文章信息
- 陈沛竹, 侯旭宏, 贾伟平.
- Chen Peizhu, Hou Xuhong, Jia Weiping.
- 探寻肥胖切点的方法在糖尿病筛查/诊断中的应用
- The methods of exploring obesity cutoffs for screening/diagnosing diabetes
- 中华流行病学杂志, 2016, 37(4): 582-586
- Chinese Journal of Epidemiology, 2016, 37(4): 582-586
- http://dx.doi.org/10.3760/cma.j.issn.0254-6450.2016.04.029
-
文章历史
- 收稿日期: 2015-12-17
根据2014年国际糖尿病联盟(IDF)的数据估计,全球20~79岁成年人糖尿病的患病率为8.3%(约3.82亿糖尿病患者),我国糖尿病患病人数接近1亿,居世界首位[1]。BMI和腰围作为简易有效的体脂参数对糖尿病有良好的筛查价值[2, 3, 4, 5, 6],并被多个组织推荐在临床和人群干预研究中使用。
合适的肥胖切点有助于发现糖尿病及其高危人群,是实施肥胖干预的依据。目前的肥胖切点多建立在对欧美地区人群研究的基础上[7, 8],由于遗传、环境和体脂分布的差异,在相同BMI或腰围情况下,亚洲人具有较多的体脂和内脏脂肪组织[9]。有研究显示在任一相同的BMI或腰围水平下,亚洲人的糖尿病患病率始终高于白种人[10]。因此研究者建议对不同种族采用不同的BMI和腰围切点。本文对寻找人群BMI和腰围切点的不同方法研究应用现状进行综述,以期了解不同人群糖尿病筛查或诊断的肥胖切点、明确不同方法判定切点的意义。
目前肥胖切点的制定多使用受试者工作特征曲线(receiver operating characteristic curve,ROC曲线),其他方法还有限制性立方样条(restricted cubic splines)和分式多项式模型(fractional polynomial model)。后两种方法都可以较好地拟合自变量与因变量的非线性关系,但目前在国内外尚未被广泛使用,其应用尚待推广。
1. ROC曲线:
(1)方法介绍:ROC曲线是目前国内外寻找诊断切点最常见的有效方法。当检测结果为定量资料或等级资料时,以不同检测值作为判定阳性、阴性结果的阈值(切点),分别计算出其对应的灵敏度和特异度,以灵敏度为纵坐标,以1-特异度为横坐标,绘制ROC曲线[11]。根据曲线下面积(AUC)来评价某种方法筛查某个疾病的价值大小,AUC越大,越接近1.0,诊断的准确性越高。常用的切点选择标准:①最大约登指数,即(灵敏度+特异度-1)最大值所对应的点。约登指数表示筛检方法发现真正的患者与非患者的总能力,指数越大,其准确性越高。②ROC曲线上最接近纵轴(0,1)点的对应点,即的最小值。③灵敏度和特异度相等时所对应的点。
(2)ROC曲线选择的BMI和腰围切点:横断面研究显示[12, 13, 14],欧美地区男性糖尿病诊断的BMI切点范围:男性为27.0~29.5 kg/m2、女性为25.0~30.0 kg/m2;腰围切点范围:男性为97.0~105.8 cm、女性为85.0~95.9 cm。一项对6 923名未患糖尿病的英国人开展的前瞻性研究显示,英国人的BMI切点范围:男性为28.0~29.0 kg/m2、女性为29.0~30.0 kg/m2;腰围切点:男性为100.0 cm、女性为92.0 cm[15]。而现有数据普遍显示亚洲人的BMI和腰围切点显著低于白种人[16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38](表 1)。一项针对155 122人的Meta分析得出亚洲人和白种人男性筛查糖尿病的BMI切点分别为23.7和27.7 kg/m2、女性分别为24.5和27.9 kg/m2,白种人男性和女性的BMI切点比亚洲人分别高出4.0和3.4 kg/m2;在该Meta分析中,男性腰围切点分别为85和99 cm、女性分别为80和85 cm,白种人男性和女性的腰围切点比亚洲人分别高出约14和5 cm[10]。而在亚洲人中,南亚人(如印度、孟加拉国等)的切点较低[32, 33]。
中国肥胖问题工作组在2002年就提出BMI≥24 和28 kg/m2分别为中国成年人超重和肥胖的界限;男性腰围≥85 cm、女性腰围≥80 cm为腹部脂肪蓄积的界限[39]。然而目前国内外针对华人BMI和腰围界限的规定尚未统一。WHO提出BMI≥25 kg/m2为超重,≥30 kg/m2为肥胖[40];IDF提出中国人中心性肥胖的诊断标准为男性腰围≥90 cm,女性腰围≥80 cm[41]。而《中国成年人血脂异常防治指南》制订联合委员会提出BMI≥24和28 kg/m2为超重和肥胖;男性腰围≥90 cm、女性腰围≥85 cm为我国成年人中心性肥胖标准[42]。近几年多个国内研究显示,我国男性和女性筛查糖尿病的BMI切点多介于24.0~26.0 kg/m2和23.3~24.5 kg/m2间;腰围切点多介于80.0~91.0 cm和77.8~85.0 cm间[16, 17, 18, 19, 20, 21]。我国台湾地区的研究显示,BMI切点:男性为25.5 kg/m2、女性为22.3~23.2 kg/m2;腰围切点:男性为86.0 cm、女性为74.7~83.0 cm[22, 23]。
总的来说,根据ROC曲线选择的切点表现为白种人的切点显著高于亚洲人,男性的腰围切点大多显著高于女性,而男女性BMI切点的差异则不明显。不同研究所得出的腰围切点变化范围大于BMI切点变化范围。
但ROC曲线在制定切点方面尚存在以下不足。Qiao和Nyamdorj[43]认为目前大多数研究中用于糖尿病诊断的腰围切点灵敏度均介于60%~70%之间,漏诊率较高,不利于临床诊断。ROC曲线寻找的切点与所选人群的腰围、BMI水平高度相关。
2. 限制性立方样条:
(1)方法介绍:样条函数是具有一定光滑度的分片或分段定义的函数,其中使用最广泛的是立方样条函数。当因变量与自变量的关系在自变量数据范围两端的两个区间内呈线性时,通过确定节点的个数及位置,选择适当的边界条件(如自然边界,固定边界,非节点边界等)可以构造完整的限制性立方样条。
