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Table 1 ARGO performance compared to alternative methods for the time period of July 6, 2013 to February 21, 2015

From: Using electronic health records and Internet search information for accurate influenza forecasting

  real-time forecast 1 week forecast 2 week forecast 3 week
RMSE
 ARGO 0.315 0.435 0.487 0.459
 Ref. [11] 0.469 0.544 0.590 0.578
 ar4 0.944 0.954 0.935 0.902
 naive 1 (0.374) 1 (0.613) 1 (0.756) 1 (0.869)
MAE
 ARGO 0.403 0.446 0.456 0.426
 Ref. [11] 0.497 0.614 0.603 0.593
 ar4 0.895 0.880 0.872 0.867
 naive 1 (0.221) 1 (0.363) 1 (0.480) 1 (0.575)
RMSPE
 ARGO 0.449 0.474 0.504 0.461
 Ref. [11] 0.655 0.677 0.657 0.691
 ar4 1.001 1.018 1.032 1.044
 naive 1 (0.126) 1 (0.194) 1 (0.246) 1 (0.293)
MAPE
 ARGO 0.481 0.458 0.454 0.419
 Ref. [11] 0.625 0.704 0.662 0.676
 ar4 0.956 0.965 0.977 0.988
 naive 1 (0.101) 1 (0.156) 1 (0.205) 1 (0.251)
Correlation     
 ARGO 0.995 0.976 0.952 0.942
 Ref. [11] 0.989 0.960 0.928 0.904
 ar4 0.954 0.871 0.804 0.748
 naive 0.951 0.867 0.796 0.727
Error reduction of ARGO over the best available alternative (in %)
 RMSE 32.90 [16.38,55.54] 20.07 [5.13,31.38] 17.40 [1.29,28.82] 20.53 [11.82,27.33]
 MAE 18.79 [0.23,36.67] 27.44 [10.28,39.18] 24.41 [7.66,34.53] 28.13 [15.84,36.38]
 RMSPE 31.50 [21.63,40.84] 29.90 [9.42,41.95] 23.26 [4.69,33.00] 33.32 [19.94,41.69]
 MAPE 22.92 [7.93,35.94] 34.95 [18.59,46.76] 31.42 [12.90,43.04] 38.02 [26.00,47.26]
  1. The evaluation metrics between the prediction \( \widehat{p_t} \) and the target \( \widehat{p_t} \) include RMSE \( \left(=\sqrt{\frac{1}{T}\sum_{t=1}^T{\left(\widehat{p_t}-{p}_t\right)}^2}\right),\mathrm{MAE}\left(=\frac{1}{T}\sum_{t=1}^T|\widehat{p_t}-{p}_t|\right),\mathrm{RMSPE}\left(=\sqrt{\frac{1}{T}\sum_{t=1}^T{\left(\frac{\widehat{p_t}-{p}_t}{p_t}\right)}^2}\right),\mathrm{MAPE}\left(=\frac{1}{T}\sum_{t=1}^T\frac{\mid \widehat{p_t}-{p}_t\mid }{p_t}\right) \), and Pearson correlation. The benchmark models include the ensemble method by Santillana et al. [11], an autoregression model with 4 lags, and a naive model, which uses prior week’s ILI level as the prediction for the current week as well as the next 3 weeks. Boldface highlights the best method for each metric in each forecasting time horizon. RMSE, MAE, RMSPE, MAPE are relative to the error of the naive method, i.e., the numbers are the ratio of the error of a given method over that of the naive method; the absolute error of the naive method is given in the round bracket. Table S3 in the Additional file 1 gives the absolute error of all methods. For each forecasting time horizon and each evaluation metrics, the error reduction of ARGO over the best alternative method is given in the second half of the table, together with 95% confidence intervals (in the square bracket) constructed using stationary bootstrap [33] with mean block size of 52 weeks.