基于ARIMA模型的II型糖尿病患者数的建模与预测

Modeling and Prediction of the Number of Patients with Type II Diabetes Mellitus Based on ARIMA Model

摘要: 目的：分析全国糖尿病疫情的时间分布特征，建立中国近年糖尿病时间序列分析的自回归移动平均模型(ARIMA)，预测病情未来发展趋势，为公众身体健康提出科学依据。方法：收集中国2000~2013年各年糖尿病患病人数数据，用R3.4.3软件构建ARIMA预测模型，对建立的模型进行参数估计、模型诊断，选择最优预测模型。利用构建的最佳模型对中国2014~2018各年糖尿病患病人数进行预测，并对预测效果进行评价。结果：ARIMA(1,1,0)模型为中国近年糖尿病人数的最优预测模型，其AIC、BIC的值分别为−38.93735、−37.80745，模型残差序列的Ljung-Box统计量，p值为0.4135，提示残差为白噪声序列，模型拟合良好。中国2014~2018糖尿病患病人数实际值与预测值的平均相对误差为2.27%，实际值均在预测值95%可信区间内。结论：ARIMA(1,1,0)模型能较好地模拟中国近年糖尿病患病人数的变化趋势，具有良好的预测效果。

Abstract: Objective: To analyze the time distribution characteristics of diabetes in China, and to establish the autoregressive moving average model (ARIMA) for diabetes time series analysis in China in recent years, so as to predict the development trend of diabetes in the future and provide scientific basis for public health. Methods: The data of diabetes mellitus in China from 2000 to 2013 were collected and ARIMA prediction model was constructed by R3.4.3 software. The parameters of the model were estimated, the model was diagnosed, and the optimal prediction model was selected. The optimal model was used to predict the number of diabetic patients in China from 2014 to 2018, and the prediction effect was evaluated. Results: ARIMA (1,1,0) model was the best prediction model for the number of diabetes mellitus in China in recent years. The AIC and BIC values of ARIMA (1,1,0) were −38.93735 and −37.80745, respectively. Ljung box statistic of model residual sequence , p value was 0.4135, indicating that the residual was white noise sequence, and the model fitted well. The average relative error between the actual value and the predicted value was 2.27%, and the actual value was within the 95% confidence interval of the predicted value. Conclusion: ARIMA (1, 1, 0) model can simulate the trend of diabetes mellitus in China in recent years, and has good prediction effect.