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Journal of Immunology Research
Volume 2015, Article ID 738030, 21 pages
http://dx.doi.org/10.1155/2015/738030
Review Article

Current Mathematical Models for Analyzing Anti-Malarial Antibody Data with an Eye to Malaria Elimination and Eradication

1London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
2Centro de Estatística da Universidade de Lisboa, Faculdade de Ciências, Universidade de Lisboa, Bloco C6, Piso 4, Campo Grande, 1749-016 Lisboa, Portugal
3MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College London, Medical School Building, Norfolk Place, London W2 1PG, UK
4Division of Population Health and Immunity, Walter and Eliza Hall Institute, 1G Royal Parade, Parkville, VIC 3052, Australia
5Department of Medical Biology, The University of Melbourne, Parkville, VIC 3010, Australia

Received 28 August 2015; Accepted 19 October 2015

Academic Editor: Francesco Pappalardo

Copyright © 2015 Nuno Sepúlveda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. World Health Organization (WHO), World Malaria Report 2014, World Health Organization (WHO), Geneva, Switzerland, 2014.
  2. R. G. A. Feachem, A. A. Phillips, J. Hwang et al., “Shrinking the malaria map: progress and prospects,” The Lancet, vol. 376, no. 9752, pp. 1566–1578, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. N. D. Karunaweera, G. N. Galappaththy, and D. F. Wirth, “On the road to eliminate malaria in Sri Lanka: lessons from history, challenges, gaps in knowledge and research needs,” Malaria Journal, vol. 13, no. 1, article 59, 2014. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Herrera, S. A. Ochoa-Orozco, I. J. González, L. Peinado, M. L. Quiñones, and M. Arévalo-Herrera, “Prospects for malaria elimination in mesoamerica and hispaniola,” PLOS Neglected Tropical Diseases, vol. 9, no. 5, Article ID e0003700, 2015. View at Publisher · View at Google Scholar
  5. J. Monteiro Rodriguez, J. O. Guintran, C. Gomes et al., “Moving to malaria elimination in Cape Verde,” Malaria Journal, vol. 11, supplement 1, article O9, 2012. View at Publisher · View at Google Scholar
  6. G. Stresman, T. Kobayashi, A. Kamanga et al., “Malaria research challenges in low prevalence settings,” Malaria Journal, vol. 11, article 353, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. M. G. Cunha, E. S. Silva, N. Sepúlveda et al., “Serologically defined variations in malaria endemicity in Pará state, Brazil,” PLoS ONE, vol. 9, no. 11, Article ID 0113357, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Bousema, R. M. Youssef, J. Cook et al., “Serologic markers for detecting malaria in areas of low endemicity, Somalia, 2008,” Emerging Infectious Diseases, vol. 16, no. 3, pp. 392–399, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. World Health Organization (WHO), Malaria Entomology and Vector Control. Guide for Participants, WHO, Geneva, Switzerland, 2013.
  10. M. Service, Mosquito Ecology—Field Sampling Methods, Applied Science Publishers, London, UK, 1976.
  11. L. S. Tusting, T. Bousema, D. L. Smith, and C. Drakeley, “Measuring changes in plasmodium falciparum transmission. Precision, accuracy and costs of metrics,” Advances in Parasitology, vol. 84, pp. 151–208, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Corran, P. Coleman, E. Riley, and C. Drakeley, “Serology: a robust indicator of malaria transmission intensity?” Trends in Parasitology, vol. 23, no. 12, pp. 575–582, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. C. J. Drakeley, P. H. Corran, P. G. Coleman et al., “Estimating medium- and long-term trends in malaria transmission by using serological markers of malaria exposure,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 14, pp. 5108–5113, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. M. T. Bretscher, S. Supargiyono, M. A. Wijayanti et al., “Measurement of Plasmodium falciparum transmission intensity using serological cohort data from Indonesian schoolchildren,” Malaria Journal, vol. 12, article 21, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Cook, I. Kleinschmidt, C. Schwabe et al., “Serological markers suggest heterogeneity of effectiveness of malaria control interventions on Bioko Island, Equatorial Guinea,” PLoS ONE, vol. 6, no. 9, Article ID e25137, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Cook, H. Reid, J. Iavro et al., “Using serological measures to monitor changes in malaria transmission in Vanuatu,” Malaria Journal, vol. 9, no. 1, article 169, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. E. J. Remarque, B. W. Faber, C. H. M. Kocken, and A. W. Thomas, “Apical membrane antigen 1: a malaria vaccine candidate in review,” Trends in Parasitology, vol. 24, no. 2, pp. 74–84, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. B. W. Faber, S. Younis, E. J. Remarque et al., “Diversity covering AMA1-MSP119 fusion proteins as malaria vaccines,” Infection and Immunity, vol. 81, no. 5, pp. 1479–1490, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. P. D. Crompton, M. A. Kayala, B. Traore et al., “A prospective analysis of the Ab response to Plasmodium falciparum before and after a malaria season by protein microarray,” Proceedings of the National Academy of Sciences of the United States of America, vol. 107, no. 15, pp. 6958–6963, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. D. A. Helb, K. K. Tetteh, P. L. Felgner et al., “Novel serologic biomarkers provide accurate estimates of recent Plasmodium falciparum exposure for individuals and communities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 112, no. 32, pp. E4438–E4447, 2015. View at Publisher · View at Google Scholar
