Statistical methods for body mass index: A selective review

Abstract

Obesity rates have been increasing over recent decades, causing significant concern among policy makers. Excess body fat, commonly measured by body mass index, is a major risk factor for several common disorders including diabetes and cardiovascular disease, placing a substantial burden on health care systems. To guide effective public health action, we need to understand the complex system of intercorrelated influences on body mass index. This paper, based on all eligible articles searched from Global health, Medline and Web of Science databases, reviews both classical and modern statistical methods for body mass index analysis. We give a description of each of these methods, exploring the classification, links and differences between them and the reasons for choosing one over the others in different settings. We aim to provide a key resource and statistical library for researchers in public health and medicine to deal with obesity and body mass index data analysis.

Keywords

Body mass index obesity regression model risk factors statistical analysis

Get full access to this article

View all access options for this article.

References

Ells

Cavill

. Preventing childhood obesity through lifestyle change interventions 2009. A briefing paper for commissioners. Oxford: National Obesity Observatory.

Organization WH. Obesity: Preventing and managing the global epidemic. Report of a WHO consultation. Technical report, World Health Organization, 2000.

Vandenbroeck I, Goossens I and Clemens M. Foresight tackling obesities: Future choicesbuilding the obesity system map. Technical report, Government Office for Science, UK Government’s Foresight Programme, 2007.

Renehan

Tyson

Mea

Egger

. Body-mass index and incidence of cancer: A systematic review and meta-analysis of prospective observational studies. Lancet 2008; 371: 569–578.

Larsson

Wolk

. Excess body fatness: An important cause of most cancers. Lancet 2008; 371: 536–537.

Torloni

Betrán

Bea

Horta

. Prepregnancy BMI and the risk of gestational diabetes: A systematic review of the literature with meta-analysis. Obesity Rev 2009; 10: 194–203.

Dinsdale H, Ridler C and Ells L. A simple guide to classifying body mass index in children. Technical report, National Obesity Observatory, 2011.

Tangugsorn

Krogstad

Espeland

. Obstructive sleep apnea: A canonical correlation of cephalometric and selected demographic variables in obese and nonobese patients. Angle Orthod 2001; 71: 23–35.

Hannah

Gray

. Effects of obesity and body fat distribution on lipids and lipoproteins in nondiabetic American Indians: The strong heart study. Obesity Res 2000; 8: 411–421.

10.

Yang

Müller

Stadtmüller

. Functional singular component analysis. J R Statist Soc B 2011; 73: 303–324.

11.

Newby

Weismayer

Åkesson

. Longitudinal changes in food patterns predict changes in weight and body mass index and the effects are greatest in obese women. J Nutr 2006; 136: 2580–2587.

12.

Frayling

Timpson

Weedon

. A common variant in the FTO gene is associated with body mass index and predisposes to childhood and adult obesity. Am Assoc Adv Sci 2007; 316: 889–894.

13.

Abarin

Warrington

. The impact of breastfeeding on FTO-related bmi growth trajectories: an application to the raine pregnancy cohort study. Int J Epidemiol 2012; 41: 1650–1660.

14.

Warrington

Pennell

. Modelling BMI trajectories in children for genetic association studies. PloS One 2013; 8: e53897–e53897.

15.

Boffetta

McLerran

Chen

. Body mass index and diabetes in asia: A cross-sectional pooled analysis of 900,000 individuals in the Asia cohort consortium. PloS One 2011; 6: e19930–e19930.

16.

Razak

Corsi

Subramanian

. Change in the body mass index distribution for women: Analysis of surveys from 37 low-and middle-income countries. PLoS Med 2013; 10: e1001367–e1001367.

17.

Beyerlein

Fahrmeir

Mansmann

. Alternative regression models to assess increase in childhood BMI. BMC Med Res Methodol 2008; 8: 59–59.

18.

Beyerlein

Toschke

von Kries

. Breastfeeding and childhood obesity: Shift of the entire BMI distribution or only the upper parts & quest. Obesity 2008; 16: 2730–2733.

19.

Thas

Neve

Lea

Clement

. Probabilistic index models. J R Statist Soc B 2012; 74: 623–671.

20.

Bottai

Frongillo

Sui

. Use of quantile regression to investigate the longitudinal association between physical activity and body mass index. Obesity 2014; 22: E149–CE156.

21.

Koenker

Hallock

. Quantile regression: An introduction. Obesity 2001; 15: 43–56.

22.

Stander

. Quantile regression: Applications and current research areas. J R Statist Soc D 2003; 52: 331–350.

23.

Chen

Chang

Yeh

. A quantile regression approach to re-investigate the relationship between sleep duration and body mass index in Taiwan. Int J Public Health 2012; 57: 485–493.

24.

Yang

Matthews

Chen

. Stochastic variability in stress, sleep duration, and sleep quality across the distribution of body mass index: Insights from quantile regression. Int J Behav Med 2014; 21: 282–291.

25.

Costa-Font

Fabbri

Gil

. Decomposing body mass index gaps between mediterranean countries: A counterfactual quantile regression analysis. Econ Hum Biol 2009; 7: 351–365.

26.

Fenske

Kneib

Hothorn

. Identifying risk factors for severe childhood malnutrition by boosting additive quantile regression. J Am Statist Assoc 2011; 106: 494–510.

27.

Sturm

Datar

. Body mass index in elementary school children, metropolitan area food prices and food outlet density. Public Health 2005; 119: 1059–1068.