假设有n个节点:Ki,i=1,…,n,共有n-1个区间,产生n-1个基样条变量Si(X),i=1,…,n-1,X为原变量,限制性立方样条的表达式[44]:
式中S1(X)=X, 式中常用的选择节点位置的方法:①选择自变量和因变量关系发生突然转折的一些特殊关键节点;②选择在原始变量边际分布的等距百分位数(如若选取3个节点,则取P10、P50和P90百分位数为节点位置)[44]。节点的个数决定曲线的形状,其对限制性立方样条的拟合影响较大。由于节点个数的选择和自由度有关,当样本量较大时可以取较多的节点[45]。Harrell[44]建议一般情况下选取3~7个节点。
在相同参数个数、相同节点下,限制性立方样条的曲线结合logistic回归拟合情况较分段logistic回归效果更好。该方法对流行病学病因推断以及剂量反应关系的分析有着重要价值[45]。通过对体脂参数与糖尿病患病率(发病率)进行限制性立方样条非线性拟合,可以寻找某一糖尿病患病率(发病率)水平下合适的体脂参数切点。
(2)限制性立方样条选择的BMI和腰围切点:Ntuk等[46]使用限制性立方样条图,以白种人的BMI切点(30 kg/m2)和腰围切点(男:102 cm;女:88 cm)所对应的糖尿病患病率水平为参照,寻找其他种族人群在相同糖尿病患病率水平下所对应的BMI及腰围切点。该研究中南亚人(印度、巴基斯坦、孟加拉国)、华人和黑人(非洲、加勒比)男性的BMI切点依次为21.6、26.0和26.0 kg/m2;女性为22.0、24.0和26.0 kg/m2。南亚人、华人和黑人男性的腰围切点分别为79、88和88 cm;女性为70、74和79 cm。在排除糖尿病患病5年以上的患者后,华人和黑人的BMI和腰围切点与之前结果接近,南亚人的切点则略微升高。
在一项多种族队列研究(研究对象为59 824名居住于加拿大安大略省的未患糖尿病成年人)中,Chiu等[47]也使用限制性立方样条对BMI与糖尿病发病的关系进行拟合。根据Harrell[44]建议的3~7个节点选择方法,结果显示当限制性立方样条的节点选取4个时,南亚、华人和黑人的BMI切点分别为24、25、26 kg/m2;节点选取5个时,南亚人的切点为25 kg/m2,而华人和黑人的BMI切点均未有变化。
使用限制性立方样条选择的切点主要表现为欧美地区白种人具有较高的BMI和腰围切点,华人的切点略低于或接近黑色人种,而南亚人的切点最低。此外,在排除了糖尿病患病5年以上的患者后,Ntuk等[46]的研究发现南亚人的切点略微升高,该现象提示研究中若纳入已知糖尿病患者可能会影响BMI和腰围切点的大小。Chiu等[47]的研究则提示限制性立方样条的节点个数改变时,切点的大小也可能受到影响。
3. 分式多项式模型:
(1)方法介绍:分式多项式模型可以有效地处理连续型自变量对结果变量的影响,设X为自变量,分式多项式模型的表达式:
其中P1,…,Pm表示指数,常用的取值范围为{-2,-1,-0.5,0,0.5,1,2,3};m表示模型的阶数,通常m=1或2就可以形成较好地拟合数据。
当有多个预测变量(可为连续或分类变量)时,则使用多变量分式多项式(multivariable fractional polynomials,MFP)模型。在选择分式多项式模型时常利用后退法,从较为复杂的二阶模型出发对变量进行筛选。
(2)MFP模型选择的BMI和腰围切点:Bodicoat等[48]在排除已知糖尿病患者的南亚人群中通过拟合分式多项式模型来探讨南亚人群BMI及腰围切点,分别以FPG和餐后2 h血糖(连续性变量)作为结局变量,以种族(分类变量)、BMI及腰围(连续性变量)、BMI与种族的交互项(连续性变量)作为自变量,并调整年龄因素进行曲线拟合,以白种人BMI切点(30 kg/m2)和腰围切点(男:102 cm;女:88 cm)所对应的血糖值作为参照,基于FPG值的结果显示,南亚人的BMI切点分别为25 kg/m2(移居英国)和18 kg/m2(本地);腰围切点:男性为90 cm(移居英国)和87 cm(本地);女性为77 cm(移居英国)和54 cm(本地)。此外,研究还发现基于餐后2 h血糖值所寻找的南亚人BMI和腰围切点较基于FPG值低。
采用MFP模型选择切点的研究提示南亚人的BMI和腰围切点均显著低于白种人,而其中移居英国的南亚人的切点高于本地南亚人,说明肥胖切点不仅与种族有关,还可能与环境等外界因素有关。此外,研究还发现基于FPG和餐后2 h血糖选择的切点存在差异,提示使用不同的结局变量进行分析也可能会影响切点的大小。
小结:由于遗传和环境等因素的影响,用于不同人群糖尿病筛查或诊断的BMI和腰围切点存在较大差异。不同种族应制定不同的肥胖切点,同时在进一步的研究中需注意不同研究设计方法(横断面研究或前瞻性研究)、研究样本的选择标准(是否排除已知糖尿病患者,只选用新病例)、研究对象的人口学特征、统计分析方法(寻找切点的方法、结局变量是否相同)在寻找不同人群中筛查或诊断糖尿病的肥胖切点的差异。限制性立方样条和MFP这两种方法均可结合多因素回归分析[49]来评估调整混杂因素后不同BMI和腰围切点的选择对结局变量的影响[50],得到不同切点下糖尿病患病/发病风险的相对危险度。
利益冲突 无[1] International Diabetes Federation. IDF Diabetes Atlas(Sixth Edition)[EB/OL].(2014)[2015-12-15]. http://www.idf.org/diabetesatlas/data. |
[2] Vazquez G,Duval S,Jacobs DR Jr,et al. Comparison of body mass index,waist circumference,and waist/hip ratio in predicting incident diabetes:a meta-analysis[J]. Epidemiol Rev,2007,29(1):115-128. DOI:10.1093/epirev/mxm008. |
