Model Validation And Sensitivity And Uncertainty Analysis

An essential aspect of the use of mathematical models in infectious disease epidemiology is validation of model results against real data, validation here referring simply to the ability to satisfy oneself that the model results are consistent with the available data relating to the population which is being modeled (or in its absence, data from a population sharing similar characteristics). It is not necessary for this process to be one of fitting, in the statistical sense, as we are dealing with model results which are qualitative rather than quantitative, and it is usually therefore more important that the model can reproduce the change in shape over time of the data being used for validation rather than absolute values. Thus the process is more one of inspection and fitting by eye rather than statistical fitting. Given that we can establish the validity of the model results in this way, it is important to know how sensitive these results are to the values of the model parameters. Depending upon the structure of the model and the role played by each parameter in the model, very small changes in the values of some parameters can lead to large variations in model results; for other parameters the situation may be reversed and relatively large changes in values may have little impact on the results. It is the role of sensitivity analysis to establish how variation in parameter values might impact on model outputs; if the model should prove to be too sensitive, the results will be useless. This can either be done simply by varying the values of each parameter in turn and observing what effect each has, or more systematically by the use of ''Latin hypercube'' sampling (cf. Latin square), which involves specifying a distribution for the values of each parameter (which could simply be a uniform distribution if the true distribution is not known) and sampling at random and without replacement parameter values from the combined set of distributions (Seaholm et al., 1988). Once the sensitivity of the model to its parameters has been established, it is necessary to consider how much uncertainty there is in our knowledge about the true values of each parameter in relation to the population being considered. In uncertainty analysis we are considering what the plausible range of values for each parameter might be, and exploring the variation in model results which arises when parameter values are varied within this set of ranges; the variation in model outputs then provides an indication of uncertainty about the likely way in which, for example, prevalence or incidence of an infection may change over time in the population being studied.

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