Skip to main content
Top
Published in: Osteoporosis International 4/2015

01-04-2015 | Original Article

Calcium intake and bone mineral density as an example of non-linearity and threshold analysis

Author: L. P. Breitling

Published in: Osteoporosis International | Issue 4/2015

Login to get access

Abstract

Summary

Non-linearity is a likely phenomenon in bone metabolism, but is often ignored in pertinent epidemiological studies. Using NHANES III data on calcium intake and bone mineral density, the most important non-linear methods are introduced and discussed. The results should motivate researchers to consider non-linearity in this field more frequently.

Introduction

Many relationships in bone metabolism and homeostasis are likely to follow non-linear patterns. Detailed dose-response analyses allowing for non-linear associations nonetheless remain scarce in this field.

Methods

A detailed analysis of NHANES III data on dietary calcium intake and bone mineral density was used to demonstrate the application and some of the challenges of the most important dose-response methods, including LOESS, categorical analysis, fractional polynomials, restricted cubic splines, and segmented regression.

Results

The spline estimate suggested increasing bone mineral density up to a calcium intake of about 1 g/day and a plateau thereafter. In segmented regression, the break-point marking the beginning of the plateau was placed at an intake of 0.58 (95 % confidence interval, 0.33 to 0.82) g/day. Sensitivity analyses suggested a less curved dose-response in women.

