A Body Shape Index (ABSI) achieves better mortality risk stratification than alternative indices of abdominal obesity: results from a large European cohort

Abdominal and general adiposity are independently associated with mortality, but there is no consensus on how best to assess abdominal adiposity. We compared the ability of alternative waist indices to complement body mass index (BMI) when assessing all-cause mortality. We used data from 352,985 participants in the European Prospective Investigation into Cancer and Nutrition (EPIC) and Cox proportional hazards models adjusted for other risk factors. During a mean follow-up of 16.1 years, 38,178 participants died. Combining in one model BMI and a strongly correlated waist index altered the association patterns with mortality, to a predominantly negative association for BMI and a stronger positive association for the waist index, while combining BMI with the uncorrelated A Body Shape Index (ABSI) preserved the association patterns. Sex-specific cohort-wide quartiles of waist indices correlated with BMI could not separate high-risk from low-risk individuals within underweight (BMI < 18.5 kg/m2) or obese (BMI ≥ 30 kg/m2) categories, while the highest quartile of ABSI separated 18–39% of the individuals within each BMI category, which had 22–55% higher risk of death. In conclusion, only a waist index independent of BMI by design, such as ABSI, complements BMI and enables efficient risk stratification, which could facilitate personalisation of screening, treatment and monitoring.


Supplementary Note: Mathematical rational for Body Mass Index and A Body Shape Index
In the text below symbols and represent regression coefficients ( is the intercept) and numbers in square brackets [ref.] correspond to references in the main document.
A Body Shape Index (ABSI) is the logical complement of Body Mass Index (BMI), because they are both based on the principle of allometry. The main concept of allometry is that mathematical models of the type: describe the general rules according to which the size of individual body parts (represented by Y) changes proportional to the change in the overall size of an organism (represented by X) [23,24].
Model (1) is mathematically equivalent to a log-linear model: Body mass index (BMI) was originally derived from the following model [25]: Formula (3) determines the statistical rule according to which weight increases proportional to the increase in body size reflected in height, i.e. the rule determining how weight is scaled with height.
The residuals of model (3), i.e. the part of weight not explained by the theoretical rule, can be derived for each individual as the difference between log of measured weight (Weightmeasured) and log of weight predicted by formula (3) for an average individual with the same measured height (Heightmeasured): log(Weightmeasured) -log() -* log(Heightmeasured) Taking exponent from (4), to remove the log, and taking into account that: exp(*log(X)) = X  , transforms equation (4) to: Weightmeasured / (* Heightmeasured  ) The familiar formula for BMI can be derived from (5), taking into account that the coefficient  was estimated as 2 in the original study [25] and ignoring the coefficient , which is constant and does not alter the shape of the association of weight with height: BMI is, thus, a relative measure of general obesity, as it is proportional to the ratio of measured weight and weight theoretically predicted for an average individual with the same height.
Krakauer & Krakauer similarly used a log-linear allometric model to determine how waist circumference (WC) is scaled with weight and height in individuals participating in the National Health and Nutrition Examination Survey (NHANES) 1999(NHANES) -2004. They used a model similar to (3) to determine the theoretical rule describing how WC increases when body size increases due to an increase in weight and/or height: log(WC) = log() + * log(Weight) + * log(Height) The residuals of model (7), i.e. the part of WC not explained by the theoretical rule, can be derived for each individual as the difference between log of measured WC (WCmeasured) and log of WC predicted from formula (7) for an average individual with the same measured weight and height: Taking exponent from formula (8), to remove the log, and taking into account that: exp (*log(X) Supplementary Material for Christakoudi et al. (2020): Obesity indices and mortality in EPIC S3 +*log(Y)) = X  * Y  , gives a formula similar to (5): In the original study defining ABSI [22], the regression coefficients estimated from model (7) ABSI is, thus, a relative measure of abdominal obesity, as it is proportional to the ratio of measured WC and WC theoretically expected for an average individual with the same weight and height.
To express ABSI with respect to BMI, the right side of formula (10) can be simultaneously multiplied and divided by Height -4/3 . Taking into account that a multiplication with Height -4/3 is mathematically equivalent to a multiplication with (Height -2 ) 2/3 and a division by Height -4/3 is mathematically equivalent to a multiplication with Height 4/3 or Height 8/6 : ABSI = WC / [(Weight * Height -2 ) 2/3 * Height 8/6 * Height -5/6 ] Taking into account that BMI = Weight / Height 2 = Weight * Height -2 and consolidating the two terms for Height, results in a formula that illustrates the relationship between ABSI and BMI: Although formulas (10) and (12) are mathematically equivalent, formula (10) is more appropriate for calculating ABSI, as it uses two measured entities (Weight and Height) and, thus, minimises the rounding error which arises from using a calculated entity such as BMI.

Supplementary Fig. S1 Flow-diagram for participants included in the study
Each step up to the main analysis dataset shows sequential exclusions determined by data availability and quality. The boxes below the main dataset show the subgroups used for cross-classification according to the major risk factors for death, which could also influence obesity; n -number of individuals; d -number of deaths. WWI -Weight-adjusted Waist Index; Waist indices were categorised using sex-specific cohort-wide quartiles (see cut-offs in Supplementary Table S1); Bars -the width for waist indices is proportional to the number of individuals included in the corresponding waist quartile, colour-coded from white for the lowest to dark for the highest quartile; No waist -mortality estimates for the total BMI category, without further stratification according to a waist index; d -number of deaths recorded during the first 15 years of follow-up per BMI category; n -number of individuals per BMI category.

S9
Supplementary  Summaries -mean (standard deviation); Died -includes individuals who died during a given year; Survived -includes individuals who survived to the end of the corresponding year, which includes individuals who died in subsequent years; p-value -Wald test from a linear model regressing BMI on vital status at the end of each year, with adjustment only for study centre; p-value (age) -Wald test from a linear model regressing BMI on vital status at the end of each year, with adjustment for study centre and age at recruitment.