Validation of the Broca index as the most practical method to calculate the ideal body weight

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Research Article
Journal of Clinical Investigation and Studies
J Clin Invest Stud, 2018 doi: 10.15761/JCIS.1000105 Volume 1(1): 1-4
ISSN: 2631-4002
Validation of the Broca index as the most practical method
to calculate the ideal body weight
Weber-Sanchez Alejandro1*, Velázquez Ortega Sofía2 and Weber-Álvarez Pablo3
1General Surgery Department, Hospital Ángeles Lomas, México
2Nutriologist, Hospital Angeles Lomas, México
3General Physician, Hospital Angeles Lomas, México
Abstract
Ideal body weight (IBW) calculation is useful in clinical practice, but most of the formulas to calculate it are complicated. Broca index (BI) is still a simple and
eective method to determine IBW although seems to be abandoned. Our objective is to verify validity of BI compared with Hammond and Robinson formulas,
and with IBW calculated from ideal body mass index (BMI) (22.5kg/m2) in a population. We made a correlational study from 400 patients of nutrition and surgery
consult, from 2010 to 2015. Patients were classied according to their BMI in group A <30kg/m2 and B ≥30kg/m2. Age, sex, height and weight, were recorded to
calculate IBW with Hammond, Robinson and BI formulas and the IBW calculated from ideal BMI. we analyzed, statistical signicance with student’s t test, Pearson
coecient and linear regression. Of the 400 patients, 221 were group A, 49.7% men, and 50.3% women. Average age, height, actual weight and actual BMI were
38.9years-old, 167cm, 67.6kg, and 24.1kg/m2 respectively; and group B, 179 patients; 44.6% men, 55.4% women. Average age, height and actual weight, and actual
BMI were 38.4years-old, 168cm, 112.3kg and 39.7kg/m2 respectively.
Both groups showed normal distribution. When comparing IBW using BI, with the other formulas analysed with t-test, result was signicant in all (p 0.000).
Utilizing Pearson coecient also all showed signicance (p 0.000) for both groups. Linear regression with Hammond, Robinson formulas and weight calculated from
ideal BMI showed relationship of 95.7%, 96.5% and 99.8% respectively and between the 4 IBW formulas together, 100% relationship for both groups.
BI seems to oer the same accuracy as other more complex formulas for the calculation of the IBW. BI continues to have validity and utility in clinical practice, so we
promote it as a useful clinical tool because of its simplicity.
*Correspondence to: Alejandro Weber Sánchez, MD, Vialidad de la Barranca
s/n C410, Valle de las Palmas, Huixquilucan, 52763, Estado de México, México,
Tel: 52469527; E-mail: awebersanchez@gmail.com
Key words: body mass index, weight calculation, weight equations, weight
formulas
Received: June 07, 2018; Accepted: June 14, 2018; Published: June 19, 2018
Introduction
Weight and height are the simplest, practical and most common
anthropometric measures to initially assess the general nutritional
status and ideal body weight (IBW) patients should have, and are
useful in clinical practice, particularly for the general physician.
ere are many formulas to calculate the IBW, most of them are
complicated and require charts or calculators. e Broca index (BI)
(height in centimeters-100=IBW) despite having more than 100 years
of formulated, is still a valid and eective method to determine IBW
with the benet of its simplicity although nowadays seems to be
abandoned.
e body mass index (BMI) has been used since the seventies as the
main criteria to dene the desirable range of weight according to the
constitution of the patient, and it is used as an indicator of the severity
of obesity with implications in morbidity and mortality. e IBW
calculated with BI correlates with the weight calculated from ideal BMI
of 22.5 kg/m2 associated with the lowest mortality rate, which makes it
a useful tool, easy to obtain in clinical practice [1].
Objective
Verify the validity and utility of the BI to determine IBW compared
with Hammond and Robinson formulas, and with the weight calculated
from ideal BMI (22.5kg/m2) [2], both in non- obese patients (BMI < 30
kg / m2) and obese patients (≥ 30 kg/m2).
Hypothesis
e IBW calculated with BI, adequately correlates with Hammond
and Robinson formulas, and with the weight calculated from ideal BMI
(22.5kg / m2).
Material and methods
is is a retrospective, observational, correlational and descriptive
study obtained from the clinical records of 400 patients of a nutrition
and bariatric surgery consult of our medical group, collected from
January 01, 2010 to December 31, 2015. e patients were classied in
two groups according to the BMI, patients with BMI < 30 kg/m2 (group
A) and patients with BMI ≥ 30 kg/m2 (group B). Microso® Excel v.
