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Article: Marian T. Hannan, Heather J. Litman, Andre B. Araujo, Christine E. McLennan, Robert R. McLean, John B. McKinlay, Tai C. Chen, and Michael F. Holick Serum 25-Hydroxyvitamin D and Bone Mineral Density in a Racially and Ethnically Diverse Group of Men J Clin Endocrinol Metab 2007; 0: jc.2007-1217v1 [Abstract]

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Correlation coefficients are not appropriate for assessing differences among populations

Hussein F Saadi, Nico Nagelkerke   (21 May 2008)

Correlation coefficients are not appropriate for assessing differences among populations 21 May 2008
Hussein F Saadi, Associate Professor of Medicine Faculty of Medicine and Health Sciences, UAE University, Nico Nagelkerke Send letter to journal: Re: Correlation coefficients are not appropriate for assessing differences among populations saadih{at}uaeu.ac.ae Hussein F Saadi, et al.	With great interest we read the paper by Hannan et al. (1) on racial differences in the relationship between serum 25-hydroxyvitamin D [25(OH)D] and bone mineral density (BMD) of Black, Hispanic and White men. Because only white men showed a significant positive, but partial correlation between 25(OH)D and BMD (range of correlation coefficients: 0.00-0.14), the authors conclude that there are race and ethnic differences in the association, and raise the possibility that the detrimental effects of low serum 25(OH)D concentrations are in some way mitigated in black and Hispanic men. Unfortunately, the statistical methods used by the authors are not very helpful in determining whether such racial and ethnic differences in the association between 25(OH)D and BMD really exist. Correlation coefficients are not an appropriate statistical tool for assessing such differences among populations. The correlation coefficients between two variables X and Y may differ significantly between two populations, even when the functional relationship between X and Y (i.e. how Y depends on X) in the two populations is identical. The main reason for this is that the distribution of one of the variables may differ between the two populations. For example, in the study by Hannan et al. (1), a significantly higher percentage of black and Hispanic men had 25(OH)D concentrations in the lowest quartile compared to white men. This, by itself, may have resulted in lack of correlation between serum 25(OH)D concentration and BMD in black and Hispanic men. Perhaps, if more black and Hispanic subjects with normal vitamin D concentrations had been included in the analysis then a significant correlation coefficient may have been detected. To judge whether the relationships differ between the three racial groups the authors could have carried out, for example, a formal statistical test of non-parallelism. This is even made easier by the fact that sampling weights can normally be ignored when estimating functional relationships using regression analysis. Reference 1. Hannan MT, Litman HJ, Araujo AB, McLennan CE, McLean RR, McKinlay JB, Chen TC, Holick MF. 2008. Serum 25-Hydroxyvitamin D and Bone Mineral Density in a Racially and Ethnically Diverse Group of Men. J Clin Endocrinol Metab 93:40-46