  21. A. Voller, G. Huldt, C. Thors, and E. Engvall, “New serological test for malaria antibodies,” British Medical Journal, vol. 1, no. 5959, pp. 659–661, 1975. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Bousema, J. Stevenson, A. Baidjoe et al., “The impact of hotspot-targeted interventions on malaria transmission: study protocol for a cluster-randomized controlled trial,” Trials, vol. 14, article 36, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. T. Benaglia, D. Chauveau, D. R. Hunter, and D. S. Young, “Mixtools: an R package for analyzing finite mixture models,” Journal of Statistical Software, vol. 32, no. 6, pp. 1–29, 2009. View at Google Scholar · View at Scopus
  24. S. Bosomprah, “A mathematical model of seropositivity to malaria antigen, allowing seropositivity to be prolonged by exposure,” Malaria Journal, vol. 13, article 12, 2014. View at Publisher · View at Google Scholar · View at Scopus
  25. D. Modiano, A. Chiucchiuini, V. Petrarca et al., “Humoral response to Plasmodium falciparum Pf155/ring-infected erythrocyte surface antigen and Pf332 in three sympatric ethnic groups of Burkina Faso,” The American Journal of Tropical Medicine and Hygiene, vol. 58, no. 2, pp. 220–224, 1998. View at Google Scholar · View at Scopus
  26. D. Modiano, V. Petrarca, B. S. Sirima et al., “Different response to Plasmodium falciparum malaria in west African sympatric ethnic groups,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 23, pp. 13206–13211, 1996. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Richardson and P. J. Green, “On Bayesian analysis of mixtures with an unknown number of components,” Journal of the Royal Statistical Society, Series B: Methodological, vol. 59, no. 4, pp. 731–792, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Z. Zhang, K. L. Chan, Y. Wu, and C. Chen, “Learning a multivariate Gaussian mixture model with the reversible jump MCMC algorithm,” Statistics and Computing, vol. 14, no. 4, pp. 343–355, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. P. Vounatsou, T. Smith, and A. F. M. Smith, “Bayesian analysis of two-component mixture distributions applied to estimating malaria attributable fractions,” Journal of the Royal Statistical Society C: Applied Statistics, vol. 47, no. 4, pp. 575–587, 1998. View at Google Scholar · View at Scopus
  30. J. Qin and D. H. Leung, “A semiparametric two-component compound mixture model and its application to estimating malaria attributable fractions,” Biometrics, vol. 61, no. 2, pp. 456–464, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. H. Muench, Catalytic Models in Epidemiology, Harvard University Press, Cambridge, Mass, USA, 1959.
  32. J. H. Pull and B. Grab, “A simple epidemiological model for evaluating the malaria inoculation rate and the risk of infection in infants,” Bulletin of the World Health Organization, vol. 51, no. 5, pp. 507–516, 1974. View at Google Scholar · View at Scopus
  33. A. Bekessy, L. Molineaux, and J. Storey, “Estimation of incidence and recovery rates of Plasmodium falciparum parasitaemia from longitudinal data,” Bulletin of the World Health Organization, vol. 54, no. 6, pp. 685–693, 1976. View at Google Scholar · View at Scopus
  34. N. Sepúlveda and C. J. Drakeley, “Sample size determination for estimating antibody seroconversion rate under stable malaria transmission intensity,” Malaria Journal, vol. 14, article 141, 2015. View at Publisher · View at Google Scholar
  35. C. I. Bliss, “The calculation of the dosage-mortality curve,” Annals of Applied Biology, vol. 22, no. 1, pp. 134–167, 1935. View at Publisher · View at Google Scholar
  36. M. E. von Fricken, T. A. Weppelmann, B. Lam et al., “Age-specific malaria seroprevalence rates: a cross-sectional analysis of malaria transmission in the Ouest and Sud-Est departments of Haiti,” Malaria Journal, vol. 13, article 361, 2014. View at Publisher · View at Google Scholar · View at Scopus
  37. B. G. Williams and C. Dye, “Maximum likelihood for parasitologists,” Parasitology Today, vol. 10, no. 12, pp. 489–493, 1994. View at Publisher · View at Google Scholar · View at Scopus
  38. T. Bonnefoix, P. Bonnefoix, P. Verdiel, and J.-J. Sotto, “Fitting limiting dilution experiments with generalized linear models results in a test of the single-hit poisson assumption,” Journal of Immunological Methods, vol. 194, no. 2, pp. 113–119, 1996. View at Publisher · View at Google Scholar · View at Scopus
