LMS方法及其在流量数据中的应用
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摘要
LMS模型是分析生长发育最常用的方法之一。本文详细阐述了LMS模型的构造原理;基于流量数据提出了费希尔信息矩阵与惩罚贝叶斯后验对数似然算法两种模型算法;利用中国健康营养调查(CHNS)1989-2011年中9年的流量数据,以所提出的LMS曲线算法为基础,通过计算BMI(Body Mass Index)绘制生长发育曲线研究我国青少年儿童生长发育情况和中年人健康问题。研究结果表明:1989-2011年间,我国0～18岁年龄段青少年儿童BMI中位数提高5%左右,生长发育高峰期有提前趋势;中年人群BMI中位数提高了10%左右,2000年后55周岁以上中年人体质差异有增大趋势。
The LMS model is one of the most commonly used methods for the growth pattern analysis. The structure principle of LMS model is described in detail and two model algorithms are proposed based on the Streaming Data. The Fisher Information Matrix and the Penalzied Bayesian Posterior Likelihood algorithm are proposed respectively by applying 9 years' streaming data from 1989 to 2011 from Chinese Health Nutrition Survey(CHNS). Based on the proposed LMS curve algorithm, we calculate Body Mass Index(BMI) to draw the growth pattern curve to study the growth and development of children and adolescents and the health problems of middle-aged people in China. The results show that in the 20 years around the 21st century, the median BMI of adolescents and children aged 0-18 in China has increased by about 5%.There is an advance trend in the peak period of growth and development. The median BMI of middle-aged people has increased by 10 % approximately, and the difference of body constitution among middle-aged people over 55 years old tends to increase after 2000.
The LMS model is one of the most commonly used methods for the growth pattern analysis. The structure principle of LMS model is described in detail and two model algorithms are proposed based on the Streaming Data. The Fisher Information Matrix and the Penalzied Bayesian Posterior Likelihood algorithm are proposed respectively by applying 9 years' streaming data from 1989 to 2011 from Chinese Health Nutrition Survey(CHNS). Based on the proposed LMS curve algorithm, we calculate Body Mass Index(BMI) to draw the growth pattern curve to study the growth and development of children and adolescents and the health problems of middle-aged people in China. The results show that in the 20 years around the 21st century, the median BMI of adolescents and children aged 0-18 in China has increased by about 5%.There is an advance trend in the peak period of growth and development. The median BMI of middle-aged people has increased by 10 % approximately, and the difference of body constitution among middle-aged people over 55 years old tends to increase after 2000.
引文
[1]WHO Expert Consultation.Appropriate Body-mass Index for Asian Populations and Its Implications for Policy and Intervention Strategies[J].The Lancet,2004 (363):157-163.
[2]A A Hedley,et al.Prevalence of Overweight and Obesity Among US Children,Adolescents,and Adults,1999-2002[J].Jama,2004 (23):28-47.
[3]钱绍中.世界卫生组织 (WHO) 0～18 岁儿童身高体重参考值及评价标准[M].北京:原子能出版社,1999:12-19.
[4]李磊,胡博,郑妍妍.肥胖会传染吗?[J].经济学(季刊),2016 (2):429-452.
[5]李婷,张闫龙.出生队列效应下老年人健康指标的生长曲线及其城乡差异[J].人口研究,2014 (2):18-35.
[6]H Wang,et al.Trends in the Distribution of Body Mass Index among Chinese Adults,Aged 20～45 Years (1989-2000) [J].International Journal of Obesity,2007 (2):272-278.
[7]K M Flegal,T J Cole.Construction of LMS Parameters for the Centers for Disease Control and Prevention 2000 Growth Charts[J].National Health Statistics Reports,2013 (63):1-3.
[8]T J Cole,et al.Age- and Size-related Reference Ranges:a Case Study of Spirometry through Childhood and Adulthood[J].Statistics in Medicine,2009 (5):880-898.
[9]T J Cole,P J Green.Smoothing Reference Centile Curves:the LMS Method and Penalized Likelihood[J].Statistics in Medicine,1992 (10):1305-1319.
