Objective To construct and compare various combined forecasting models for health human resources based on personnel number in Anhui Province's healthcare institutions, to explore strategies for developing the optimal combined forecasting model.

Methods Data on the personnel number in healthcare institutions in Anhui Province from 1988 to 2022 was obtained from the Anhui Statistical Yearbook. All possible combined models were constructed using the Holt model, ARIMA model, NNAR model, GM (1,1) , and random forest model. The personnel number in Anhui Province's healthcare institutions from 2018 to 2022 was predicted. The optimal combined model was selected by comparing 3 error metrics of mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).

Results The combined model of the GM(1,1) and random forest achieved the lowest prediction error among all combined models, with MSE, MAE and MAPE values were 146,101,146, 10,587.465 and 2.267, which was the optimal combined forecasting model.

Conclusion A certain number of individual models are initially selected, and all possible combinations are generated. These combined models are then evaluated using error metrics to effectively identify the one with the smallest prediction error. This strategy can scientifically and rationally screen various models, ultimately yielding the optimal combined forecasting model.

1. 张瑜洁, 王健, 王辛, 等. 基于文献计量法的卫生人力预测模型研究现状分析[J]. 中国医院, 2022, 26(2): 43-46.ZhangYJ, WangJ, WangX, et al. Analysis of research status of health workforce prediction model based on bibliometric method[J]. Chinese Hospitals, 2022, 26(2): 43-46.

2. 李慧超, 谢学勤, 邓小虹. 北京市医疗机构卫生专业技术人员需求预测——基于人力人口比值法[J]. 中国卫生政策研究, 2013, 6(4): 56-59.LiHC, XieXQ, DengXH. Forecasting of health professionals in Beijing medical institutions: using a human population ratio method[J]. Chinese Journal of Health Policy, 2013, 6(4): 56-59.

3. 吕邦亮, 汤质如, 彭婧, 等. 基于灰色GM(1,1)模型的安徽省“十四五”期间医疗卫生资源配置预测研究[J]. 卫生软科学, 2024, 38(1): 52-57.LyuBL, TangZR, PengJ, et al. Prediction of medical and health resources allocation in Anhui Province during the 14th Five⁃Year Plan period based on grey GM(1,1) model[J]. Soft Science of Health, 2024, 38(1): 52-57.

4. 林志添, 张健明, 丁海峰. 基于ARIMA模型的我国长三角地区卫生人力资源需求预测分析[J]. 中国医疗管理科学, 2021, 11(3): 5-11. doi：10.3969/j.issn.2095-7432.2021.03.002LinZT, ZhangJM, DingHF. Predictive analysis of healthcare human resources demand in the Yangtze River Delta Region based on the ARIMA model[J]. Chinese Journal of Medical Management Sciences, 2021,11(3): 5-11. doi：10.3969/j.issn.2095-7432.2021.03.002

5. 石丛, 王健. 基于BP神经网络和时间序列的我国卫生人力资源研究[J]. 中国初级卫生保健, 2013, 27(11): 22-24.ShiC, WangJ. Study of health human resource in China based on the model of BP-ANN and Arima[J]. Chinese Primary Health Care, 2013, 27(11): 22-24.

6. 谢俏丽. 基于组合预测模型的湖北省卫生人力资源需求预测研究[D]. 武汉:华中科技大学, 2016.XieQL. Research on the demand forecast of health human resources in Hubei province based on combination forecasting model[D]. Wuhan: Huazhong University of Science and Technology, 2016.

7. 朱泉同, 高山. 基于组合预测模型的江苏省卫生人力资源需求预测探讨[J]. 中国卫生统计, 2020, 37(6): 862-865. doi：10.3969/j.issn.1002-3674.2020.06.016ZhuQT, GaoS. Discussion on the forecast of health human resource demand in Jiangsu province based on combination forecasting model[J]. Chinese Journal of Health Statistics, 2020, 37(6): 862-865. doi：10.3969/j.issn.1002-3674.2020.06.016

8. 侯雅楠, 王丹, 陈芸, 等. 山东省卫生人力资源组合预测模型构建及应用[J]. 卫生软科学, 2021, 35(4): 72-75, 79. doi：10.3969/j.issn.1003-2800.2021.04.017HouYN, WangD, ChenY, et al. Construction and application of combination forecasting model of health human resources in Shandong province[J]. Soft Science of Health, 2021, 35(4): 72-75, 79. doi：10.3969/j.issn.1003-2800.2021.04.017

