mBio 8, e00796\u201317 (2017).","journal-title":"mBio"},{"key":"10447_CR42","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1056\/NEJM200107193450307","volume":"345","author":"PM Small","year":"2001","unstructured":"Small, P. M. & Fujiwara, P. I. Management of tuberculosis in the United States. N. Engl. J. Med. 345, 189\u2013200 (2001).","journal-title":"N. Engl. J. Med."},{"key":"10447_CR43","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2334-14-340","volume":"14","author":"JS Lopes","year":"2014","unstructured":"Lopes, J. S. et al. Interpreting simple measures of tuberculosis transmission: a case study on the Portuguese population. BMC Infect. Dis. 14, 340 (2014).","journal-title":"BMC Infect. Dis."},{"key":"10447_CR44","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1017\/S0950268807008552","volume":"136","author":"E Vynnycky","year":"2008","unstructured":"Vynnycky, E., Borgdorff, M. W., Leung, C. C., Tam, C. M. & Fine, P. E. Limited impact of tuberculosis control in Hong Kong: attributable to high risks of reactivation disease. Epidemiol. Infect. 136, 943\u2013052 (2008).","journal-title":"Epidemiol. Infect."},{"key":"10447_CR45","doi-asserted-by":"publisher","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","volume":"25","author":"A Raue","year":"2009","unstructured":"Raue, A. et al. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25, 1923\u20131929 (2009).","journal-title":"Bioinformatics"},{"key":"10447_CR46","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1098\/rsif.2008.0172","volume":"6","author":"T Toni","year":"2009","unstructured":"Toni, T., Welch, D., Strelkowa, N., Ipsen, A. & Stumpf, M. P. H. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 187\u2013202 (2009).","journal-title":"J. R. Soc. Interface"},{"key":"10447_CR47","unstructured":"Gelman, A. et al. Bayesian Data Analysis\u2014Third Edition. (Chapman & Hall\/CRC Texts in Statistical Science. CRC Press, Taylor & Francis Group: New York, 2013."},{"key":"10447_CR48","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s11222-006-9438-0","volume":"16","author":"H Haario","year":"2006","unstructured":"Haario, H., Laine, M., Mira, A. & Saksman, E. DRAM: Efficient adaptive MCMC. Stat. Comput. 16, 339\u2013354 (2006).","journal-title":"Stat. Comput."}],"container-title":["Nature Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41467-019-10447-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-019-10447-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-019-10447-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T02:51:33Z","timestamp":1721357493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41467-019-10447-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,6]]},"references-count":48,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["10447"],"URL":"https:\/\/doi.org\/10.1038\/s41467-019-10447-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/380865","asserted-by":"object"}]},"ISSN":["2041-1723"],"issn-type":[{"value":"2041-1723","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,6]]},"assertion":[{"value":"23 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"2480"}}