[10]G E P Box,D R Cox.An Analysis of Transformations[J].Journal of the Royal Statistical Society,1964 (2):211-252.
[11]A Indrayan.Demystifying LMS and BCPE Methods of Centile Estimation for Growth and other Health Parameters[J].Indian pediatrics,2014 (1):37-43.
[12]R A Rigby,D M Stasinopoulos.Generalized Additive Models for Location,Scale and Shape[J].Journal of the Royal Statistical Society:Series C (Applied Statistics),2005 (3):507-554.
[13]I J Good,R A Gaskins.Nonparametric Roughness Penalties for Probability Densities[J].Biometrika,1971 (2):25-277.
[14]刘静,欧阳资生,吴喜之.广义部分线性单指数模型的惩罚样条估计[J].统计研究,2009 (8):102-112.
[15]P J Green,B W Silverman.Nonparametric Regression and Generalized Linear Models:A Roughness Penalty Approach [M].London:Chapman & Hall,1994:342-343.
[16]Todd,John.Survey of Numerical Analysis [M].New York:McGraw-Hill,1962:36-50.
[17]贺媛,曾强,赵小兰.中国成人体质指数、年龄与血压水平相关性分析[J].中国公共卫生,2016 (1):69-72.
(1)中国健康与营养调查(China Health and Nutrition Survey,CHNS)是由美国北卡罗来纳大学人口发展研究中心与中国预防科学医学院联合举行的大规模社会健康调查,调查范围涉及我国黑龙江、辽宁、山东、河南、山西、湖北、湖南、江苏、浙江、贵州、云南、广西等15个省份,约7200户家庭,超过30000个个体。
(2)LMS模型来自希腊字母Lambda(λ)、Mu(μ)和Sigma(σ)的第一个字母简写得到,具体形式见下文。
(3)中国成人超重和肥胖症预防与控制指南建议,男性WC值大于85cm、女性WC值大于80cm是肥胖的标准,高于此标准需要减肥。
(4)BMI=体重(KG)/身高2(m)。国际生命科学学会中国办事处中国肥胖问题工作组提出对中国成人判断超重和肥胖程度的界限值为:BMI值在24.0～27.9之间为超重,大于等于28为肥胖。
(5)体脂率(体脂百分比)是身体脂肪含量占体重的百分比,用F%表示。
(6)Box-Cox变换下可以使参数估计量同时满足线性性、独立性、方差齐性以及正态性,又不丢失原始数据的信息。
(7)大规模流量数据(数据量过大)容易造成估计过程中运算量太大,甚至无法得到正确的估计参数,还可能造成样本相关性等其他问题。
(8)该条件依据Green 和Silverman(1994)[15]书中定理2.1得到。
(9)符号“?”表示左右两边近似相等。
(10)由于篇幅所限,证明过程见《统计研究》网站所列附件。
(11)世界卫生组织将青少年期确定为年龄在10～19岁之间,而本文的研究对象是针对0～18岁的青少年儿童,研究对象的确立符合我国居民大众对于青少年儿童年龄范围的普遍认知,适用范围更广。
(12)由于Box-Cox变换不改变数据的任何数值特征,为简化,本文此后实际数据分析说明中用BMI代替变换后的BMI数值。
(13)资料来源:世界卫生组织,肥胖和超重实况报告(第311号),详见网址https://www.who.int/countries/chn/en/。
(14)中位数相对稳健,不受离群点以及异常点的影响,可以从一定程度上说明平均值不能解释的问题。
[2]A A Hedley,et al.Prevalence of Overweight and Obesity Among US Children,Adolescents,and Adults,1999-2002[J].Jama,2004 (23):28-47.
[3]钱绍中.世界卫生组织 (WHO) 0～18 岁儿童身高体重参考值及评价标准[M].北京:原子能出版社,1999:12-19.
[4]李磊,胡博,郑妍妍.肥胖会传染吗?[J].经济学(季刊),2016 (2):429-452.
[5]李婷,张闫龙.出生队列效应下老年人健康指标的生长曲线及其城乡差异[J].人口研究,2014 (2):18-35.
[6]H Wang,et al.Trends in the Distribution of Body Mass Index among Chinese Adults,Aged 20～45 Years (1989-2000) [J].International Journal of Obesity,2007 (2):272-278.