9. 徐瑞璞, 钱国宏, 路杰, 等. 基于组合模型预测短期甘肃省医护人才需求[J]. 中国卫生统计, 2024, 41(2): 287-290. doi：10.11783/j.issn.1002-3674.2024.02.030XuRP, QianGH, LuJ, et al. Predicting short-term demand for medical and nursing talents in Gansu province based on a combined model[J]. Chinese Journal of Health Statistics, 2024, 41(2): 287-290. doi：10.11783/j.issn.1002-3674.2024.02.030

10. 黄锐. 基于最优加权组合模型的重庆市卫生人力资源需求预测研究[D]. 重庆: 重庆医科大学, 2022.HuangR. Research on the forecast of health human resource demand in Chongqing based on the optimal weighted combination model[D]. Chongqing: Chongqing Medical University, 2022.

11. 苗开超. 基于指数平滑模型的农产品价格预测研究[D]. 合肥: 合肥工业大学, 2009.MiaoKC. Research on agricultural product price forecasting based on exponential smoothing model[D]. Hefei: Hefei University of Technology, 2009.

12. 李志超, 刘升. 基于ARIMA模型、灰色模型和回归模型的预测比较[J]. 统计与决策, 2019, 35(23): 38-41.LiZC, LiuS. Prediction comparison based on ARIMA model, grey model, and regression model[J]. Statistics & Decision, 2019, 35(23): 38-41.

13. 张欣, 刘振球, 袁黄波, 等. 神经网络自回归模型在丙肝发病趋势和预测研究中的应用[J]. 中国卫生统计, 2020, 37(4): 524-526.ZhangX, LiuZQ, YuanHB, et al. Application of neural network autoregressive model in the study of hepatitis C incidence trend and prediction[J]. Chinese Journal of Health Statistics, 2020, 37(4): 524-526.

14. 陈嘉琳. 基于灰色GM(1,1)模型的广东省卫生总费用预测分析[J]. 中国医疗管理科学, 2021, 11(5): 5-11.ChenJL. Prediction of total expenditure on health in Guangdong province based on grey GM (1,1) model[J]. Chinese Journal of Medical Management Sciences, 2021, 11(5): 5-11.

15. 毕慧, 马丹华, 许桂丽, 等. 基于年龄-时期-队列模型的中国物质使用障碍疾病负担及预测研究[J]. 药物流行病学杂志, 2024, 33(7):760-769.BiH, MaDH, XuGL, et al. Study on the disease burden and prediction of substance use disorder in China based on age-period-cohort model[J]. Chinese Journal of Pharmacoepidemiology, 2024, 33(7):760-769.

16. 李欣海. 随机森林模型在分类与回归分析中的应用[J]. 应用昆虫学报, 2013, 50(4): 1190-1197. doi：10.7679/j.issn.2095-1353.2013.163LiXH. Using "random forest" for classification and regression[J]. Chinese Journal of Applied Entomology, 2013, 50(4): 1190-1197. doi：10.7679/j.issn.2095-1353.2013.163

17. 林小龙, 张杰, 林伟. 2022—2026年我国鼻咽癌发病率与死亡率的预测: 基于GM(1,1)和ARIMA模型[J]. 医学新知, 2025, 35(9): 1017-1023.LinXL, ZhangJ, LinW. Prediction of incidence and mortality rates of nasopharyngeal carcinoma in China from 2022 to 2026: based on GM(1,1) and ARIMA models[J]. Yixue Xinzhi Zazhi, 2025, 35(9): 1017-1023.

18. 吴国平, 袁有树, 王志伟. 河南省中医类医院卫生人力资源需求预测组合模型的构建[J]. 郑州大学学报(医学版), 2025, 60(6): 808-812.WuGP, YuanYS, WangZW. Construction of a combination model for predicting human resource demand in traditional Chinese medicine hospitals in Henan Province[J]. Journal of Zhengzhou University (Medical Sciences), 2025, 60(6): 808-812.

19. 刘吉莉, 王凤美, 刘阳, 等. 基于机器学习方法构建幽门螺杆菌感染的风险预测模型[J]. 药学前沿, 2025, 29(2): 265-276.LiuJL, WangFM, LiuY, et al. Construction of the risk prediction model of Helicobacter pylori infection based on machine learning method[J]. Frontiers in Pharmaceutical Sciences, 2025, 29(2): 265-276.

20. 刘鸿宇, 孙玉凤, 王健. 卫生人力资源需求预测研究进展、问题探讨及展望[J]. 中国卫生事业管理, 2016, 33(11): 828-830, 860.LiuHY, SunYF, WangJ. Progress, problems and trend of projection of HRH demand research[J]. Chinese Health Service Management, 2016, 33(11): 828-830, 860.