[3] Kodama S,Horikawa C,Fujihara K,et al. Comparisons of the strength of associations with future type 2 diabetes risk among anthropometric obesity indicators, including waist-to-height ratio:a meta-analysis[J]. Am J Epidemiol,2012,176(11):959-969. DOI:10.1093/aje/kws172. |
[4] 陈冯梅,胡晓抒,郭志荣,等. 不同方法评价肥胖相关健康风险效果分析[J]. 中国公共卫生,2006,22(12):1521-1523. DOI:10.3321/j.issn:1001-0580.2006.12.063. Chen FM,Hu XS,Guo ZR,et al. Different methods of evaluating the effect of obesity-related health risk analysis[J]. Chin J Public Health,2006,22(12):1521-1523. DOI:10.3321/j.issn:1001-0580.2006.12.063. |
[5] Janssen I,Katzmarzyk PT,Ross R. Waist circumference and not body mass index explains obesity-related health risk[J]. Am J Clin Nutr,2004,79(3):379-384. |
[6] Stevens J,Couper D,Pankow J,et al. Sensitivity and specificity of anthropometrics for the prediction of diabetes in a biracial cohort[J]. Obes Res,2001,9(11):696-705. DOI:10.1038/oby.2001.94. |
[7] Han TS,Van Leer EM,Seidell JC,et al. Waist circumference action levels in the identification of cardiovascular risk factors:prevalence study in a random sample[J]. BMJ,1995,311(7017):1401-1405. DOI:10.1136/bmj.311.7017.1401. |
[8] Centre for Public Health Excellence at NICE(UK),National Collaborating Centre for Primary Care(UK). Obesity:Guidance on the prevention,identification,assessment and management of overweight and obesity in adults and children[M]. London:National Institute for Health and Clinical Excellence(UK),2006. |
[9] Lear SA,James PT,Ko GT,et al. Appropriateness of waist circumference and waist-to-hip ratio cutoffs for different ethnic groups[J]. Eur J Clin Nutr,2010,64(1):42-61. DOI:10.1038/ejcn.2009.70. |
[10] Obesity in Asia Collaboration. Waist circumference thresholds provide an accurate and widely applicable method for the discrimination of diabetes[J]. Diabetes Care,2007,30(12):3116-3118. DOI:10.2337/dc07-1455. |
[11] Zweig MH,Campbell G. Receiver-operating characteristic(ROC) plots:a fundamental evaluation tool in clinical medicine[J]. Clin Chem,1993,39(4):561-577. |
[12] Schneider HJ,Glaesmer H,Klotsche J,et al. Accuracy of anthropometric indicators of obesity to predict cardiovascular risk[J]. J Clin Endocrinol Metab,2007,92(2):589-594. DOI:10. 1210/jc.2006-0254 |
[13] Balkau B,Sapinho D,Petrella A,et al. Prescreening tools for diabetes and obesity-associated dyslipidaemia:comparing BMI,waist and waist hip ratio. The D.E.S.I.R. Study[J]. Eur J Clin Nutr,2006,60(3):295-304. DOI:10.1038/sj.ejcn.1602308. |
[14] Diaz VA,Mainous Ⅲ AG,Baker R,et al. How does ethnicity affect the association between obesity and diabetes?[J]. Diabet Med,2007,24(11):1199-1204. DOI:10.1111/j.1464-5491. 2007.02244.x. |
[15] Wannamethee SG,Papacosta O,Whincup PH,et al. Assessing prediction of diabetes in older adults using different adiposity measures:a 7 year prospective study in 6923 older men and women[J]. Diabetologia,2010,53(5):890-898. DOI:10.1007/s00125-010-1670-7. |