Conclusions

Knowing about the possibilities and limitations of non-linear dose-response approaches should encourage researchers to consider these methods more frequently in studies on bone health and disease. The example analysis suggested bone mineral density to reach a plateau slightly below current calcium intake recommendations, with fairly pronounced differences of the dose-response shape by sex and menopausal status.
Appendix
Available only for authorised users
Literature
1.
go back to reference Ahmad O, Ramamurthi K, Wilson KE, Engelke K, Prince RL, Taylor RH (2010) Volumetric DXA (VXA): A new method to extract 3d information from multiple in vivo DXA images. J Bone Min Res 25(12):2744–51CrossRef Ahmad O, Ramamurthi K, Wilson KE, Engelke K, Prince RL, Taylor RH (2010) Volumetric DXA (VXA): A new method to extract 3d information from multiple in vivo DXA images. J Bone Min Res 25(12):2744–51CrossRef
2.
go back to reference Alaimo K, McDowell MA, Briefel RR et al (1994) Dietary intake of vitamins, minerals, and fiber of persons ages 2 months and over in the United States: Third National Health and Nutrition Examination Survey, phase 1, 1988-91. Adv Data 258:1–28PubMed Alaimo K, McDowell MA, Briefel RR et al (1994) Dietary intake of vitamins, minerals, and fiber of persons ages 2 months and over in the United States: Third National Health and Nutrition Examination Survey, phase 1, 1988-91. Adv Data 258:1–28PubMed
4.
go back to reference Autier P, Koechlin A, Smans M et al (2012) Mammography screening and breast cancer mortality in Sweden. J Natl Cancer Inst 104:1080–93CrossRefPubMed Autier P, Koechlin A, Smans M et al (2012) Mammography screening and breast cancer mortality in Sweden. J Natl Cancer Inst 104:1080–93CrossRefPubMed
5.
go back to reference Bass M, Ford MA, Brown B et al (2006) Variables for the prediction of femoral bone mineral status in American women. South Med J 99(2):115–22CrossRefPubMed Bass M, Ford MA, Brown B et al (2006) Variables for the prediction of femoral bone mineral status in American women. South Med J 99(2):115–22CrossRefPubMed
6.
go back to reference Bischoff-Ferrari HA, Kiel DP, Dawson-Hughes B et al (2009) Dietary calcium and serum 25-hydroxyvitamin D status in relation to BMD among US adults. J Bone Mineral Res 24(5):935–42CrossRef Bischoff-Ferrari HA, Kiel DP, Dawson-Hughes B et al (2009) Dietary calcium and serum 25-hydroxyvitamin D status in relation to BMD among US adults. J Bone Mineral Res 24(5):935–42CrossRef
8.
go back to reference Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83(403):596–610CrossRef Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83(403):596–610CrossRef
9.
go back to reference Dawson-Hughes B, Harris SS (2002) Calcium intake influences the association of protein intake with rates of bone loss in elderly men and women. Am J Clin Nutr 75:773–9PubMed Dawson-Hughes B, Harris SS (2002) Calcium intake influences the association of protein intake with rates of bone loss in elderly men and women. Am J Clin Nutr 75:773–9PubMed
10.
go back to reference Desquilbet L, Mariotti F (2010) Dose-response analyses using restricted cubic spline functions in public health research. Stat Med 29:1037–57PubMed Desquilbet L, Mariotti F (2010) Dose-response analyses using restricted cubic spline functions in public health research. Stat Med 29:1037–57PubMed
11.
go back to reference Dionyssiotis Y, Paspati I, Trovas G et al (2010) Association of physical exercise and calcium intake with bone mass measured by quantitative ultrasound. BMC Women’s Health 10:12CrossRefPubMedCentralPubMed Dionyssiotis Y, Paspati I, Trovas G et al (2010) Association of physical exercise and calcium intake with bone mass measured by quantitative ultrasound. BMC Women’s Health 10:12CrossRefPubMedCentralPubMed
12.
go back to reference Feuer EJ, Kessler LG, Baker SG et al (1991) The impact of breakthrough clinical trials on survival in population based tumor registries. J Clin Epidemiol 44:141–53CrossRefPubMed Feuer EJ, Kessler LG, Baker SG et al (1991) The impact of breakthrough clinical trials on survival in population based tumor registries. J Clin Epidemiol 44:141–53CrossRefPubMed
13.
go back to reference Field A, Miles J (2010) Discovering statistics using SAS. London Field A, Miles J (2010) Discovering statistics using SAS. London
14.
go back to reference Fox J, Weisberg HS (2011) An R companion to applied regression, 2nd ed. Thousand Oaks Fox J, Weisberg HS (2011) An R companion to applied regression, 2nd ed. Thousand Oaks
15.
go back to reference Govindarajulu US, Malloy EJ, Ganguli B (2009) The comparison of alternative smoothing methods for fitting non-linear exposure-response relationships with Cox models in a simulation study. Int J Biostat 5(1), article 2 Govindarajulu US, Malloy EJ, Ganguli B (2009) The comparison of alternative smoothing methods for fitting non-linear exposure-response relationships with Cox models in a simulation study. Int J Biostat 5(1), article 2
16.
