Abstract
Here, we address the issue of experimental design for animal and crop disease transmission experiments, where the goal is to identify some characteristic of the underlying infectious disease system via a mechanistic disease transmission model. Design for such non-linear models is complicated by the fact that the optimal design depends upon the parameters of the model, so the problem is set in simulation-based, Bayesian framework using informative priors. This involves simulating the experiment over a given design repeatedly using parameter values drawn from the prior, calculating a Monte Carlo estimate of the utility function from those simulations for the given design, and then repeating this over the design space in order to find an optimal design or set of designs.
Here we consider two agricultural scenarios. The first involves an experiment to characterize the effectiveness of a vaccine-based treatment on an animal disease in an in-barn setting. The design question of interest is on which days to make observations if we are limited to being able to observe the disease status of all animals on only two days. The second envisages a trial being carried out to estimate the spatio-temporal transmission dynamics of a crop disease. The design question considered here is how far apart to space the plants from each other to best capture those dynamics. In the in-barn animal experiment, we see that for the prior scenarios considered, observations taken very close to the beginning of the experiment tend to lead to designs with the highest values of our chosen utility functions. In the crop trial, we see that over the prior scenarios considered, spacing between plants is important for experimental performance, with plants being placed too close together being particularly deleterious to that performance.
References
Anderson, R., and R. May. 1991. Infectious Diseases of Humans. New York: Oxford University Press.Search in Google Scholar
Becker, N. G., and T. Britton. 2001. “Design Issues for Studies of Infectious Diseases.” Journal of Statistical Planning and Inference 96: 41–66.10.1016/S0378-3758(00)00323-2Search in Google Scholar
Becker, N. G., and G. Kersting. 1983. “Design Problems for the Pure Birth Process.” Advances in Applied Probability 15 (2): 255–73.10.2307/1426436Search in Google Scholar
Clyde, M. A. 2001. “Experimental Design: A Bayesian Perspective.” In International Encyclopedia of the Social and Behavioral Sciences, edited by Smelser et al. New York: Elsevier Science.10.1016/B0-08-043076-7/00421-6Search in Google Scholar
Cook, A. R., G. J. Gibson, and C. A. Gilligan. 2008. “Optimal Observation Times in Experimental Epidemic Processes.” Biometrics 64 (3): 860–68.10.1111/j.1541-0420.2007.00931.xSearch in Google Scholar PubMed
Deardon, R., S. P. Brooks, B. T. Grenfell, M. J. Keeling, M. J. Tildesley, N. J. Savill, D. J. Shaw, and M. E. J. Woolhouse. 2010. “Inference for Individual-Level Models of Infectious Diseases in Large Populations.” Statistica Sinica 20: 239–61.Search in Google Scholar
Deardon, R., S. G. Gilmour, N. A. Butler, K. Phelps, and R. Kennedy. 2004. “A Method for Ascertaining and Controlling Representation Bias in Field Trials for Airborne Plant Pathogens.” Journal of Applied Statistics 31 (3): 329–43.10.1080/0266476042000184073Search in Google Scholar
Deardon, R., S. G. Gilmour, N. A. Butler, K. Phelps, and R. Kennedy. 2006. “Designing Field Experiments which are Subject to Representation Bias.” Journal of Applied Statistics 33 (7): 663–78.10.1080/02664760600708681Search in Google Scholar
Dehideniya, M. B., C. C. Drovandi, and J. M. McGree. 2018. “Optimal Bayesian Design for Discriminating Between Models with Intractable Likelihoods in Epidemiology.” Computational Statistics & Data Analysis 124 (C): 277–97.10.1016/j.csda.2018.03.004Search in Google Scholar
Drovandi, C. C., and A. N. Pettitt. 2013. “Bayesian Experimental Design for Models with Intractable Likelihoods.” Biometrics 69 (4): 937–48.10.1111/biom.12081Search in Google Scholar PubMed