[16] Wildman RP,Gu DF,Reynolds K,et al. Appropriate body mass index and waist circumference cutoffs for categorization of overweight and central adiposity among Chinese adults[J]. Am J Clin Nutr,2004,80(5):1129-1136. |
[17] Li R,Lu W,Jia J,et al. Relationships between indices of obesity and its cardiovascular comorbidities in a Chinese population[J]. Circ J,2008,72(6):973-978. DOI:10.1253/circj.72.973. |
[18] Zeng Q,He Y,Dong SY,et al. Optimal cut-off values of BMI,waist circumference and waist:height ratio for defining obesity in Chinese adults[J]. Br J Nutr,2014,112(10):1735-1744. DOI:10.1017/S0007114514002657. |
[19] Xiao XC,Liu YJ,Sun CL,et al. Evaluation of different obesity indices as predictors of type 2 diabetes mellitus in a Chinese population[J]. J Diabetes,2015,7(3):386-392. DOI:10.1111/1753-0407. |
[20] Jia ZX,Zhou Y,Liu XR,et al. Comparison of different anthropometric measures as predictors of diabetes incidence in a Chinese population[J]. Diabetes Res Clin Pract,2011,92(2):265-271. DOI:10.1016/j.diabres.2011.01.021. |
[21] Dong XL,Liu Y,Yang J,et al. Efficiency of anthropometric indicators of obesity for identifying cardiovascular risk factors in a Chinese population[J]. Postgrad Med J,2011,87(1026):251-256. DOI:10.1136/pgmj.2010.100453. |
[22] Tseng CH,Chong CK,Chan TT,et al. Optimal anthropometric factor cutoffs for hyperglycemia,hypertension and dyslipidemia for the Taiwanese population[J]. Atherosclerosis,2010,210(2):585-589. DOI:10.1016/j.atherosclerosis.2009.12.015. |
[23] Chu FL,Hsu CH,Jeng C. Lowered cutoff points of obesity indicators are better predictors of hypertension and diabetes mellitus in premenopausal Taiwanese women[J]. Obes Res Clin Pract,2015,9(4):328-335. DOI:10.1016/j.orcp.2014.08.001. |
[24] Kawada T,Otsuka T,Inagaki H,et al. Optimal cut-off levels of body mass index and waist circumference in relation to each component of metabolic syndrome(MetS) and the number of MetS component[J]. Diabetes Metab Syndr,2011,5(1):25-28. DOI:10.1016/j.dsx.2010.05.012. |
[25] Choi SJ,Keam B,Park SH,et al. Appropriate waist circumference cut-offs to predict diabetes in the Korean population-the Korean Genome and Epidemiology Study[J]. Circ J,2010,74(7):1357-1363. DOI:10.1253/circj.CJ-09-0739. |
[26] Park SH,Choi SJ,Lee KS,et al. Waist circumference and waist-to-height ratio as predictors of cardiovascular disease risk in Korean adults[J]. Circ J,2009,73(9):1643-1650. DOI:10.1253/circj.CJ-09-0161. |
[27] Kim HK,Kim CH,Park JY,et al. Lower waist-circumference cutoff point for the assessment of cardiometabolic risk in Koreans[J]. Diabetes Res Clin Pract,2009,85(1):35-39. DOI:10.1016/j.diabres.2009.04.009. |
