Journal of Data Science logo


Login Register

  1. Home
  2. Issues
  3. Volume 22, Issue 1 (2024)
  4. Association Between Body Fat and Body Ma ...

Journal of Data Science

Submit your article Information
  • Article info
  • Related articles
  • More
    Article info Related articles

Association Between Body Fat and Body Mass Index from Incomplete Longitudinal Proportion Data: Findings from the Fels Study
Volume 22, Issue 1 (2024), pp. 116–137
Xin Tong   Seohyun Kim   Dipankar Bandyopadhyay ORCID icon link to view author Dipankar Bandyopadhyay details     All authors (4)

Authors

 
Placeholder
https://doi.org/10.6339/23-JDS1104
Pub. online: 15 June 2023      Type: Data Science In Action      Open accessOpen Access

Received
20 May 2022
Accepted
14 May 2023
Published
15 June 2023

Abstract

Obesity rates continue to exhibit an upward trajectory, particularly in the US, and is the underlying cause of several comorbidities, including but not limited to high blood pressure, high cholesterol, diabetes, heart disease, stroke, and cancers. To monitor obesity, body mass index (BMI) and proportion body fat (PBF) are two commonly used measurements. Although BMI and PBF changes over time in an individual’s lifespan and their relationship may also change dynamically, existing work has mostly remained cross-sectional, or separately modeling BMI and PBF. A combined longitudinal assessment is expected to be more effective in unravelling their complex interplay. To mitigate this, we consider Bayesian cross-domain latent growth curve models within a structural equation modeling framework, which simultaneously handles issues such as individually varying time metrics, proportion data, and potential missing not at random data for joint assessment of the longitudinal changes of BMI and PBF. Through simulation studies, we observe that our proposed models and estimation method yielded parameter estimates with small bias and mean squared error in general, however, a mis-specified missing data mechanism may cause inaccurate and inefficient parameter estimates. Furthermore, we demonstrate application of our method to a motivating longitudinal obesity study, controlling for both time-invariant (such as, sex), and time-varying (such as diastolic and systolic blood pressure, biceps skinfold, bioelectrical impedance, and waist circumference) covariates in separate models. Under time-invariance, we observe that the initial BMI level and the rate of change in BMI influenced PBF. However, in presence of time-varying covariates, only the initial BMI level influenced the initial PBF. The added-on selection model estimation indicated that observations with higher PBF values were less likely to be missing.

Supplementary material

 Supplementary Material
Additional Tables summarizing model comparisons and parameter estimation from the two studies are available as Supplementary Materials associated with this article.

References

 
Bandyopadhyay D, Galvis DM, Lachos VH (2017). Augmented mixed models for clustered proportion data. Statistical Methods in Medical Research, 26: 880–897. https://doi.org/10.1177/0962280214561093
 
Caussy C, Wallet F, Laville M, Disse E (2020). Obesity is Associated with Severe Forms of COVID-19. Obesity, 28(7): 1175. https://doi.org/10.1002/oby.22842
 
Demerath EW, Li J, Sun SS, Chumlea WC, Remsberg KE, Czerwinski SA, et al. (2004). Fifty-year trends in serial body mass index during adolescence in girls: The Fels Longitudinal Study. The American Journal of Clinical Nutrition, 80(2): 441–446. https://doi.org/10.1093/ajcn/80.2.441
 
Demerath EW, Schubert CM, Maynard LM, Sun SS, Chumlea WC, Pickoff A, et al. (2006). Do changes in body mass index percentile reflect changes in body composition in children? Data from the Fels Longitudinal Study. Pediatrics, 117(3): e487–e495. https://doi.org/10.1542/peds.2005-0572
 
Deurenberg P, Weststrate JA, Seidell JC (1991). Body mass index as a measure of body fatness: Age- and sex-specific prediction formulas. British Journal of Nutrition, 65: 105–114. https://doi.org/10.1079/BJN19910073
 
Diggle P, Kenward MG (1994). Informative drop-out in longitudinal data analysis. Journal of the Royal Statistical Society. Series C. Applied Statistics, 43(1): 49–73.
 
