Computational and Applied Mathematics

, Volume 32, Issue 2, pp 303–313

On the use of chance-adjusted agreement statistic to measure the assortative transmission of infectious diseases

Article

Abstract

There have been only a small number of statistical measures to assess the assortativeness. The present study discusses the applicability of two chance-adjusted agreement statistics, kappa and AC1 as measures of the assortative transmission of infectious diseases. First, we show that the so-called assortativity coefficient corresponds to the proportion of contacts that are spent for within-group mixing in the preferential mixing formulation of heterogeneous transmission, and also that the assortative coefficient is identical to the Cohen’s kappa statistic. Second, we demonstrate that the kappa statistic is vulnerable to the paradoxes in measuring infectious disease transmission, because the assortative transmission involves not only contact heterogeneity but also other intrinsic and extrinsic factors including relative susceptibility and infectiousness. AC1 can be a useful measure due to its paradox resistant nature, and we discuss the relevance of preferential mixing formulation to the computation of AC1.

Keywords

Epidemiology Network Mathematical model Cluster Inter-observer variation 

Mathematics Subject Classification (2000)

Primary 92B05 Secondary 62P10 

References

  1. Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89:208701CrossRefGoogle Scholar
  2. Jacquez JA, Simon CP, Koopman J, Sattenspiel L, Perry T (1988) Modeling and analyzing HIV transmission: the effect of contact patterns. Math Biosci 92:119–199MathSciNetMATHCrossRefGoogle Scholar
  3. Nishiura H, Chowell G, Safan M, Castillo-Chavez C (2010) Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009. Theor Biol Med Model 7:1CrossRefGoogle Scholar
  4. Nishiura H, Cook AR, Cowling BJ (2011) Assortativity and the probability of epidemic extinction: a case study of Pandemic Influenza A (H1N1-2009). Interdiscip Perspect Infect Dis 2011:194507Google Scholar
  5. Lam EH, Cowling BJ, Cook AR, Wong JY, Lau MS, Nishiura H (2011) The feasibility of age-specific travel restrictions during influenza pandemics. Theor Biol Med Model 8:44CrossRefGoogle Scholar
  6. Nold A (1980) Heterogeneity in disease-transmission modeling. Math Biosci 52:227–240MathSciNetMATHCrossRefGoogle Scholar
  7. Kiss IZ, Simon PL, Kao RR (2009) A contact-network-based formulation of a preferential mixing model. Bull Math Biol 4:888–905MathSciNetCrossRefGoogle Scholar
  8. Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, Hollingsworth TD, Griffin J, Baggaley RF, Jenkins HE, Lyons EJ, Jombart T, Hinsley WR, Grassly NC, Balloux F, Ghani AC, Ferguson NM, Rambaut A, Pybus OG, Lopez-Gatell H, Alpuche-Aranda CM, Chapela IB, Zavala EP, Guevara DM, Checchi F, Garcia E, Hugonnet S, Roth C, WHO Rapid Pandemic Assessment Collaboration (2009) Pandemic potential of a strain of influenza A (H1N1): early findings. Science 324:1557–1561Google Scholar
  9. Wallinga J, Teunis P, Kretzschmar M (2006) Using data on social contacts to estimate age-specific transmission parameters for respiratory-spread infectious agents. Am J Epidemiol 164:936–944CrossRefGoogle Scholar
  10. Mossong J, Hens N, Jit M, Beutels P, Auranen K, Mikolajczyk R, Massari M, Salmaso S, Tomba GS, Wallinga J, Heijne J, Sadkowska-Todys M, Rosinska M, Edmunds WJ (2008) Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med 5:e74CrossRefGoogle Scholar
  11. Del Valle SY, Hyman JM, Hethcote HW, Eubank SG (2007) Mixing patterns between age groups in social networks. Soc Netw 29:539–554CrossRefGoogle Scholar
  12. Newman MEJ (2003) Mixing patterns in networks. Phys Rev E 67:026126MathSciNetCrossRefGoogle Scholar
  13. Farrington CP, Whitaker HJ, Wallinga J, Manfredi P (2009) Measures of disassortativeness and their application to directly transmitted infections. Biom J 51:387–407MathSciNetCrossRefGoogle Scholar
  14. Gupta S, Anderson RM, May RM (1989) Networks of sexual contacts: implications for the pattern of spread of HIV. AIDS 3:807–817CrossRefGoogle Scholar
  15. Glasser J, Feng Z, Moylan A, Del Valle S, Castillo-Chavez C (2012) Mixing in age-structured population models of infectious diseases. Math Biosci 235:1–7MathSciNetMATHCrossRefGoogle Scholar
  16. Diekmann O, Heesterbeek JA, Roberts MG (2010) The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface 7:873–885CrossRefGoogle Scholar
  17. Nishiura H, Oshitani H (2011) Household transmission of influenza (H1N1-2009) in Japan: age-specificity and reduction of household transmission risk by zanamivir treatment. J Int Med Res 39:619–628CrossRefGoogle Scholar
  18. Cohen J (1960) A coefficient of agreement for nominal scales. Educ Psychol Measure 20:37–46Google Scholar
  19. Feinstein AR, Cicchetti DV (1990) High agreement but low kappa: I. The problems of two paradoxes. J Clin Epidemiol 43:543–549CrossRefGoogle Scholar
  20. Feinstein AR, Cicchetti DV (1990) High agreement but low kappa: II. Resolving the paradoxess. J Clin Epidemiol 43:551–558CrossRefGoogle Scholar
  21. Gwet KL (2010) Handbook of Inter-rater Reliability (2nd edn). Advanced Analytics. Gaithersburg, MD, USAGoogle Scholar
  22. Gwet KL (2008) Computing inter-rater reliability and its variance in the presence of high agreement. Br J Math Stat Psychol 61:29–48Google Scholar
  23. Meyers LA, Newman ME, Pourbohloul B (2006) Predicting epidemics on directed contact networks. J Theor Biol 240:400–418MathSciNetCrossRefGoogle Scholar
  24. Ejima K, Omori R, Cowling BJ, Aihara K, Nishiura H (2012a) The time required to estimate the case fatality ratio of influenza using only the tip of an iceberg: joint estimation of the virulence and the transmission potential. Comput Math Methods Med 2012:978901Google Scholar
  25. Ejima K, Omori R, Aihara K, Nishiura H (2012b) Real-time investigation of measles epidemics with estimate of vaccine efficacy. Int J Biol Sci 8:620–629Google Scholar
  26. Farrington CP, Whitaker HJ (2005) Contact surface models for infectious diseases: estimation from serologic survey data. J Am Stat Soc 100:370–379MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013

Authors and Affiliations

  • Keisuke Ejima
    • 1
    • 2
  • Kazuyuki Aihara
    • 1
    • 3
  • Hiroshi Nishiura
    • 2
    • 4
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan
  2. 2.School of Public HealthThe University of Hong KongPokfulamHong Kong
  3. 3.Institute of Industrial ScienceThe University of TokyoTokyoJapan
  4. 4.PRESTOJapan Science and Technology AgencySaitamaJapan

Personalised recommendations