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

DOI: 10.1007/s40314-013-0017-7

Ejima, K., Aihara, K. & Nishiura, H. Comp. Appl. Math. (2013) 32: 303. doi:10.1007/s40314-013-0017-7

## 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

EpidemiologyNetworkMathematical modelClusterInter-observer variation

### Mathematics Subject Classification (2000)

Primary 92B05Secondary 62P10

## 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