go back to reference Greenland S (1995) Dose-response and trend analysis in epidemiology: alternatives to categorical analysis. Epidemiology 6:356–65CrossRefPubMed Greenland S (1995) Dose-response and trend analysis in epidemiology: alternatives to categorical analysis. Epidemiology 6:356–65CrossRefPubMed
17.
go back to reference Greenland S (2008) Introduction to regression models. In: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology, 3rd ed. Philadelphia. Chapter 20, 381–417 Greenland S (2008) Introduction to regression models. In: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology, 3rd ed. Philadelphia. Chapter 20, 381–417
18.
go back to reference Hahs-Vaughn DL (2005) A primer for using and understanding weights with national datasets. J Exp Educ 73(3):221–48CrossRef Hahs-Vaughn DL (2005) A primer for using and understanding weights with national datasets. J Exp Educ 73(3):221–48CrossRef
19.
go back to reference Harrell FE (2001) Regression modeling strategies: with applications to linear models, logistic regression and survival analysis. Springer, New YorkCrossRef Harrell FE (2001) Regression modeling strategies: with applications to linear models, logistic regression and survival analysis. Springer, New YorkCrossRef
20.
go back to reference Hong H, Kim EK, Lee JS (2013) Effects of calcium intake, milk and dairy product intake, and blood vitamin D level on osteoporosis risk in Korean adults: analysis of the 2008 and 2009 Korea National Health and Nutrition Examination Survey. Nutr Res Pract 7(5):409–17CrossRefPubMedCentralPubMed Hong H, Kim EK, Lee JS (2013) Effects of calcium intake, milk and dairy product intake, and blood vitamin D level on osteoporosis risk in Korean adults: analysis of the 2008 and 2009 Korea National Health and Nutrition Examination Survey. Nutr Res Pract 7(5):409–17CrossRefPubMedCentralPubMed
21.
go back to reference Hunt CD, Johnson LK (2007) Calcium requirements: new estimations for men and women by cross-sectional statistical analyses of calcium balance data from metabolic studies. Am J Clin Nutr 86:1054–63PubMed Hunt CD, Johnson LK (2007) Calcium requirements: new estimations for men and women by cross-sectional statistical analyses of calcium balance data from metabolic studies. Am J Clin Nutr 86:1054–63PubMed
22.
go back to reference Jacoby WG (2000) Loess: a nonparametric, graphical tool for depicting relationships between variables. Elect Stud 19(4):577–613CrossRef Jacoby WG (2000) Loess: a nonparametric, graphical tool for depicting relationships between variables. Elect Stud 19(4):577–613CrossRef
23.
go back to reference Kim H, Fay MP, Feuer EJ et al (2000) Permutation tests for joinpoint regression with applications to cancer rates. Stat Med 19:335–51CrossRefPubMed Kim H, Fay MP, Feuer EJ et al (2000) Permutation tests for joinpoint regression with applications to cancer rates. Stat Med 19:335–51CrossRefPubMed
24.
go back to reference Looker AC, Wahner HW, Dunn WL et al (1998) Updated data on proximal femur bone mineral levels of US adults. Osteoporos Int 8:468–89CrossRefPubMed Looker AC, Wahner HW, Dunn WL et al (1998) Updated data on proximal femur bone mineral levels of US adults. Osteoporos Int 8:468–89CrossRefPubMed
25.
go back to reference MacDougall J (2006) Analysis of dose-response studies—Emax model. In: Ting N (ed) Dose finding in drug development. Springer, New York MacDougall J (2006) Analysis of dose-response studies—Emax model. In: Ting N (ed) Dose finding in drug development. Springer, New York
26.
go back to reference Matkovic V, Heaney RP (1992) Calcium balance during human growth: evidence for threshold behavior. Am J Clin Nutr 55:992–6PubMed Matkovic V, Heaney RP (1992) Calcium balance during human growth: evidence for threshold behavior. Am J Clin Nutr 55:992–6PubMed
27.
28.
go back to reference Muggeo VMR (2008) Segmented: an R package to fit regression models with broken-line relationships. R News 8:20–5 Muggeo VMR (2008) Segmented: an R package to fit regression models with broken-line relationships. R News 8:20–5
29.
go back to reference Myer PA, Mannalithara A, Singh G et al (2012) Proximal and distal colorectal cancer resection rates in the United States since widespread screening by colonoscopy. Gastroenterology 143:1227–36CrossRefPubMed Myer PA, Mannalithara A, Singh G et al (2012) Proximal and distal colorectal cancer resection rates in the United States since widespread screening by colonoscopy. Gastroenterology 143:1227–36CrossRefPubMed
30.
go back to reference National Center for Health Statistics (1994) Plan and operation of the Third National Health and Nutrition Examination Survey, 1988–94. Vital Health Stat 1(32) National Center for Health Statistics (1994) Plan and operation of the Third National Health and Nutrition Examination Survey, 1988–94. Vital Health Stat 1(32)
32.
go back to reference Nelson KM, Reiber G, Boyko EJ (2002) Diet and exercise among adults with type 2 diabetes: findings from the Third National Health and Nutrition Examination Survey (NHANES III). Diabetes Care 25:1722–8CrossRefPubMed Nelson KM, Reiber G, Boyko EJ (2002) Diet and exercise among adults with type 2 diabetes: findings from the Third National Health and Nutrition Examination Survey (NHANES III). Diabetes Care 25:1722–8CrossRefPubMed