Dulloo AG, Jacquet J, Solinas G, Montani JP, Schutz Y (2010). Body composition phenotypes in pathways to obesity and the metabolic syndrome. International Journal of Obesity, 34(2): S4–S17. https://doi.org/10.1038/ijo.2010.234
 
Duncan TE, Duncan SC (2004). An introduction to latent growth curve modeling. Behavior Therapy, 35(2): 333–363. https://doi.org/10.1016/S0005-7894(04)80042-X
 
Enders CK (2011). Missing not at random models for latent growth curve analyses. Psychological Methods, 16(1): 1–16. https://doi.org/10.1037/a0022640
 
Ferrari S, Cribari-Neto F (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7): 799–815. https://doi.org/10.1080/0266476042000214501
 
Gallagher D, Visser M, Sepulveda D, Pierson RN, Harris T, Heymsfield SB (1996). How useful is body mass index for comparison of body fatness across age, sex, and ethnic groups? American Journal of Epidemiology, 143(3): 228–239. https://doi.org/10.1093/oxfordjournals.aje.a008733
 
Gelman A, Meng XL, Stern H (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4): 733–760.
 
Geweke J (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bayesian Statistics 4 (JM Bernardo, JO Berger, AP Dawid, AFM Smith, eds.), 169–193. Clarendon Press, Oxford.
 
Gomes M, Kenward MG, Grieve R, Carpenter J (2020). Estimating treatment effects under untestable assumptions with nonignorable missing data. Statistics in Medicine, 39(11): 1658–1674. https://doi.org/10.1002/sim.8504
 
Guo SS, Chumlea WC, Roche AF, Siervogel RM (1997). Age-and maturity-related changes in body composition during adolescence into adulthood: The Fels Longitudinal Study. International Journal of Obesity, 21(12): 1167–1175. https://doi.org/10.1038/sj.ijo.0800531
 
Guo SS, Zeller C, Chumlea WC, Siervogel RM (1999). Aging, body composition, and lifestyle: The Fels Longitudinal Study. The American Journal of Clinical Nutrition, 70(3): 405–411. https://doi.org/10.1093/ajcn/70.3.405
 
Harring JR, Strazzeri MM, Blozis SA (2021). Piecewise latent growth models: Beyond modeling linear-linear processes. Behavior Research Methods, 53: 593–608. https://doi.org/10.3758/s13428-020-01420-5
 
Ho-Pham LT, Lai TQ, Nguyen MTT, Nguyen TV (2015). Relationship between body mass index and percent body fat in Vietnamese: Implications for the diagnosis of obesity. PLoS ONE, 10(5): e0127198. https://doi.org/10.1371/journal.pone.0127198
 
Ibrahim JG, Chen MH, Lipsitz SR, Herring AH (2005). Missing-data methods for generalized linear models: A comparative review. Journal of the American Statistical Association, 100(469): 332–346. https://doi.org/10.1198/016214504000001844
 
Jackson A, Stanforth P, Gagnon J (2002). The effect of sex, age and race on estimating percentage body fat from body mass index: The heritage family study. International Journal of Obesity, 26: 789–796. https://doi.org/10.1038/sj.ijo.0802006
 
Jelena J, Baltic Z, Milica G, Jelena I, Marija B, Milka P, et al. (2016). Relationship between body mass index and body fat percentage among adolescents from Serbian Republic. Journal of Childhood Obesity, 1(2): 10. https://doi.org/10.21767/2572-5394.100009
 
Kenward MG (1998). Selection models for repeated measurements with non-random dropout: An illustration of sensitivity. Statistics in Medicine, 17(23): 2723–2732. https://doi.org/10.1002/(SICI)1097-0258(19981215)17:23<2723::AID-SIM38>3.0.CO;2-5
 
Lee K, Whittaker TA (2018). Statistical power of the multiple domain latent growth model for detecting group differences. Structural Equation Modeling: A Multidisciplinary Journal, 25(5): 700–714. https://doi.org/10.1080/10705511.2018.1426990
 
Little TD (2013). Longitudinal Structural Equation Modeling. Guilford press.
 
Makris A, Foster GD (2011). Dietary approaches to the treatment of obesity. The Psychiatric Clinics of North America, 34: 813–827. https://doi.org/10.1016/j.psc.2011.08.004
 
McQueen MA (2009). Exercise aspects of obesity treatment. The Ochsner Journal, 9: 140–143.
 
Mehta PD, Neale MC (2005). People are variables too: Multilevel structural equations modeling. Psychological Methods, 10: 259–284. https://doi.org/10.1037/1082-989X.10.3.259
 
Muthén B, Asparouhov T (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3): 313–335. https://doi.org/10.1037/a0026802
 
Nahhas RW, Choh AC, Lee M, Chumlea WMC, Duren DL, Siervogel RM, et al. (2010). Bayesian longitudinal plateau model of adult grip strength. American Journal of Human Biology, 22: 648–656. https://doi.org/10.1002/ajhb.21057
 
Nasr Eldeen SK, Al-Buni R, Al Yami A, Alali H (2017). Relationship between body mass index (BMI) and body fat percentage in a group of Saudi Arabian adults. Annals of Public Health and Research, 4(2): 1059.
 