28.

Stifel

Averett

. Childhood overweight in the United States: A quantile regression approach. Econ Hum Biol 2009; 7: 387–397.

29.

Popkin

. Recent dynamics suggest selected countries catching up to us obesity. Am J Clin Nutr 2010; 91: 284S–288S.

30.

Koenker

Portnoy

. Quantile smoothing splines. Biometrika 1994; 81: 673–680.

31.

Graubard

Korn

. Application of nonparametric quantile regression to body mass index percentile curves from survey data. Stat Med 2010; 29: 558–572.

32.

Jones

. Local linear quantile regression. J Am Statist Assoc 1998; 93: 228–237.

33.

Cole

. Fitting smoothed centile curves to reference data. J R Statist Soc A 1998; 151: 385–418.

34.

Cole

. The lMS method for constructing normalized growth standards. Eur J Clin Nutr 1990; 44: 45–60.

35.

Cole

Green

. Smoothing reference centile curves: The lMS method and penalized likelihood. Stat Med 1992; 11: 1305–1319.

36.

Cole

Freeman

Preece

. Body mass index reference curves for the UK, 1990. Arch Dis Child 1995; 73: 25–29.

37.

Cole

Bellizzi

Flegal

. Establishing a standard definition for child overweight and obesity worldwide: International survey. BMJ 2000; 320: 1240–1240.

38.

Cole

Flegal

Dea

Nicholls

. Body mass index cut offs to define thinness in children and adolescents: International survey. BMJ 2007; 335: 194–194.

39.

Ogden

Kuczmarski

Flegal

. Centers for disease control and prevention 2000 growth charts for the United States: Improvements to the 1977 national center for health statistics version. Pediatrics 2002; 109: 45–60.

40.

Onis

Onyango

Borghi

. Development of a WHO growth reference for school-aged children and adolescents. Bull World Health Organ 2007; 85: 660–667.

41.

Heagerty

Pepe

. Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children. J R Statist Soc C 1999; 48: 533–551.

42.

Dunson

Pillai

Park

. Bayesian density regression. J R Statist Soc B 2007; 69: 163–183.

43.

Elliott

Stettler

. Using a mixture model for multiple imputation in the presence of outliers: The ‘healthy for life’ project. J R Statist Soc C 2007; 56: 63–78.

44.

Little

Zhang

. Subsample ignorable likelihood for regression analysis with missing data. J R Statist Soc C 2011; 60: 591–605.

45.

Little

Rubin

. Statistical analysis with missing data, New York: Wiley, 2002.

46.

Bound

Brown

Mathiowetz

Measurement error in survey data. In: Heckman

Leamer

(eds). Handbook of econometrics 2001; Chapter 59, Vol. 5. 1st ed. Elsevier, pp. 3705–3843.

47.

Cawley

. The impact of obesity on wages. J Hum Resour 2004; 39: 451–474.

48.

Rubin

. Inference and missing data. Biometrika 1976; 63: 581–592.

49.

Little

. A class of pattern-mixture models for normal incomplete data. Biometrika 1994; 81: 471–483.

50.

Yuan

Little

. Model-based estimates of the finite population mean for two-stage cluster samples with unit non-response. J R Statist Soc C 2007; 56: 79–97.

51.

Horvitz

Thompson

. A generalization of sampling without replacement from a finite universe. J Am Statist Assoc 1952; 47: 663–685.

52.

Nandram

Choi

. A Bayesian analysis of body mass index data from small domains under nonignorable nonresponse and selection. J Am Statist Assoc 2010; 105: 120–135.

53.

Remmers

Sleddens

Gubbels

. Relationship between physical activity and the development of BMI in children. Med Sci Sports Exerc 2013; 46: 177–184.

54.

Branum

Parker

Keim

. Prepregnancy body mass index and gestational weight gain in relation to child body mass index among siblings. Am J Epidemiol 2011; 174: 1159–1165.

55.

Liang

Zeger

. Longitudinal data analysis using generalized linear models. Biometrika 1986; 73: 13–22.

56.

Lai

Small

. Marginal regression analysis of longitudinal data with time-dependent covariates: A generalized method-of-moments approach. J R Statist Soc B 2007; 69: 79–99.

57.

Hansen

. Large sample properties of generalized method of moments estimators. Econometrica 1982; 50: 1029–1054.

58.

Hastie

Tibshirani

. Generalized additive models, London: Chapman and Hall, 1990.

59.

Gregory C. Wages, BMI, and age: A generalized additive model using the oracle estimator. http://ssrn.com/abstract=1975044 or https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.1975044.

60.

Frank

Friedman

. A statistical view of some chemometrics regression tools. Technometrics 1993; 35: 109–135.

61.

Tibshirani

. Regression shrinkage and selection via the lasso. J R Statist Soc B 1996; 58: 267–288.

62.

Zou

Hastie

. Regularization and variable selection via the elastic net. J R Statist Soc B 2005; 67: 301–320.

63.

Fan

. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Statist Assoc 2001; 96: 1348–1360.

64.

Hesterberg

Choi

Meier

. Least angle and l₁ penalized regression: A review. Stat Surveys 2008; 2: 61–93.

65.

Bradic

Fan

Wang

. Penalized composite quasi-likelihood for ultrahigh dimensional variable selection. J R Statist Soc B 2008; 73: 325–349.

66.

Liu

. Variable selection in quantile regression. Stat Sin 2009; 19: 801–801.