15.23 was used to register the following variables: age, sex, height (cm),
weight (kg), and to perform calculations of the Hammond, Robinson,
BI and weight calculated from ideal BMI (22.5kg / m2). Statistical
package for Social Sciences SPSS v. 21 was used to analyze data from
both groups separately and verify their normal distribution according

Weber-Sánchez A (2018) Validation of the Broca index as the most practical method to calculate the ideal body weight
Volume 1(1): 2-4
J Clin Invest Stud, 2018 doi: 10.15761/JCIS.1000105
to the Kolmogorov-Smirno test. Independent samples t test was used
to compare the BI (height cm - 100) with Hammond’s equation IBW=
(48kg for 150cm) + 1.1 kg/cm for men and (45kg for 150cm) + 0.9kg/
cm for women; Robinson’s equation IBW= (50kg + 0.75) X height cm
-152.4 for men and (45.5Kg + 0.67) X height cm -152.4 for women; and
with the IBW calculated from ideal BMI (22.5kg/m2) for both group A
and B, considering p<0.05 signicant. Pearson correlation coecient
and linear regression analysis were also utilized to investigate BI relation
with the other three formulas. We also analyzed Pearson correlation for
both groups separated by sex and height.
Results
Of the total population of 400 patients, 221 were assigned to group
A, of which 110 where men (49.7%) and 111 women (50.3%) with an
average age of 38.9 years old (range 19 to 66), average height of 167cm
(range 133 to 190) DS 0.09. In group B, there were 179 patients; 80 men
(44.6%) and 99 women (55.4%) with an average age of 38.4 (range of
15 to 70), average height of 168cm (range 152 to 194cm) DS 0.08. e
average of the patient´s actual weight in group A was 67.6kg DS 11.3,
and an average of actual BMI of 24.1kg/m2 DS 2.8. Group B had an
average of 112.3kg of actual weight SD 21.9, and average of actual BMI
of 39.7kg/m2 SD 5.8.
Both groups showed a normal distribution according to the
Kolmogorov-Smirno test for both weight and height. When
comparing the calculated IBW obtained using BI, with the IBW
obtained from the Hammond and Robinson’s equations, as well as with
the weight calculated from ideal BMI (22.5kg / m2) analysed with the
student's t-test for related samples, the result was signicant in all (p
0.000). Utilizing Pearson correlation coecient to contrast the BI with
the other formulas, also all showed statistical signicance (p 0.000) for
both groups, when analysed by sex and height in both groups separately
the signicance was also p 0.000.
With linear regression analysis, the BI compared with Hammond’s
equation showed a relationship of 95.7%, with Robinson’s 96.5% and
with the weight calculated from ideal BMI (22.5kg/m2) 99.8%. (Figures
1-3). e linear regression analysis between the 4 IBW formulas,
showed 100% relationship for both groups.
When compared considering dierent height ranges, <140cm, 141-
150, 151-160, 161-170, 171-180, >1.81 we found no dierences between
both groups, but minor ranges of height tend to have less correlation
with BI, and the ranges >160cm has a correlation higher than 50%.
Discussion
e most commonly used anthropometric measures used in
clinical practice to initially assess the nutritional status of an individual,
are weight and height. ey are simple, practical and easily obtained.
e calculation of the IBW of a patient has been searched for a long
time. In the middle of the 19th century, Quetelet, a Belgium astronomist,
developed an index showing that the body weight in adults was related
to the quadrate height in a constant relationship. A few years later in
1871 a French surgeon, Pier Broca, pioneer in physical anthropology
and known by his multiple works on the brain and cranial
Figure 1. Linear regression Boca’s Index and Hammond’s formula
Figure 2. Linear regression Boca’s Index and Robinson’s formula
Figure 3. Linear regression Boca’s Index and weight calculated with ideal BMI.

Weber-Sánchez A (2018) Validation of the Broca index as the most practical method to calculate the ideal body weight
Volume 1(1): 3-4
J Clin Invest Stud, 2018 doi: 10.15761/JCIS.1000105
anthropometry, introduced in clinical practice the index that bears his
name for the determination of this important parameter obtained in
adults empirically by subtracting 100cm from the patient's height [3-5].
