小区域癌症数据典型空间插值方法比较研究

doi:10.11821/dlyj020200680

摘要/Abstract

摘要：

癌症已成为危害全球居民健康的重大民生问题,选取合适的空间插值方法分析小区域癌症数据的空间特征可对区域性癌症防控工作的有效开展提供依据。本研究以湖南省苏仙区2012和2016年以村为单位的肺癌死亡率数据为研究对象,以平均误差和均方根误差为评价指标,对反距离加权（IDW）、普通克里金（OK）、趋势面分析（TSA）、多元线性回归（MLR）与协同克里金（CK）五种典型空间插值方法进行精度效果对比及参数优选,并结合不同插值方法的优缺点,确定癌症数据的最优插值方法。结果表明：插值精度方面,CK法的均方根误差最小、插值精度最高,OK、IDW（幂值=1）和MLR次之,TSA（阶数=5）最低;插值效果方面,五种插值方法的实测值和预测值均显著相关,除CK外,其它四种方法均对死亡率低估程度较大,CK和OK插值结果的空间分布效果更好。同时考虑空间因素和影响因子的CK方法是小区域苏仙区2012年、2016年肺癌死亡率最优插值方法,应用该方法可对区域性癌症防控工作的有效开展提供最优的技术支撑。本论文的研究思路也可为小区域癌症数据空间插值方法及参数优选提供参考。

关键词: 小区域, 癌症死亡率, 空间插值

Abstract:

Cancer has become a major livelihood problem endangering the health of global residents. And selecting an appropriate spatial interpolation method to analyze the spatial characteristics of cancer data in a small area can provide a basis for the effective development of regional cancer prevention and control efforts. In this study, we took the 2012 and 2016 lung cancer mortality data in Suxian District of Hunan Province as the research object, and used the average error and the root mean square error as the evaluation indicators. Five typical spatial interpolation methods, namely, inverse distance weighting (IDW), ordinary kriging (OK), trend surface analysis (TSA), multiple linear regression (MLR) and co-kriging (CK), were compared in terms of accuracy and effectiveness and parameter optimization. And then the optimal interpolation method for cancer data was determined in combination of the advantages and disadvantages of different interpolation methods. The results showed that: in terms of interpolation accuracy, the co-kriging (CK) method had the lowest root mean square error of lung cancer mortality in any year, with the interpolation accuracy being the highest, followed by ordinary kriging (OK), inverse distance weighting (IDW) (power=1) and multiple linear regression (MLR), while trend surface analysis (TSA) (order=5) had the lowest root mean square error; in terms of interpolation effect, the measured and predicted values of the five interpolation methods were significantly correlated, except for co-kriging (CK), the other four methods had a greater degree of underestimation of mortality, and the spatial distribution of co-kriging (CK) and ordinary kriging (OK) interpolation results were better. The co-kriging (CK) method, which considers both spatial factors and impact factors, is the optimal interpolation method for lung cancer mortality in 2012 and 2016 in the study area. The application of this method can provide the optimal technical support for the effective implementation of regional cancer prevention and control. This paper can also provide a great reference for the spatial interpolation method and parameter optimization of small area cancer data.

Key words: small area, cancer mortality, spatial interpolation method

王士博, 王勇. 小区域癌症数据典型空间插值方法比较研究[J]. 地理研究, 2021, 40(7): 2102-2118.

WANG Shibo, WANG Yong. Comparative research on typical spatial interpolation methods for cancer data in small regions[J]. GEOGRAPHICAL RESEARCH, 2021, 40(7): 2102-2118.

