我国肺结核月报告死亡病例数的自回归移动平均模型的建立及预测

目的: 分析我国肺结核月报告死亡病例数的变化趋势以建立及确定最佳预测自回归移动平均模型(autoregressive integrated moving average model,ARIMA)。方法: 搜集《疾病监测》杂志发布的2010—2020年全国 (不包括我国港澳台地区,下同)每月报告的肺结核死亡病例数,共计报告21055例。以2010—2018年数据作为建模数据库组成时间序列并拟合ARIMA模型。以2019年和2020年每月报告的实际数据作为验证数据库,对ARIMA模型进行筛选与评价,选择出最佳模型并预测2021年1—12月我国肺结核月报告死亡病例数。 结果: 基于2010—2018年我国肺结核月报告死亡病例数构建模型,经参数评估与整体诊断初步筛选出3个备选模型,即平稳决定系数最大(R²=0.589)的ARIMA(0,1,1)(1,1,0)₁₂模型、均方根误差值最小(RMSE=24.572)的ARIMA(0,1,2)模型和标准化贝叶斯信息准则值最小(NBIC=6.517)的ARIMA(0,1,1)模型。运用备选模型预测2019年和2020年我国肺结核月报告死亡病例数并与实际数据相比较,筛选出最优预测模型为ARIMA(0,1,1),其预测2019年和2020年数据的相对误差分别为6.56%(147/2241)和58.52%(910/1555)。以ARIMA(0,1,1)模型预测2021年1—12月我国肺结核死亡病例数约为2542例,平均月报告死亡病例数为212例。结论: ARIMA模型的短期预测效果较好,可用于预测近期我国肺结核月报告死亡病例数,但在预测远期或受到较大因素影响年份的数据时效果欠佳。

Establishment and prediction of autoregressive integrated moving average model of monthly reported deaths of pulmonary tuberculosis in China

Objective: To analysis the trend of monthly reported deaths of pulmonary tuberculosis in China, to establish and determine the optimal autoregressive integrated moving average model (ARIMA). Methods: Monthly reported deaths of pulmonary tuberculosis in China (excluding Hong Kong, Macao and Taiwan) reported on Disease Surveillance from 2010 to 2020 was collected, and the total number was 21055.Date from 2010 to 2018 were used as modeling databases to form the time series and fit the ARIMA model. The actual date monthly reported in 2019 and 2020 were used as verification database to screen and evaluate the ARIMA models, then the optimal model was selected and used to predict monthly reported deaths of pulmonary tuberculosis from January 2021 to December 2021 in China. Results: The model was constructed based on the number of monthly reported deaths of pulmonary tuberculosis in China from 2010 to 2018, and three alternative models were preliminarily screened out through parameter evaluation and overall diagnosis; they were ARIMA (0,1,1) (1,1,0)₁₂ with the maximum stationary R-square (R ²=0.589), ARIMA(0,1,2) with the minimum root mean squared error (RMSE=24.572) and ARIMA (0,1,1) with the minimum value of standardized Bayesian information criterion (NBIC=6.517), respectively. The alternative model was used to predict the number of monthly reported deaths of pulmonary tuberculosis in China from 2019 to 2020. Compared with the actual data, ARIMA (0,1,1) was the optimal prediction model, and the relative errors of the predicted data in 2019 and 2020 were 6.56% (147/2241) and 58.52% (910/1555), respectively. ARIMA (0,1,1) model was used to predict the monthly reported deaths of pulmonary tuberculosis in China, the total number from January 2021 to December 2021 would be about 2542, with average of 212 cases monthly. Conclusion: ARIMA model had a good short-term prediction effect and could be used to predict the number of monthly reported deaths of pulmonary tuberculosis in China; however, it was not effective in predicting long-term or year date affected by some large factors.