Historically, the IBW was dened as the one associated with the
lowest mortality, which is why it has great importance. According to
the actuarial data of insurers obtained from the evaluation of weight
and height from a large healthy population, charts to obtain the IBW
were created. e rst documented table was published in 1913 by
Medico-Actuarial Mortality Investigation and subsequently in 1942 the
Metropolitan Life Insurance Company, released its own charts based
on longevity [6,7]. Because of their lack of practicality, these tables were
replaced by equations to estimate the ideal weight.
In 1963 and 1964, Hamwi [8] and Devine [9] developed and
published formulas to calculate IBW to obtain the adequate doses of
certain drugs according to it. Since then, several similar formulas and
equations have been created for the same purpose through regression
analysis of weight and height data like Robinson's [10] equation in 1983
developed with the same intention. In the same year, Miller et al. [11]
also formulated other equations based on Metropolitan Life Insurance
Company’s tables. More recently in 2000, Hammond [12] created a
metric system version from the Hamwi equation.
It was not until the end of the 1970s, when it was suggested that BMI
was preferable to other weight indexes to estimate the IBW [13]. Because
adult weight increases proportionally to the square of height, BMI has
a good correlation with fat mass with values of r 0.7 in population
studies. Gray’s paramount study in 1989 showed that in a population
of 750000 people, the BMI range between 20 to 25kg/m2 was the one
that correlated better with the lower mortality rate, and that it increased
exponentially as it increased, becoming more of 200% in patients with
BMI >40 kg/m2 [13-16]. erefore, BMI has also been used as criteria
to determine a desirable weight range and is internationally accepted
by both the World Health Organization (WHO) and the National
Institutes of Health (NIH), dening the dierent intervals to classify
patients as overweight, obesity I, II, morbid obesity or higher [16,17].
Any of the above-mentioned equations so far, as well as the ideal
BMI can be used to calculate the IBW, however, they are not easy to use
in daily clinical practice without a calculator and consumes time.
Some authors emphasize that a deeper analysis in this regard should
be done, and that we should forget both the IBW and the BMI because
of the disadvantage that they do not distinguish fat mass from fat-free
mass [12], however, studies that analyze body composition and give us
this data, are more expensive and are not available in everyday clinical
practice.
Shan et al. [1], compiled a list of IBW formulas used to evaluate
the relationship between height-weight tables and IBW equations, and
to determine which formula or table t best within the BMI of 22 kg/
m2 using linear regression and correlations, nding that most of the
slopes of the formulas fall between BMI range of 20 to 25 kg/m2, with
dierences between men and women, therefore, they proposed that
formulas could be used as a guide to asses body weight rather than
assessing weight from various height-weight tables.
Our study was aimed to assess the validity of the BI. We wanted
to know if there were dierences between Hammond and Robinson
equations and the weight calculated from ideal BMI of 22.5 kg/m2, and to
asses if there were dierences between obese and non-obese population,
as well as between men and women and dierent ranks of height, so we
divided the patients into two groups accordingly to their BMI greater
or less than 30kg/m2 and analyzed the data separately between men
and women and dierent ranges of height and to verify if there was
dierence between these groups in healthy adults. We did not include
children since the utility of this index is limited to the adult population.
Comparing the BI with the other three formulas used in this study,
the comparative analysis using the t-student statistic and Pearson's
correlation had statistical signicance in both groups (p 0.000). When
using linear regression, comparing all the mentioned formulas, a value
of 100% (R2 1,000) was obtained, which seems to corroborate that the
BI has the same accuracy as the other three equations and can be used
for this propose with condence independently of weight, BMI and
height in adults. When we compared dierent height ranges we found
that BI higher ranges have more correlation than lower ones.
Conclusion
It seems that BI oers the same accuracy as other more complex
formulas such as Hammond and Robinson’s for the calculation of the
IBW, and also correlates well with the weight calculated from ideal BMI,
and that it continues to have validity and utility in clinical practice,
so we promote its use in clinical practice in view of its simplicity and
practicality.
Conict of interest
e authors involved in this investigation declare that they don’t
have conict of interest.
Author’s contributions
Dr. Alejandro Weber: Conception and design of the investigation.
Main author, principal reviewer and investigator. General supervisor.
Lic. Sofía Ortega: Investigator and reviewer, Acquisition of data
and analysis.
Dr. Pablo Weber Alvarez: Investigator and reviewer, Statistical
analysis and interpretation of data.
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Weber-Sánchez A (2018) Validation of the Broca index as the most practical method to calculate the ideal body weight
Volume 1(1): 4-4
J Clin Invest Stud, 2018 doi: 10.15761/JCIS.1000105
Copyright: ©2018 Weber-Sánchez A. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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