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	最大值（/10万）	最小值（/10万）	平均值（/10万）	标准差（/10万）	变异系数
2012年	274.66	3.18	35.29	30.22	0.856
2016年	252.27	11.53	34.41	25.32	0.736

影响因素	相关系数		容忍度	方差膨胀因子
影响因素	2012年	2016年	容忍度	方差膨胀因子
到河流距离	-0.194*	-0.249**	0.455	2.200
到道路距离	-0.092	-0.229*	0.450	2.220
到采矿场距离	-0.129	-0.234*	0.222	4.508
人口密度	0.025	0.249*	0.262	3.818
地区生产总值	0.352**	0.295**	0.154	6.477
高程	0.208*	-0.340*	0.110	9.111
坡度	0.127*	-0.394**	0.128	7.796
植被覆盖度	-0.164	-0.464**	0.288	3.473
年均温度	-0.138	0.470*	0.186	5.366
年均降雨	0.394**	-0.065	0.369	2.708
年均相对湿度	-0.059	-0.199**	0.118	8.504
年均相对气压	-0.297**	0.133**	0.171	5.855
PM2.5	0.126	0.272**	0.141	7.084
Cd	-0.204*	-0.208*	0.513	1.949

	插值方法	插值参数			平均误差ME	均方根误差RMSE
2012年	反距离加权插值（IDW）	幂值 = 1			0.044	0.616
		幂值 = 2			0.033	0.619
		幂值 = 3			0.028	0.617
	趋势面分析（TSA）	多项式的阶 = 3			-0.005	0.727
		多项式的阶 = 4			-0.005	0.702
		多项式的阶 = 5			0.001	0.701
		多项式的阶 = 6			0.012	0.703
	普通克里金插值（OK）	块金常数C₀	偏基台值 C	变程 Range
	球状Spherical	0.058	0.737	14506.22	0.003	0.620
	指数Exponential	0.001	0.837	18262.84	0.002	0.620
	高斯Gaussian	0.181	0.619	12601.85	0.004	0.615
2016年	反距离加权插值（IDW）	幂值 = 1			0.001	0.800
		幂值 = 2			0.021	0.807
		幂值 = 3			0.044	0.851
	趋势面分析（TSA）	多项式的阶 = 3			-0.004	0.946
		多项式的阶 = 4			-0.004	0.962
		多项式的阶 = 5			0.005	0.886
		多项式的阶 = 6			-0.020	0.988
	普通克里金插值（OK）	块金常数C₀	偏基台值 C	变程 Range
	球状Spherical	0.016	1.160	10321.07	-0.009	0.813
	指数Exponential	0.010	1.240	13383.30	-0.007	0.803
	高斯Gaussian	0.244	0.954	9386.33	-0.001	0.826

	影响因素	参数估计	t	p
2012年	截距	383.236	6.839	0.000
	到河流距离	-0.410	-4.422	0.000
	高程	-0.425	-2.524	0.013
	坡度	0.321	1.934	0.050
	人口密度	-0.293	-2.441	0.016
	地区生产总值	0.216	1.466	0.014
	年均相对气压	-1.122	-7.851	0.000
	年均温度	-0.281	-2.199	0.030
	到矿区距离	0.371	2.848	0.005
	植被覆盖度	-0.260	-2.260	0.026
	年均相对湿度	0.580	3.438	0.001
2016年	截距	-97.284	-3.028	0.003
	到道路距离	0.164	1.558	0.022
	高程	-0.401	-2.867	0.005
	地区生产总值	0.195	2.065	0.041
	到矿区距离	-0.339	-3.445	0.001
	年均相对湿度	0.596	2.333	0.021
	年均温度	1.157	3.528	0.001
	年均降雨	0.692	3.600	0.000
	Cd	-0.395	-1.997	0.048

	类别	第一主成分	第二主成分	第三主成分	第四主成分	第五主成分	第六主成分	第七主成分
2012年	特征值	4.73600	2.22700	1.28400	0.61000	0.27300	0.11200	0.07300
	贡献度	0.57326	0.27054	0.07629	0.02934	0.02093	0.01745	0.01219
	累计贡献度	0.57326	0.84380	0.92009	0.94943	0.97036	0.98781	1
2016年	特征值	2.96600	1.87900	0.73000	0.66200	0.29200	0.15700	0.07000
	贡献度	0.57494	0.29225	0.07082	0.03242	0.01746	0.00783	0.00399
	累计贡献度	0.57494	0.86749	0.93831	0.97072	0.98818	0.99601	1