Garthwaite, P. H., J. B. Kadane, and A. O’Hagan. 2005. “Statistical Methods for Eliciting Probability Distributions.” Journal of the American Statistical Association 100 (470): 680–701.10.1198/016214505000000105Search in Google Scholar
Hainy M., Müller W .G., and Wagner H. 2013. “Likelihood-Free Simulation-Based Optimal Design: An Introduction.” In Springer Proceedings in Mathematics & Statistics, edited by V. Melas, S. Mignani, P. Monari, L. Salmaso, Topics in Statistical Simulation., vol 114. New York, NY: Springer.10.1007/978-1-4939-2104-1_26Search in Google Scholar
Huan, X., and Y. M. Marzouk. 2013. “Simulation-Based Optimal Bayesian Experimental Design for Nonlinear Systems.” Journal of Computational Physics 232 (1): 288–317.10.1016/j.jcp.2012.08.013Search in Google Scholar
Hughes, G., N. McRoberts, L. V. Madden, and S. C. Nelson. 1997. “Validating Mathematical Models of Plant-Disease Progress in Space and Time.” Mathematical Medicine and Biology: A Journal of the IMA 14 (2): 85–112.10.1093/imammb/14.2.85Search in Google Scholar
Kwong, G. P., Z. Poljak, R. Deardon, and C. E. Dewey. 2013. “Bayesian Analysis of Risk Factors for Infection with a Genotype of Porcine Reproductive and Respiratory Syndrome Virus in Ontario Swine Herds Using Monitoring Data.” Preventive Veterinary Medicine 110 (3): 405–17.10.1016/j.prevetmed.2013.01.004Search in Google Scholar
Leone, F. C., L. S. Nelson, and R. B. Nottingham. 1961. “The Folded Normal Distribution.” Technometrics 3 (4): 543–50.10.1080/00401706.1961.10489974Search in Google Scholar
McKinley, T. J., J. V. Ross, R. Deardon, and A. R. Cook. 2014. “Simulation-Based Bayesian Inference for Epidemic Models.” Computational Statistics & Data Analysis 71: 434–47.10.1016/j.csda.2012.12.012Search in Google Scholar
Mondaca-Fernandez, E., T. Meyns, C. Muoz-Zanzi, C. Trincado, and R. B. Morrison. 2007. “Experimental Quantification of the Transmission of Porcine Reproductive and Respiratory Syndrome Virus.” Canadian Journal of Veterinary Research 71 (2): 157–60.Search in Google Scholar
Muller, P. 1999. “Simulation-Based Optimal Design.” Bayesian Statistics 6: 459–74.10.1016/S0169-7161(05)25017-4Search in Google Scholar
Overstall, A. M., and D. C. Woods. 2017. “Bayesian Design of Experiments Using Approximate Coordinate Exchange.” Technometrics 59 (4): 458–70.10.1080/00401706.2016.1251495Search in Google Scholar
Pagendam, D. E., and P. K. Pollett. 2009. “Optimal Sampling and Problematic Likelihood Functions in a Simple Population Model.” Environmental Modeling and Assessment 14 (6): 759–67.10.1007/s10666-008-9159-1Search in Google Scholar
Pagendam, D. E., and P. K. Pollett. 2010. “Locally Optimal Designs for the Simple Death Process.” Journal of Statistical Planning and Inference 140 (11): 3096–105.10.1016/j.jspi.2010.04.017Search in Google Scholar
Pokharel, G., and R. Deardon. 2016. “Gaussian Process Emulators for Spatial Individual-Level Models of Infectious Disease.” Canadian Journal of Statistics 44 (4): 480–501.10.1002/cjs.11304Search in Google Scholar
Romanescu, R., and R. Deardon. 2016. “Modelling Two Strains of Disease Via Aggregate-Level Infectivity Curves.” Journal of Mathematical Biology 72 (5): 1195–224.10.1007/s00285-015-0910-3Search in Google Scholar
Ryan, E., C. Drovandi, and A. Pettitt. 2015. “Simulation-Based Fully Bayesian Experimental Design for Mixed Effects Models.” Computational Statistics & Data Analysis 92.10.1016/j.csda.2015.06.007Search in Google Scholar
Ryan, E. G., C. C. Drovandi, J. M. McGree, and A. N. Pettitt. 2016. “A Review of Modern Computational Algorithms for Bayesian Optimal Design.” International Statistical Review 84 (1): 128–54.10.1111/insr.12107Search in Google Scholar
Velthuis, A., M. D. Jong, E. Kamp, N. Stockhofe, and J. Verheijden. 2003. “Design and Analysis of an Actinobacillus Pleuropneumoniae Transmission Experiment.” Preventive Veterinary Medicine 60 (1): 53–68.10.1016/S0167-5877(03)00082-5Search in Google Scholar
Woods, D. C., A. M. Overstall, M. Adamou, and T. W. Waite. 2017. “Bayesian Design of Experiments for Generalized Linear Models and Dimensional Analysis with Industrial and Scientific Application.” Quality Engineering 29 (1): 91–103.Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston