Abstract
Advances in scientific computing have allowed the development of complex models that are being routinely applied to problems in disease epidemiology, public health and decision making. The utility of these models depends in part on how well they can reproduce empirical data. However, fitting such models to real world data is greatly hindered both by large numbers of input and output parameters, and by long run times, such that many modelling studies lack a formal calibration methodology. We present a novel method that has the potential to improve the calibration of complex infectious disease models (hereafter called simulators). We present this in the form of a tutorial and a case study where we history match a dynamic, event-driven, individual-based stochastic HIV simulator, using extensive demographic, behavioural and epidemiological data available from Uganda. The tutorial describes history matching and emulation. History matching is an iterative procedure that reduces the simulator's input space by identifying and discarding areas that are unlikely to provide a good match to the empirical data. History matching relies on the computational efficiency of a Bayesian representation of the simulator, known as an emulator. Emulators mimic the simulator's behaviour, but are often several orders of magnitude faster to evaluate. In the case study, we use a 22 input simulator, fitting its 18 outputs simultaneously. After 9 iterations of history matching, a non-implausible region of the simulator input space was identified that was times smaller than the original input space. Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs. History matching and emulation are useful additions to the toolbox of infectious disease modellers. Further research is required to explicitly address the stochastic nature of the simulator as well as to account for correlations between outputs.
Highlights
Complex computer models are being used in many scientific disciplines and are becoming increasingly common in basic science, climate modelling, communicable and non-communicable disease epidemiology and public health [1,2,3,4,5,6]
Modern computer models typically have a large number of input and output parameters, and long running times, a consequence of their increasing computational complexity
We propose a method that can help the calibration of models with long running times and several inputs and outputs
Summary
Complex computer models (hereafter called simulators) are being used in many scientific disciplines and are becoming increasingly common in basic science, climate modelling, communicable and non-communicable disease epidemiology and public health [1,2,3,4,5,6]. Recent advances that have been usefully applied in the field of dynamic epidemic modelling include maximum likelihood via iterated filtering [9]; data augmented and/or reversible-jump Markov chain Monte Carlo (MCMC; [10,11,12,13]) and stochastic differential equations [14]. These systems can sometimes become mathematically or computationally intractable, leading to the development of various approximation techniques [15,16]
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