Petridou A, Siopi A, Mougios V (2019). Exercise in the management of obesity. Metabolism, Clinical and Experimental, 92: 163–169. https://doi.org/10.1016/j.metabol.2018.10.009
 
Plummer M (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing, 12(125), 1–10. Vienna, Austria.
 
Ranasinghe C, Gamage P, Katulanda P, Andraweera N, Thilakarathne S, Tharanga P (2013). Relationship between body mass index (BMI) and body fat percentage, estimated by bioelectrical impedance, in a group of Sri Lankan adults: A cross sectional study. BMC Public Health, 13(1): 797. https://doi.org/10.1186/1471-2458-13-797
 
Roche AF (1992). Growth, Maturation, and Body Composition: The Fels Longitudinal Study 1929-1991. Cambridge University Press, New York.
 
Rubin DB (1976). Inference and Missing Data. Biometrika, 63(3): 581–592. https://doi.org/10.1093/biomet/63.3.581
 
Sabo RT, Lu Z, Daniels S, Sun SS (2012a). Serial childhood BMI and associations with adult hypertension and obesity: The Fels Longitudinal Study. Obesity, 20(8): 1741–1743. https://doi.org/10.1038/oby.2012.58
 
Sabo RT, Ren C, Sun SS (2012b). Comparing height-adjusted waist circumference indices: The Fels Longitudinal Study. Open Journal of Endocrine and Metabolic Diseases, 2(3): 40–48. https://doi.org/10.4236/ojemd.2012.23006
 
Samuels JD (2020). Obesity Phenotype is a Predictor of COVID-19 Disease Susceptibility. Obesity, 28(8): 1368. https://doi.org/10.1002/oby.22866
 
Shi D, Tong X (2022). Mitigating selection bias: A Bayesian approach to two-stage causal modeling with instrumental variables for nonnormal missing data. Sociological Methods & Research, 51(3): 1052–1099. https://doi.org/10.1177/0049124120914920
 
Sterba SK (2014). Fitting nonlinear latent growth curve models with individually varying time points. Structural Equation Modeling, 21: 630–647. https://doi.org/10.1080/10705511.2014.919828
 
Suk HW, West SG, Fine KL, Grimm KJ (2019). Nonlinear growth curve modeling using penalized spline models: A gentle introduction. Psychological Methods, 24(3): 269–290. https://doi.org/10.1037/met0000193
 
Sun SS, Deng X, Sabo R, Carrico R, Schubert CM, Wan W, et al. (2012). Secular trends in body composition for children and young adults: The Fels Longitudinal Study. American Journal of Human Biology, 24(4): 506–514. https://doi.org/10.1002/ajhb.22256
 
Vehtari A, Gabry J, Magnusson M, Yao Y, Gelman A (2019). loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models. R package version 2.2.0.
 
Vehtari A, Gelman A, Gabry J (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27: 1413–1432. https://doi.org/10.1007/s11222-016-9696-4
 
Watanabe S (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11: 3571–3594.
 
Wells JC, Fewtrell MS (2006). Measuring body composition. Archives of Disease in Childhood, 91(7): 612–617. https://doi.org/10.1136/adc.2005.085522
 
WHO (2017). World Health Organization report on prevalence of obesity among adults, BMI ⩾ 30, age-standardized, estimates by country. https://apps.who.int/gho/data/view.main.CTRY2450A?lang=en. Accessed: 2023-03-31.
 
Wu MC, Carroll RJ (1988). Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics, 44: 175–188. https://doi.org/10.2307/2531905

Related articles PDF XML
Related articles PDF XML

Copyright
2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
by logo by logo
Open access article under the CC BY license.

Keywords
cross-domain latent growth curve model individually varying time metrics missing data obesity proportion data

Funding
This research was supported by grants R01AG048801, R01DE031134, and R21DE031879 from the United States National Institutes of Health, and a 4-VA grant from the Commonwealth of Virginia.

Metrics
since February 2021
513

Article info
views

289

PDF
downloads

Export citation

Copy and paste formatted citation
Placeholder

Download citation in file


Share


RSS

Journal of data science

  • Online ISSN: 1683-8602
  • Print ISSN: 1680-743X

About

  • About journal

For contributors

  • Submit
  • OA Policy
  • Become a Peer-reviewer

Contact us

  • JDS@ruc.edu.cn
  • No. 59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China
Powered by PubliMill  •  Privacy policy