In this work, we developed a theoretical framework leading to
misclassification of the final size epidemic data for the stochastic SIR (Susceptible-Infective-Removed),
household epidemic model, with false negative and false positive
misclassification probabilities. Maximum likelihood based algorithm is then
employed for its inference. We then analyzed and compared the estimates of the
two dimensional model with those of the three and four dimensional models
associated with misclassified final size data over arrange of theoretical
parameters, local and global infection rates and corresponding proportion
infected in the permissible region, away from its boundaries and
misclassification probabilities.The
adequacies of the three models to the final size data are examined. The four
and three-dimensional models are found to outperform the two dimensional model
on misclassified final size data.
References
[1]
Addy, C., Longini Jr., I.M. and Haber, M. (1991) A Generalised Stochastic Model for the Analysis of Infectious Disease Final Size Data. Biometrics, 47, 961-974.
https://doi.org/10.2307/2532652
[2]
Ball, F.G. (1983) The Threshold Behaviour of Epidemic Models. Journal of Applied Probability, 20, 227-241. https://doi.org/10.2307/3213797
[3]
Ball, F.G. (1986) A Unified Approach to the Distribution of the Total Size and Total Area under the Trajectory of Infection in Epidemic Models. Advances in Applied Probability, 18, 289-310. https://doi.org/10.2307/1427301
[4]
Ball, F.G., Mollison, D. and Scalia-Tomba, G. (1997) Epidemics with Two Levels of Mixing. Annals of Applied Probability, 7, 46-89.
https://doi.org/10.1214/aoap/1034625252
[5]
Ball, F. and Donnelly, P. (1995) Strong Approximations for Epidemic Models. Stochastic Processes and Their Application, 55, 1-21.
https://doi.org/10.1016/0304-4149(94)00034-Q
[6]
Ball, F.G., O’Neill, P. and Pike, J. (2007) Stochastic Epidemics in Structured Populations Featuring Dynamic Vaccination and Isolation. Journal of Applied Probability, 44, 571-585. https://doi.org/10.1239/jap/1189717530
[7]
Clancy, D. and O’NeiIl, P.D. (2007) Exact Bayesian Inference and Model Selection for Stochastic Models of Epidemics among a Community of Households. Scandinavian Journal of Statistics, 34, 259-274.
https://doi.org/10.1111/j.1467-9469.2006.00522.x
[8]
Baron, B.A. (1977) The Effects of Misclassification on Estimation of Relative Risk. Biometrics, 33, 414-418. https://doi.org/10.2307/2529795
[9]
Gustafson, P. (2009) Measurement Error and Misclassification in Statistics and Epidemiology, Impacts and Bayesian Adjustment. Chapman and Hall/CRC, London.
[10]
Ball, F.G. and Neal, P. (2002) A General Model for the Stochastic SIR Epidemic with Two Levels of Mixing. Mathematical Biosciences, 180, 73-102.
https://doi.org/10.1016/S0025-5564(02)00125-6
[11]
Neal, P. (2012) Efficient Likelihood-Free Bayesian Computation for Household Epidemics. Journal of Statistics and Computing, 22, 1239-1256.
https://doi.org/10.1007/s11222-010-9216-x
[12]
Becker, N.G. (1970) A Stochastic Model for Interacting Population. Journal of Applied Probability, 7, 544-564. https://doi.org/10.2307/3211937
[13]
Ball, F.G. and Lyne, O.D. (2000) Epidemics among a Population of Households. In: Castillo-Chavez, C., Blower, S., Driessche, P., Kirschner, D. and Yakubu, A.-A., Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory, Springer, Berlin, Vol. 126, 115-125.
https://doi.org/10.1007/978-1-4613-0065-6_7
[14]
Longini Jr., I.M. and Koopman, J.S. (1982) Household and Community Transmission Parameters from Final Distribution of Infections in Households. Biometrics, 38, 115-126. https://doi.org/10.2307/2530294
[15]
Neal, P. (2016) A Household SIR Epidemic Model Incorporating Time of Day Effects. Journal of Applied Probability, 53, 489-501.
https://doi.org/10.1017/jpr.2016.15
