Editing Body mass index (section)

==Alternatives==

===Corpulence index (exponent of 3)===
The [[corpulence index]] uses an exponent of 3 rather than 2. The corpulence index yields valid results even for very short and very tall people,<ref>{{Cite book |last=Ditmier |first=Lawrence F. |title=New Developments in Obesity Research |publisher=Nova Science Publishers |year=2006 |isbn=1-60021-296-4 |location=Hauppauge, New York}}{{page needed|date=April 2012}}</ref> which is a problem with BMI. For example, a {{convert|152.4|cm|ftin|abbr=on}} tall person at an ideal body weight of {{convert|48|kg|lb|abbr=on}} gives a normal BMI of 20.74 and CI of 13.6, while a {{convert|200|cm|ftin|abbr=on}} tall person with a weight of {{convert|100|kg|lb|abbr=on}} gives a BMI of 24.84, very close to an overweight BMI of 25, and a CI of 12.4, very close to a normal CI of 12.<ref>{{Cite journal|title=Taller people should have Higher BMI's and Blood Pressure Measurements as their Normal|url=https://biomedres.us/pdfs/BJSTR.MS.ID.001381.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://biomedres.us/pdfs/BJSTR.MS.ID.001381.pdf |archive-date=2022-10-09 |url-status=live|journal=Biomed J Sci & Tech Res|year=2018|doi=10.26717/BJSTR.2018.06.001381|doi-access=free|last1=v Roth|first1=Jonathan|volume=6|issue=4}}</ref>

===New BMI (exponent of 2.5)===
A study found that the best exponent E for predicting the fat percent would be between 2 and 2.5 in <math>\text{mass}/\text{height}^E</math>.<ref>{{cite journal |url=https://www.sciencedirect.com/science/article/pii/S0002916523274547 |title=Scaling of human body composition to stature: new insights into body mass index |author=Heymsfield Steven B, Gallagher Dympna, Mayer Laurel, Beetsch Joel ja Pietrobelli Angelo|volume=86 |issue=1 |date=July 2007 |pages=82–91 |journal=The American Journal of Clinical Nutrition|doi=10.1093/ajcn/86.1.82 |pmid=17616766 |pmc=2729090 }}</ref> 

An exponent of 5/2 or 2.5 was proposed by Quetelet in the 19th century:<ref name=":0">Quetelet A. A Treatise on Man and the Development of his Faculties</ref>
<blockquote>In general, we do not err much when we assume that during development the squares of the weight at different ages are as the fifth powers of the height</blockquote>

This exponent of 2.5 is used in a revised formula for Body Mass Index, proposed by [[Nick Trefethen]], Professor of numerical analysis at the [[University of Oxford]],<ref name = "Trefethen">{{cite web| vauthors = Trefethen N |title=New BMI (Body Mass Index)|url=https://people.maths.ox.ac.uk/trefethen/bmi.html|website=Ox.ac.uk|publisher=Mathematical Institute, [[University of Oxford]]|access-date=5 February 2019}}</ref> which minimizes the distortions for shorter and taller individuals resulting from the use of an exponent of 2 in the traditional BMI formula:

<math display="block">\mathrm{BMI}_\text{new} = 1.3 \times \frac{\text{mass}_\text{kg}}{\text{height}_\text{m}^{2.5}}</math>

The scaling factor of 1.3 was determined to make the proposed new BMI formula align with the traditional BMI formula for adults of average height, while the exponent of 2.5 is a compromise between the exponent of 2 in the traditional formula for BMI and the exponent of 3 that would be expected for the scaling of weight (which at constant density would theoretically scale with volume, i.e., as the cube of the height) with height. In Trefethen's analysis, an exponent of 2.5 was found to fit empirical data more closely with less distortion than either an exponent of 2 or 3.

===BMI prime (exponent of 2, normalization factor)===
BMI Prime, a modification of the BMI system, is the ratio of actual BMI to upper limit optimal BMI (currently defined at 25&nbsp;kg/m<sup>2</sup>), i.e., the actual BMI expressed as a proportion of upper limit optimal. BMI Prime is a [[dimensionless number]] independent of units. Individuals with BMI Prime less than 0.74 are underweight; those with between 0.74 and 1.00 have optimal weight; and those at 1.00 or greater are overweight. BMI Prime is useful clinically because it shows by what ratio (e.g. 1.36) or percentage (e.g. 136%, or 36% above) a person deviates from the maximum optimal BMI.

For instance, a person with BMI 34&nbsp;kg/m<sup>2</sup> has a BMI Prime of 34/25 = 1.36, and is 36% over their upper mass limit. In South East Asian and South Chinese populations (see [[#International variations|§ international variations]]), BMI Prime should be calculated using an upper limit BMI of 23 in the denominator instead of 25. BMI Prime allows easy comparison between populations whose upper-limit optimal BMI values differ.<ref>{{cite journal | vauthors = Gadzik J | title = 'How much should I weigh?'--Quetelet's equation, upper weight limits, and BMI prime | journal = Connecticut Medicine | volume = 70 | issue = 2 | pages = 81–88 | date = February 2006 | pmid = 16768059 }}</ref>

