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Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

Nishiura H - Biomed Eng Online (2011)

Bottom Line: The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful.Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details.

View Article: PubMed Central - HTML - PubMed

Affiliation: PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, Japan. nishiura@hku.hk

ABSTRACT

Background: Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting.

Methods: A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions.

Results: The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.

Conclusions: Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

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Mean absolute error by week of prediction. The vertical axis shows an average of absolute differences between observed and predicted values that represent the forecast error throughout the course of the epidemic. It should be noted that the vertical axis is in logarithmic scale. The dashed vertical line indicates the week at which the largest incidence (the peak) was observed (week 21). The horizontal axis represents the week of prediction.
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Figure 4: Mean absolute error by week of prediction. The vertical axis shows an average of absolute differences between observed and predicted values that represent the forecast error throughout the course of the epidemic. It should be noted that the vertical axis is in logarithmic scale. The dashed vertical line indicates the week at which the largest incidence (the peak) was observed (week 21). The horizontal axis represents the week of prediction.

Mentions: Despite accurate estimates of Ri, because of the large variation in the estimates of S0, the predicted final size varied greatly with the week of prediction (Table 1). The observed total number of cases was 203×105 and at week 44 the model slightly underestimated the final size perhaps because of the approximate linear modeling approach to the epidemic curve, however, the observed value was within the 95% CI. Although the prediction at week 18 underestimated the final size, the predicted final size at weeks 21 and 24 was included within the 95% CIs. In addition to the data given in Table 1, Figure 4 shows continuously evaluated MAE values for the weeks of prediction from weeks 5 to 35. The error fluctuated and was extremely large before the peak of the epidemic curve. At and after the peak the error was greatly reduced, reflecting the accuracies of forecasts mentioned above. In the present case study, an abrupt decline in MAE was seen in week 18, three weeks before observing the peak incidence (Figure 4).


Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

Nishiura H - Biomed Eng Online (2011)

Mean absolute error by week of prediction. The vertical axis shows an average of absolute differences between observed and predicted values that represent the forecast error throughout the course of the epidemic. It should be noted that the vertical axis is in logarithmic scale. The dashed vertical line indicates the week at which the largest incidence (the peak) was observed (week 21). The horizontal axis represents the week of prediction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3045989&req=5

Figure 4: Mean absolute error by week of prediction. The vertical axis shows an average of absolute differences between observed and predicted values that represent the forecast error throughout the course of the epidemic. It should be noted that the vertical axis is in logarithmic scale. The dashed vertical line indicates the week at which the largest incidence (the peak) was observed (week 21). The horizontal axis represents the week of prediction.
Mentions: Despite accurate estimates of Ri, because of the large variation in the estimates of S0, the predicted final size varied greatly with the week of prediction (Table 1). The observed total number of cases was 203×105 and at week 44 the model slightly underestimated the final size perhaps because of the approximate linear modeling approach to the epidemic curve, however, the observed value was within the 95% CI. Although the prediction at week 18 underestimated the final size, the predicted final size at weeks 21 and 24 was included within the 95% CIs. In addition to the data given in Table 1, Figure 4 shows continuously evaluated MAE values for the weeks of prediction from weeks 5 to 35. The error fluctuated and was extremely large before the peak of the epidemic curve. At and after the peak the error was greatly reduced, reflecting the accuracies of forecasts mentioned above. In the present case study, an abrupt decline in MAE was seen in week 18, three weeks before observing the peak incidence (Figure 4).

Bottom Line: The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful.Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details.

View Article: PubMed Central - HTML - PubMed

Affiliation: PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, Japan. nishiura@hku.hk

ABSTRACT

Background: Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting.

Methods: A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions.

Results: The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.

Conclusions: Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Show MeSH
Related in: MedlinePlus