33.
go back to reference Peacock M (2010) Calcium metabolism in health and disease. Clin J Am Soc Nephorl 5:S23–30CrossRef Peacock M (2010) Calcium metabolism in health and disease. Clin J Am Soc Nephorl 5:S23–30CrossRef
34.
go back to reference Royston P, Ambler G, Sauerbrei W (1999) The use of fractional polynomials to model continuous risk variables in epidemiology. Int J Epidemiol 28:964–74CrossRefPubMed Royston P, Ambler G, Sauerbrei W (1999) The use of fractional polynomials to model continuous risk variables in epidemiology. Int J Epidemiol 28:964–74CrossRefPubMed
36.
go back to reference Sauerbrei W, Meier-Hirmer C, Benner A et al (2006) Multivariable regression model building by using fractional polynomials: description of SAS, STATA and R programs. Comput Stat Data Anal 50:3464–85CrossRef Sauerbrei W, Meier-Hirmer C, Benner A et al (2006) Multivariable regression model building by using fractional polynomials: description of SAS, STATA and R programs. Comput Stat Data Anal 50:3464–85CrossRef
37.
go back to reference Shafique K, Oliphant R, Morrison DS (2012) The impact of socio-economic circumstances on overall and grade-specific prostate cancer incidence: a population-based study. Br J Cancer 107:575–82CrossRefPubMedCentralPubMed Shafique K, Oliphant R, Morrison DS (2012) The impact of socio-economic circumstances on overall and grade-specific prostate cancer incidence: a population-based study. Br J Cancer 107:575–82CrossRefPubMedCentralPubMed
38.
go back to reference Shea B, Wells G, Cranney A et al (2004) Calcium supplementation on bone loss in postmenopausal women. Cochrane Database Syst Rev 1, CD004526PubMed Shea B, Wells G, Cranney A et al (2004) Calcium supplementation on bone loss in postmenopausal women. Cochrane Database Syst Rev 1, CD004526PubMed
39.
go back to reference Steenland K, Deddens JA (2004) A practical guide to dose-response analyses and risk assessment in occupational epidemiology. Epidemiology 15:63–70CrossRefPubMed Steenland K, Deddens JA (2004) A practical guide to dose-response analyses and risk assessment in occupational epidemiology. Epidemiology 15:63–70CrossRefPubMed
40.
go back to reference Stone KL, Seeley DG, Lui LY et al (2003) BMD at multiple sites and risk of fracture of multiple types: long-term results from the Study of Osteoporotic Fractures. J Bone Miner Res 18:1947–54CrossRefPubMed Stone KL, Seeley DG, Lui LY et al (2003) BMD at multiple sites and risk of fracture of multiple types: long-term results from the Study of Osteoporotic Fractures. J Bone Miner Res 18:1947–54CrossRefPubMed
41.
go back to reference Strasak AM, Rapp K, Brant LJ et al (2008) Association of γ-glutamyltransferase and risk of cancer incidence in men: a prospective study. Cancer Res 68(10):3970–7CrossRefPubMed Strasak AM, Rapp K, Brant LJ et al (2008) Association of γ-glutamyltransferase and risk of cancer incidence in men: a prospective study. Cancer Res 68(10):3970–7CrossRefPubMed
42.
43.
go back to reference Uusi-Rasi K, Kärkkäinen MUM, Lamberg-Allardt CJE (2013) Calcium intake in health maintenance—a systematic review. Food Nutr Res Uusi-Rasi K, Kärkkäinen MUM, Lamberg-Allardt CJE (2013) Calcium intake in health maintenance—a systematic review. Food Nutr Res
44.
go back to reference Varenna M, Binelli L, Casari S et al (2007) Effects of dietary calcium intake on body weight and prevalence of osteoporosis in early postmenopausal women. Am J Clin Nutr 86:639–44PubMed Varenna M, Binelli L, Casari S et al (2007) Effects of dietary calcium intake on body weight and prevalence of osteoporosis in early postmenopausal women. Am J Clin Nutr 86:639–44PubMed
45.
go back to reference Wang MC, Dixon LB (2006) Socioeconomic influences on bone health in postmenopausal women: findings from NHANES III, 1988–1994. Osteoporos Int 17:91–8CrossRefPubMed Wang MC, Dixon LB (2006) Socioeconomic influences on bone health in postmenopausal women: findings from NHANES III, 1988–1994. Osteoporos Int 17:91–8CrossRefPubMed
46.
go back to reference Warensjö E, Byberg L, Melhus H, Gedeborg R, Mallmin H, Wolk A, Michaëlsson K (2011) Dietary calcium intake and risk of fracture and osteoporosis: prospective longitudinal cohort study. BMJ 342:d1473CrossRefPubMedCentralPubMed Warensjö E, Byberg L, Melhus H, Gedeborg R, Mallmin H, Wolk A, Michaëlsson K (2011) Dietary calcium intake and risk of fracture and osteoporosis: prospective longitudinal cohort study. BMJ 342:d1473CrossRefPubMedCentralPubMed
47.
go back to reference Wood SN (2001) Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting. Biometrics 57:240–44CrossRefPubMed Wood SN (2001) Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting. Biometrics 57:240–44CrossRefPubMed
49.
Metadata
Title
Calcium intake and bone mineral density as an example of non-linearity and threshold analysis
Author
L. P. Breitling
Publication date
01-04-2015
Publisher
Springer London
Published in
Osteoporosis International / Issue 4/2015
Print ISSN: 0937-941X
Electronic ISSN: 1433-2965
DOI
https://doi.org/10.1007/s00198-014-2996-7

Other articles of this Issue 4/2015

Osteoporosis International 4/2015 Go to the issue