===Waist circumference===
{{Main|Waist-to-height ratio|Waist-to-hip ratio}}
Waist circumference is a good indicator of [[visceral fat]], which poses more health risks than fat elsewhere. According to the U.S. [[National Institutes of Health]] (NIH), waist circumference in excess of {{cvt|1020|mm}} for men and {{cvt|880|mm}} for (non-pregnant) women is considered to imply a high risk for type 2 diabetes, [[dyslipidemia]], [[hypertension]], and [[cardiovascular disease]] CVD. Waist circumference can be a better indicator of obesity-related disease risk than BMI. For example, this is the case in populations of Asian descent and older people.<ref>{{cite web |title=Obesity Education Initiative Electronic Textbook – Treatment Guidelines |url=http://www.nhlbi.nih.gov/health-pro/guidelines/current/obesity-guidelines/e_textbook/txgd/4142.htm |url-status=live |archive-url=https://web.archive.org/web/20170501084223/https://www.nhlbi.nih.gov/health-pro/guidelines/current/obesity-guidelines/e_textbook/txgd/4142.htm |archive-date=1 May 2017 |access-date=29 July 2016 |website=US National Institutes of Health}}</ref> {{cvt|940|mm}} for men and {{cvt|800|mm}} for women has been stated to pose "higher risk", with the NIH figures "even higher".<ref>{{cite web|url=http://www.nhs.uk/chq/Pages/849.aspx?CategoryID=51|title=Why is my waist size important?|website=UK HNS Choices|access-date=29 July 2016|url-status=live|archive-url=https://web.archive.org/web/20160806210351/http://www.nhs.uk/chq/Pages/849.aspx?CategoryID=51|archive-date=6 August 2016}}</ref>

Waist-to-hip circumference ratio has also been used, but has been found to be no better than waist circumference alone, and more complicated to measure.<ref>{{cite web|url=https://www.hsph.harvard.edu/obesity-prevention-source/obesity-definition/abdominal-obesity/|title=Waist Size Matters|website=Harvard School of Public Health|date=2012-10-21|access-date=29 July 2016|url-status=live|archive-url=https://web.archive.org/web/20160821092935/https://www.hsph.harvard.edu/obesity-prevention-source/obesity-definition/abdominal-obesity/|archive-date=21 August 2016}}</ref>

A related indicator is waist circumference divided by height. A 2013 study identified critical threshold values for [[waist-to-height ratio]] according to age, with consequent significant reduction in life expectancy if exceeded. These are: 0.5 for people under 40 years of age, 0.5 to 0.6 for people aged 40–50, and 0.6 for people over 50 years of age.<ref>{{cite web | author = HospiMedica International staff writers |url=http://www.hospimedica.com/critical-care/articles/294746805/waist-height-ratio-better-than-bmi-for-gauging-mortality.html |title=Waist-Height Ratio Better Than BMI for Gauging Mortality |date=18 Jun 2013 |access-date=7 April 2016 |url-status=live |archive-url=https://web.archive.org/web/20160417064352/http://www.hospimedica.com/critical-care/articles/294746805/waist-height-ratio-better-than-bmi-for-gauging-mortality.html |archive-date=17 April 2016 }}</ref>

=== Surface-based body shape index ===
The Surface-based Body Shape Index (SBSI) is far more rigorous and is based upon four key measurements: the [[body surface area]] (BSA), vertical trunk circumference (VTC), waist circumference (WC) and height (H). Data on 11,808 subjects from the National Health and Human Nutrition Examination Surveys (NHANES) 1999–2004, showed that SBSI outperformed BMI, waist circumference, and [[Body Shape Index|A Body Shape Index]] (ABSI), an alternative to BMI.<ref>{{Cite web | vauthors = Pomeroy R | date = 29 December 2015 |title = A New Potential Replacement for Body Mass Index {{!}} RealClearScience|url = http://www.realclearscience.com/journal_club/2015/12/30/a_new_potential_replacement_for_body_mass_index_109492.html|website = realclearscience.com|access-date = 2015-12-31|url-status=live|archive-url = https://web.archive.org/web/20160101113606/http://www.realclearscience.com/journal_club/2015/12/30/a_new_potential_replacement_for_body_mass_index_109492.html|archive-date = 2016-01-01}}</ref><ref name="rahman2015">{{cite journal | vauthors = Rahman SA, Adjeroh D | title = Surface-Based Body Shape Index and Its Relationship with All-Cause Mortality | journal = PLOS ONE | volume = 10 | issue = 12 | pages = e0144639 | year = 2015 | pmid = 26709925 | pmc = 4692532 | doi = 10.1371/journal.pone.0144639 | bibcode = 2015PLoSO..1044639R | doi-access = free }}</ref>

<math display="block">\mathrm{SBSI} = \frac{(\text{H}^{7/4})(\text{WC}^{5/6})}{\text{BSA VTC}}</math>

A simplified, dimensionless form of SBSI, known as SBSI<sup>*</sup>, has also been developed.<ref name="rahman2015" />

<math display="block">\mathrm{SBSI^\star} = \frac{(\text{H}^2)(\text{WC})}{\text{BSA VTC}}</math>

===Modified body mass index===
Within some medical contexts, such as [[familial amyloid polyneuropathy]], serum albumin is factored in to produce a modified body mass index (mBMI). The mBMI can be obtained by multiplying the BMI by [[human serum albumin|serum albumin]], in grams per litre.<ref>{{cite journal|vauthors=Tsuchiya A, Yazaki M, Kametani F, Takei Y, Ikeda S|date=April 2008|title=Marked regression of abdominal fat amyloid in patients with familial amyloid polyneuropathy during long-term follow-up after liver transplantation|journal=Liver Transplantation|volume=14|issue=4|pages=563–570|doi=10.1002/lt.21395|pmid=18383093|doi-access=|s2cid=13072583}}</ref>