三种模型应用于中国2011—2020年梅毒发病趋势分析的比较

竺晓霞; 陈靓; 李秀央

doi:10.16462/j.cnki.zhjbkz.2022.06.003

三种模型应用于中国2011—2020年梅毒发病趋势分析的比较

doi: 10.16462/j.cnki.zhjbkz.2022.06.003

310009 杭州，浙江大学医学院附属第二医院临床大数据与统计中心，浙江大学流行病与卫生统计学科系

基金项目:

浙江省科技厅软科学重点项目 2022C25040

详细信息

通讯作者:
李秀央, E-mail: lixiuyang@zju.edu.cn

中图分类号: R181;R183
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- 被引次数: 0
出版历程
- 收稿日期: 2021-11-07
- 修回日期: 2022-02-14
- 网络出版日期: 2022-06-16
- 刊出日期: 2022-06-10

A comparative study of three models for syphilis incidence trend analysis in China from 2011 to 2020

Center for Clinical Big Data & Statistics Second Affiliated Hospital, Zhejiang University, College of Medicine, Department of Epidemiology & Bistatistics, Zhejiang University, Hangzhou 310009, China

Funds:

Soft Science Key Project of the Science and Technology Department of Zhejiang Province 2022C25040

More Information

Corresponding author: LI Xiu-yang, E-mail: lixiuyang@zju.edu.cn

摘要

摘要: 目的比较差分自回归移动平均(autoregressive integrated moving average model, ARIMA)模型、非线性自回归神经网络(nonlinear autoregressive neural network, NAR)模型和长短期记忆神经网络(long-short term memory neural network, LSTM)模型应用于梅毒报告发病预测的效果, 优化疫情预测模型。方法以中国31个省、自治区、直辖市(未包含中国台湾、香港和澳门)2011-2019年梅毒月报告发病率为拟合集, 建立ARIMA模型、NAR模型和LSTM模型, 比较3种模型的拟合效果。以2020年梅毒月报告发病率为预测集, 比较3种模型的预测效果。结果 ARIMA模型、NAR模型和LSTM模型拟合所得的平均绝对误差(mean absolute deviation, MAD)分别为0.013、0.011和0.002, 均方根误差(root mean squared error, RMSE)分别为0.015、0.018和0.003, 平均绝对百分比误差(mean absolute percentage error, MAPE)分别为4.266%、3.810%和0.692%;预测所得的MAD分别为0.064、0.049和0.044, RMSE分别为0.069、0.068和0.060, MAPE分别为23.310%、17.629%和18.575%。结论 LSTM模型拟合预测梅毒报告发病率的效果更好, 为梅毒疫情的防控提供数据支撑。
- 梅毒 /
- ARIMA模型 /
- NAR模型 /
- LSTM模型 /
- 预测
Abstract: Objective This study was aimed to compare the effects of the autoregressive integrated moving average (ARIMA) model, nonlinear autoregressive neural network (NAR) model and long-short term memory neural network (LSTM) model applied to predict the reported incidence of syphilis to optimize the epidemic prediction model. Methods Based on the fitting dataset of the monthly reported incidence of syphilis in 31 provinces, autonomous regions and municipalities (excluding Taiwan, Hong Kong and Macao) in China from 2011 to 2019, the ARIMA model, NAR model and LSTM model were established to compare the fitting effects of these models. Data on the incidence of syphilis in 2020 was used to compare the prediction effects of these models. Results The mean absolute deviations (MAD) of the ARIMA model, NAR model and LSTM model fitting effect were 0.013, 0.011 and 0.002, respectively. The root mean squared errors (RMSE) were 0.015, 0.018 and 0.003, respectively. The mean absolute percentage errors (MAPE) were 4.266%, 3.810% and 0.692%, respectively. The MADs of the forecasting effect were 0.064, 0.049 and 0.044, the RMSEs were 0.069, 0.068 and 0.060 and the MAPEs were 23.310%, 17.629% and 18.575%, respectively. Conclusions The LSTM model has better fitting and forecasting effects than the ARIMA and NAR models in predicting the reported incidence of syphilis, which could provide data support for the prevention and control of syphilis.
- Syphilis /
- ARIMA model /
- NAR model /
- LSTM model /
- Predicting

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图 1 梅毒月报告发病率描述性分析(A：趋势图；B：热图)