  39. D. L. Martin, R. Bid, F. Sandi et al., “Serology for trachoma surveillance after cessation of mass drug administration,” PLoS Neglected Tropical Diseases, vol. 9, no. 2, Article ID e0003555, 2015. View at Publisher · View at Google Scholar
  40. S. Delgado, R. C. Neyra, V. R. Q. Machaca et al., “A history of Chagas disease transmission, control, and re-emergence in peri-rural La Joya, Peru,” PLoS Neglected Tropical Diseases, vol. 5, no. 2, article e970, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Supargiyono, M. T. Bretscher, M. A. Wijayanti et al., “Seasonal changes in the antibody responses against Plasmodium falciparum merozoite surface antigens in areas of differing malaria endemicity in Indonesia,” Malaria Journal, vol. 12, no. 1, article 444, 2013. View at Publisher · View at Google Scholar · View at Scopus
  42. A. C. Marques, “Human migration and the spread of malaria in Brazil,” Parasitology Today, vol. 3, no. 6, pp. 166–170, 1987. View at Publisher · View at Google Scholar · View at Scopus
  43. N. M. Bowman, V. Kawai, M. Z. Levy et al., “Chagas disease transmission in periurban communities of Arequipa, Peru,” Clinical Infectious Diseases, vol. 46, no. 12, pp. 1822–1828, 2008. View at Publisher · View at Google Scholar · View at Scopus
  44. D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. van der Linde, “Bayesian measures of model complexity and fit (with discussion),” Journal of the Royal Statistical Society Series B, vol. 64, no. 4, Article ID 583639, pp. 583–639, 2002. View at Google Scholar
  45. J. Cook, N. Speybroeck, T. Sochanta et al., “Sero-epidemiological evaluation of changes in Plasmodium falciparum and Plasmodium vivax transmission patterns over the rainy season in Cambodia,” Malaria Journal, vol. 11, article 86, 2012. View at Publisher · View at Google Scholar · View at Scopus
  46. Brazilian Institute of Geography and Statistics, Census 2010, http://censo2010.ibge.gov.br/en/censo-2010.html.
  47. P. McCullagh and J. A. Nelder, Generalized Linear Models, Chapman & Hall, London, UK, 2nd edition, 1989.
  48. E. J. Bedrick, R. Christensen, and W. Johnson, “A new perspective on priors for generalized linear models,” Journal of the American Statistical Association, vol. 91, no. 436, pp. 1450–1460, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  49. P. H. Garthwaite, J. B. Kadane, and A. O'Hagan, “Statistical methods for eliciting probability distributions,” Journal of the American Statistical Association, vol. 100, no. 470, pp. 680–701, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  50. E. Pothin, Modelling antibody responses to malaria blood stage infections: a novel method to estimate malaria transmission intensity from serological data [Ph.D. thesis], Imperial College London, London, UK, 2013.
  51. M. T. White, J. T. Griffin, O. Akpogheneta et al., “Dynamics of the antibody response to Plasmodium falciparum infection in african children,” Journal of Infectious Diseases, vol. 210, no. 7, pp. 1115–1122, 2014. View at Publisher · View at Google Scholar
  52. X.-H. Zhou and W. Tu, “Comparison of several independent population means when their samples contain log-normal and possibly zero observations,” Biometrics, vol. 55, no. 2, pp. 645–651, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  53. L. Tian, “Inferences on the mean of zero-inflated lognormal data: the generalized variable approach,” Statistics in Medicine, vol. 24, no. 20, pp. 3223–3232, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  54. N. Li, D. A. Elashoff, W. A. Robbins, and L. Xun, “A hierarchical zero-inflated log-normal model for skewed responses,” Statistical Methods in Medical Research, vol. 20, no. 3, pp. 175–189, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  55. G. J. McLachlan, “On bootstrapping the likelihood ratio test for two component normal mixture model,” Applied Statistics, vol. 36, no. 3, pp. 318–324, 1987. View at Google Scholar
  56. Y. Lo, N. R. Mendell, and D. B. Rubin, “Testing the number of components in a normal mixture,” Biometrika, vol. 88, no. 3, pp. 767–778, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  57. C. Ochieng, P. Ahenda, A. Y. Vittor et al., “Seroprevalence of infections with dengue, rift valley fever and chikungunya viruses in Kenya, 2007,” PLoS One, vol. 10, no. 7, Article ID e0132645, 2015. View at Publisher · View at Google Scholar
  58. F. Lu, J. Li, B. Wang et al., “Profiling the humoral immune responses to Plasmodium vivax infection and identification of candidate immunogenic rhoptry-associated membrane antigen (RAMA),” Journal of Proteomics, vol. 102, pp. 66–82, 2014. View at Publisher · View at Google Scholar · View at Scopus
  59. N. Imai, I. Dorigatti, S. Cauchemez, N. M. Ferguson, and S. I. Hay, “Estimating dengue transmission intensity from sero-prevalence surveys in multiple countries,” PLoS Neglected Tropical Diseases, vol. 9, no. 4, Article ID e0003719, 2015. View at Publisher · View at Google Scholar