Approach for Qualitative Validation Using Aggregated Data for a Stochastic Simulation Model of the Spread of the Bovine
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Unit of Animal Health Management, Veterinary School & INRA, BP 40706, 44307 Nantes Cedex 03, France; E-mail: [email protected] 2 Unit´e de Math´ematiques et Informatique Appliqu´ees, INRA, 78352 Jouy-en-Josas Cedex, France 3 INSERM, U170, IFR69, Universit´e Paris 11, 16 av Paul Vaillant Couturier, 94807 Villejuif Cedex, France 4 CNRS UMR 8145, Universit´e Paris 5, 45 rue des Saint-P`eres, 75006 Paris, France Received 15 November 2004; accepted in final form 26 April 2006
ABSTRACT Qualitative validation consists in showing that a model is able to mimic available observed data. In population level biological models, the available data frequently represent a group status, such as pool testing, rather than the individual statuses. They are aggregated. Our objective was to explore an approach for qualitative validation of a model with aggregated data and to apply it to validate a stochastic model simulating the bovine viral-diarrhoea virus (BVDV) spread within a dairy cattle herd. Repeated measures of the level of BVDV-specific antibodies in the bulk-tank milk (total milk production of a herd) were used to summarise the BVDV herd status. First, a domain of validation was defined to ensure a comparison restricted to dynamics of pathogen spread well identified among observed aggregated data (new herd infection with a wide BVDV spread). For simulations, scenarios were defined and simulation outputs at the individual animal level were aggregated at the herd level using an aggregation function. Comparison was done only for observed data and simulated aggregated outputs that were in the domain of validation. The validity of our BVDV model was not rejected. Drawbacks and ways of improvement of the approach are discussed.
Key Words: validation, aggregated data, stochastic model, virus spread
1. INTRODUCTION Validation consists in showing that a model sufficiently represents the studied real system in order to use the model results to describe the behaviour of this system or to make decisions (Kleijnen, 1995; Rykiel, 1996). Validation strategies often consist of different steps, depending on the type and the quantity of data from the real system (Law Acta Biotheoretica (2006) 54: 207–217 DOI: 10.1007/s10441-006-8226-8
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and Kelton, 1991). Without observed data independent from the data used for estimation of model parameters, only sensitivity analyses can be done. They consist in studying the model behaviour when values of parameters are changed. If data not used for estimation of parameters are available, validation is either quantitative (including goodness of fit) or qualitative. Quantitative validation of a stochastic model consists in comparing the occurrence distribution of all behaviours of the real system with the occurrence distribution of all simulated behaviours. For such a validation, it is assumed that the observed data give a thorough description of all possible system behaviours. For some systems, such data are not available. This lack of thorough data is fr
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