Figure 1. Descriptive analysis of monthly reported incidence of syphilis (A: Trend chart; B: Heat map)

下载: 全尺寸图片幻灯片

图 2 差分后序列和残差序列的自相关图和偏自相关图

注：A：差分后序列；B：残差序列。

Figure 2. ACF and PACF of the differential sequence and residual sequence

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图 3 NAR模型残差序列自相关图和偏自相关图

注：A：自相关图；B：偏自相关图。

Figure 3. ACF and PACF of the residual sequence of NAR model

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图 4 ARIMA模型、NAR模型和LSTM模型的拟合和预测效果

注：A：ARIMA模型拟合；B：NAR模型拟合; C：LSTM模型拟合；D：三种模型预测。

Figure 4. Fitting and prediction effects of ARIMA, NAR and LSTM models

下载: 全尺寸图片幻灯片

表 1 ARIMA模型参数估计和拟合优度的结果

Table 1. Parameter estimation and goodness of fitting of ARIMA model

模型参数	β值	s_x值	t值	P值
AR(1)	-0.702	0.116	-6.042	＜0.001
AR(2)	-0.465	0.134	-3.482	0.001
MA(1)	-0.838	0.085	-9.823	＜0.001
SAR(1)	-0.286	0.090	-3.185	0.002
SAR(2)	-0.614	0.146	-4.208	＜0.001

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表 2 ARIMA模型的拟合效果

Table 2. The fitting effects of the ARIMA models

ARIMA模型	R²值	AIC	ARIMA模型	R²值	AIC
(0, 1, 1)(0, 1, 0)₁₂	0.614	-1.866	(2, 1, 1)(1, 1, 0)₁₂	0.819	-2.504
(1, 1, 1)(0, 1, 0)₁₂	0.656	-1.990	(3, 1, 1)(1, 1, 0)₁₂	0.819	-2.487
(2, 1, 1)(0, 1, 0)₁₂	0.685	-2.052	(0, 1, 1)(2, 1, 0)₁₂	0.772	-2.285
(3, 1, 1)(0, 1, 0)₁₂	0.693	-2.058	(1, 1, 1)(2, 1, 0)₁₂	0.798	-2.399
(0, 1, 1)(1, 1, 0)₁₂	0.768	-2.274	(2, 1, 1)(2, 1, 0)₁₂	0.829	-2.531
(1, 1, 1)(1, 1, 0)₁₂	0.790	-2.388	(3, 1, 1)(2, 1, 0)₁₂	0.829	-2.511

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表 3 ARIMA模型的拟合效果

Table 3. The fitting effects of the ARIMA models

模型	拟合集			预测集
模型	MAD	RMSE	MAPE(%)	MAD	RMSE	MAPE(%)
ARIMA	0.013	0.015	4.266	0.064	0.069	23.310
NAR	0.011	0.018	3.810	0.049	0.068	17.629
LSTM	0.002	0.003	0.692	0.044	0.060	18.575

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表 4 ARIMA、NAR和LSTM模型的预测效果对比

Table 4. Comparison of the prediction effects of the ARIMA, NAR and LSTM models

月份	发病率	ARIMA模型		NAR模型		LSTM模型
月份	发病率	预测值	相对误差率	预测值	相对误差率	预测值	相对误差率
2020年1月	0.283	0.349	0.232	0.352	0.243	0.335	0.184
2020年2月	0.153	0.264	0.727	0.225	0.470	0.320	1.090
2020年3月	0.293	0.402	0.371	0.472	0.609	0.307	0.047
2020年4月	0.333	0.379	0.137	0.351	0.055	0.279	0.163
2020年5月	0.333	0.403	0.210	0.364	0.093	0.316	0.050
2020年6月	0.331	0.371	0.120	0.312	0.057	0.358	0.080
2020年7月	0.358	0.411	0.148	0.451	0.260	0.355	0.008
2020年8月	0.333	0.410	0.231	0.298	0.105	0.348	0.044
2020年9月	0.348	0.389	0.119	0.364	0.046	0.371	0.067
2020年10月	0.315	0.377	0.195	0.354	0.123	0.366	0.161
2020年11月	0.321	0.381	0.186	0.335	0.044	0.377	0.174
2020年12月	0.317	0.355	0.121	0.320	0.011	0.367	0.160

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