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Bayesian history matching of complex infectious disease models using emulation: a tutorial and a case study on HIV in Uganda.

Andrianakis I, Vernon IR, McCreesh N, McKinley TJ, Oakley JE, Nsubuga RN, Goldstein M, White RG - PLoS Comput. Biol. (2015)

Bottom Line: 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.Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs.Further research is required to explicitly address the stochastic nature of the simulator as well as to account for correlations between outputs.

View Article: PubMed Central - PubMed

Affiliation: Dept. of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom.

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 10(11) 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.

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Related in: MedlinePlus

Example emulator and implausibility for toy simulator [].Panel (a) shows an emulator of the toy simulator  (black dashed line). The value of  is considered unknown apart from six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input  is implausible or not.
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pcbi-1003968-g003: Example emulator and implausibility for toy simulator [].Panel (a) shows an emulator of the toy simulator (black dashed line). The value of is considered unknown apart from six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input is implausible or not.

Mentions: Fig. 3(a) shows a simple example of a one dimensional emulator. The (toy) simulator used is the deterministic function . Because the simulator is deterministic, it holds that . The value of is considered unknown apart from the six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data () and the 95% CI () that we use to history match the simulator.


Bayesian history matching of complex infectious disease models using emulation: a tutorial and a case study on HIV in Uganda.

Andrianakis I, Vernon IR, McCreesh N, McKinley TJ, Oakley JE, Nsubuga RN, Goldstein M, White RG - PLoS Comput. Biol. (2015)

Example emulator and implausibility for toy simulator [].Panel (a) shows an emulator of the toy simulator  (black dashed line). The value of  is considered unknown apart from six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input  is implausible or not.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4288726&req=5

pcbi-1003968-g003: Example emulator and implausibility for toy simulator [].Panel (a) shows an emulator of the toy simulator (black dashed line). The value of is considered unknown apart from six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input is implausible or not.
Mentions: Fig. 3(a) shows a simple example of a one dimensional emulator. The (toy) simulator used is the deterministic function . Because the simulator is deterministic, it holds that . The value of is considered unknown apart from the six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data () and the 95% CI () that we use to history match the simulator.

Bottom Line: 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.Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs.Further research is required to explicitly address the stochastic nature of the simulator as well as to account for correlations between outputs.

View Article: PubMed Central - PubMed

Affiliation: Dept. of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom.

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 10(11) 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.

Show MeSH
Related in: MedlinePlus