[28] Cheong KC,Ghazali SM,Hock LK,et al. Optimal waist circumference cut-off values for predicting cardiovascular risk factors in a multi-ethnic Malaysian population[J]. Obes Res Clin Pract,2014,8(2):e154-162. DOI:10.1016/j.orcp.2013. 03.004. |
[29] Zaher ZM,Zambari R,Pheng CS,et al. Optimal cut-off levels to define obesity:body mass index and waist circumference,and their relationship to cardiovascular disease,dyslipidaemia,hypertension and diabetes in Malaysia[J]. Asia Pac J Clin Nutr,2009,18(2):209-216. |
[30] Aekplakorn W,Kosulwat V,Suriyawongpaisal P. Obesity indices and cardiovascular risk factors in Thai adults[J]. Int J Obes,2006,30(12):1782-1790. DOI:10.1038/sj.ijo.0803346. |
[31] An Y,Yi SY,Fitzpatrick A,et al. Appropriate body mass index and waist circumference cutoff for overweight and central obesity among adults in Cambodia[J]. PLoS One,2013,8(10):e77897. DOI:10.1371/journal.pone.0077897. |
[32] Bhowmik B,Munir SB,Diep LM,et al. Anthropometric indicators of obesity for identifying cardiometabolic risk factors in a rural Bangladeshi population[J]. J Diabetes Investig,2013,4(4):361-368. DOI:10.1111/jdi.12053. |
[33] Mohan V,Deepa M,Farooq S,et al. Anthropometric cut points for identification of cardiometabolic risk factors in an urban Asian Indian population[J]. Metabolism,2007,56(7):961-968. DOI:10.1016/j.metabol.2007.02.009. |
[34] Shabnam AA,Homa K,Reza MTM,et al. Cut-off points of waist circumference and body mass index for detecting diabetes,hypercholesterolemia and hypertension according to National Non-Communicable Disease Risk Factors Surveillance in Iran[J]. Arch Med Sci,2012,8(4):614-621. DOI:10.5114/aoms. 2012.30284. |
[35] Azimi-Nezhad M,Ghayour-Mobarhan M,Safarian M,et al. Anthropometric indices of obesity and the prediction of cardiovascular risk factors in an Iranian population[J]. Scientific World Journal,2009,9:424-430. DOI:10.1100/tsw. 2009.58. |
[36] Mirmiran P,Esmaillzadeh A,Azizi F. Detection of cardiovascular risk factors by anthropometric measures in Tehranian adults:receiver operating characteristic(ROC) curve analysis[J]. Eur J Clin Nutr,2004,58(8):1110-1118. DOI:10.1038/sj.ejcn. 1601936. |
[37] Khader YS,Batieha A,Jaddou H,et al. Anthropometric cutoff values for detecting metabolic abnormalities in Jordanian adults[J]. Diabetes Metab Syndr Obes,2010,3:395-402. DOI:10. 2147/DMSOTT.S15154. |
[38] Mansour AA,Al-Jazairi MI. Cut-off values for anthropometric variables that confer increased risk of type 2 diabetes mellitus and hypertension in Iraq[J]. Arch Med Res,2007,38(2):253-258. DOI:10.1016/j.arcmed.2006.09.014. |