[7]K M Flegal,T J Cole.Construction of LMS Parameters for the Centers for Disease Control and Prevention 2000 Growth Charts[J].National Health Statistics Reports,2013 (63):1-3.
[8]T J Cole,et al.Age- and Size-related Reference Ranges:a Case Study of Spirometry through Childhood and Adulthood[J].Statistics in Medicine,2009 (5):880-898.
[9]T J Cole,P J Green.Smoothing Reference Centile Curves:the LMS Method and Penalized Likelihood[J].Statistics in Medicine,1992 (10):1305-1319.
[10]G E P Box,D R Cox.An Analysis of Transformations[J].Journal of the Royal Statistical Society,1964 (2):211-252.
[11]A Indrayan.Demystifying LMS and BCPE Methods of Centile Estimation for Growth and other Health Parameters[J].Indian pediatrics,2014 (1):37-43.
[12]R A Rigby,D M Stasinopoulos.Generalized Additive Models for Location,Scale and Shape[J].Journal of the Royal Statistical Society:Series C (Applied Statistics),2005 (3):507-554.
[13]I J Good,R A Gaskins.Nonparametric Roughness Penalties for Probability Densities[J].Biometrika,1971 (2):25-277.
[14]刘静,欧阳资生,吴喜之.广义部分线性单指数模型的惩罚样条估计[J].统计研究,2009 (8):102-112.
[15]P J Green,B W Silverman.Nonparametric Regression and Generalized Linear Models:A Roughness Penalty Approach [M].London:Chapman & Hall,1994:342-343.
[16]Todd,John.Survey of Numerical Analysis [M].New York:McGraw-Hill,1962:36-50.
[17]贺媛,曾强,赵小兰.中国成人体质指数、年龄与血压水平相关性分析[J].中国公共卫生,2016 (1):69-72.
(1)中国健康与营养调查(China Health and Nutrition Survey,CHNS)是由美国北卡罗来纳大学人口发展研究中心与中国预防科学医学院联合举行的大规模社会健康调查,调查范围涉及我国黑龙江、辽宁、山东、河南、山西、湖北、湖南、江苏、浙江、贵州、云南、广西等15个省份,约7200户家庭,超过30000个个体。
(2)LMS模型来自希腊字母Lambda(λ)、Mu(μ)和Sigma(σ)的第一个字母简写得到,具体形式见下文。
(3)中国成人超重和肥胖症预防与控制指南建议,男性WC值大于85cm、女性WC值大于80cm是肥胖的标准,高于此标准需要减肥。
(4)BMI=体重(KG)/身高2(m)。国际生命科学学会中国办事处中国肥胖问题工作组提出对中国成人判断超重和肥胖程度的界限值为:BMI值在24.0～27.9之间为超重,大于等于28为肥胖。
(5)体脂率(体脂百分比)是身体脂肪含量占体重的百分比,用F%表示。
(6)Box-Cox变换下可以使参数估计量同时满足线性性、独立性、方差齐性以及正态性,又不丢失原始数据的信息。
(7)大规模流量数据(数据量过大)容易造成估计过程中运算量太大,甚至无法得到正确的估计参数,还可能造成样本相关性等其他问题。
(8)该条件依据Green 和Silverman(1994)[15]书中定理2.1得到。
(9)符号“?”表示左右两边近似相等。
(10)由于篇幅所限,证明过程见《统计研究》网站所列附件。
(11)世界卫生组织将青少年期确定为年龄在10～19岁之间,而本文的研究对象是针对0～18岁的青少年儿童,研究对象的确立符合我国居民大众对于青少年儿童年龄范围的普遍认知,适用范围更广。
(12)由于Box-Cox变换不改变数据的任何数值特征,为简化,本文此后实际数据分析说明中用BMI代替变换后的BMI数值。
(13)资料来源:世界卫生组织,肥胖和超重实况报告(第311号),详见网址https://www.who.int/countries/chn/en/。
(14)中位数相对稳健,不受离群点以及异常点的影响,可以从一定程度上说明平均值不能解释的问题。