Forecasting the Tuberculosis Incidence Using a Novel Ensemble Empirical Mode Decomposition-Based Data-Driven Hybrid Model in Tibet, China

Abstract

Objective: The purpose of this study is to develop a novel data-driven hybrid model by fusing ensemble empirical mode decomposition (EEMD), seasonal autoregressive integrated moving average (SARIMA), with nonlinear autoregressive artificial neural network (NARNN), called EEMD-ARIMA-NARNN model, to assess and forecast the epidemic patterns of TB in Tibet.

Methods: The TB incidence from January 2006 to December 2017 was obtained, and then the time series was partitioned into training subsamples (from January 2006 to December 2016) and testing subsamples (from January to December 2017). Among them, the training set was used to develop the EEMD-SARIMA-NARNN combined model, whereas the testing set was used to validate the forecasting performance of the model. Whilst the forecasting accuracy level of this novel method was compared with the basic SARIMA model, basic NARNN model, error-trend-seasonal (ETS) model, and traditional SARIMA-NARNN mixture model.

Results: By comparing the accuracy level of the forecasting measurements including root-mean-square error, mean absolute deviation, mean error rate, mean absolute percentage error, and root-mean-square percentage error, it was shown that the EEMD-SARIMA-NARNN combined method produced lower error rates than the others. The descriptive statistics suggested that TB was a seasonal disease, peaking in late winter and early spring and a trough in autumn and early winter, and the TB epidemic indicated a drastic increase by a factor of 1.7 from 2006 to 2017 in Tibet, with average annual percentage change of 5.8 (95% confidence intervals: 3.5-8.1).

Conclusion: This novel data-driven hybrid method can better consider both linear and nonlinear components in the TB incidence than the others used in this study, which is of great help to estimate and forecast the future epidemic trends of TB in Tibet. Besides, under present trends, strict precautionary measures are required to reduce the spread of TB in Tibet.

Keywords: forecasting; incidence rate; statistical models; time series analysis; tuberculosis.

Figure 1

Estimated autocorrelogram and partial autocorrelogram of the residual sequence to forecast the TB epidemic patterns using (A) SARIMA model, (B) basic NARNN model, (C) traditional SARIMA-NARNN hybrid model, and (D) novel EEMD-SARIMA-NARNN hybrid model. As seen, the estimated autocorrelations and partial autocorrelations of the errors from the different models almost fell into the 95% confidence intervals (CIs) with few exceptions, such as the autocorrelations at lags 15 and 19 and partial autocorrelations at lags 15 in (A), and autocorrelations and partial autocorrelations at lag 11 in (D), these are also reasonable because higher-order autocorrelations and partial autocorrelations easily exceed the 95 CIs by chance.

Figure 2

Intrinsic mode functions (IMFs) and residue components of the original TB incidence series using the EEMD.

Figure 3

Estimated autocorrelogram of the residual sequence to forecast the six intrinsic mode functions (IMFs) decomposed by the EEMD method using the SARIMA-NARNN hybrid model. (A) IMF1, (B) IMF2, (C) IMF3, (D) IMF4, (E) IMF5, and (F) IMF6. For the estimated autocorrelations of the residual series from the different IMFs, all of them are inside of the 95 CIs except for the one at lag zero, meaning that there is no correlated serial in the residuals of the best-fitting SARIMA-NARNN hybrid model. Thereby, there appears to be adequate and reasonable for forecasting upcoming epidemiological trends using these best-fitting models.

Figure 4

Time series plot showing the comparative results between original observations and fitted and predicted values using the selected best-fitting (A) SARIMA model, (B) NARNN model, (C) traditional SARIMA-NARNN hybrid model, and (D) novel EEMD-SARIMA-NARNN hybrid model (The curve at the left of the vertical black dotted line represents the fitted values, whereas the curve at the right denotes the forecasted values). As shown, the produced curve from the EEMD-SARIMA-NARNN hybrid model is closer to the actual both in the fitted and predicted aspects compared with the curves from the other models.