[39] 中国肥胖问题工作组数据汇总分析协作组. 我国成人体重指数和腰围对相关疾病危险因素异常的预测价值:适宜体重指数和腰围切点的研究[J]. 中华流行病学杂志,2002,23(1):5-10. Cooperative Meta-Analysis Group of China Obesity Task Force. Predictive values of body mass index and waist circumference to risk factors of related diseases in Chinese adult population[J]. Chin J Epidemiol,2002,23(1):5-10. |
[40] World Health Organization. Obesity:preventing and managing the global epidemic:report of a WHO consultation[R]. WHO Technical Report Series. Geneva:WHO,2000,894:253. |
[41] Zimmet P,Alberti G,Shaw J. A new IDF worldwide definition of the metabolic syndrome:the rationale and the results[J]. Diabetes Voice,2005,50(3):31-33. |
[42] 《中国成人血脂异常防治指南》制订联合委员会. 中国成人血脂异常防治指南[J]. 中华心血管病杂志,2007,35(5):390-419. Joint Committee for Developing Chinese Guidelines on Prevention and Treatment of Dyslipidemia in Adults. Chinese guidelines on prevention and treatment of dyslipidemia in adults[J]. Chin J Cardiol,2007,35(5):390-419. |
[43] Qiao Q,Nyamdorj R. The optimal cutoff values and their performance of waist circumference and waist-to-hip ratio for diagnosing typeⅡdiabetes[J]. Eur J Clin Nutr,2010,64(1):23-29. DOI:10.1038/ejcn.2009.92. |
[44] Harrell Jr FE. Regression modeling strategies[M]. New York:Springer-Verlag,2001. |
[45] 罗剑锋,金欢,李宝月,等. 限制性立方样条在非线性回归中的应用研究[J]. 中国卫生统计,2010,27(3):229-232. DOI:10.3969/j.issn.1002-3674.2010.03.002. Luo JF,Jin H,Li BY,et al. The Application of restricted cubic spline in non-linear regression[J]. Chin J Health Statistics,2010,27(3):229-232. DOI:10.3969/j.issn.1002-3674.2010.03.002. |
[46] Ntuk UE,Gill JMR,Mackay DF,et al. Ethnic-specific obesity cutoffs for diabetes risk:cross-sectional study of 490,288 UK biobank participants[J]. Diabetes Care,2014,37(9):2500-2507. DOI:10.2337/dc13-2966. |
[47] Chiu M,Austin PC,Manuel DG,et al. Deriving ethnic-specific BMI cutoff points for assessing diabetes risk[J]. Diabetes Care,2011,34(8):1741-1748. DOI:10.2337/dc10-2300. |
[48] Bodicoat DH,Gray LJ,Henson J,et al. Body mass index and waist circumference cut-points in multi-ethnic populations from the UK and India:the addition-Leicester,Jaipur heart watch and New Delhi cross-sectional studies[J]. PLoS One,2014,9(3):e90813. DOI:10.1371/journal.pone.0090813. |
[49] 徐英,张敏,周舒冬. 分式多项式模型在流行病学资料分析中的应用[J]. 中国卫生统计,2011,28(5):591-592. DOI:10.3969/j.issn.1002-3674.2011.05.040. Xu Y,Zhang M,Zhou SD. Application of fractional polynomial model in the analysis of epidemiological data[J]. Chin J Health Statistics,2011,28(5):591-592. DOI:10.3969/j.issn.1002-3674.2011.05.040. |
[50] Wang ZQ,Ma J,Si DM. Optimal cut-off values and population means of waist circumference in different populations[J]. Nutr Res Rev,2010,23(2):191-199. DOI:10.1017/S0954422410000120. |