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Body mass index (BMI) can be considered an application of a power law model to express body weight independently of height. Based on the same power law principle, we previously introduced a body shape index (ABSI) to be independent of BMI and height. Here, we develop a new hip index (HI) whose normalized value is independent of height, BMI, and ABSI. Similar to BMI, HI demonstrates a U-shaped relationship to mortality in the Third National Health and Nutrition Examination Survey (NHANES III) population. We further develop a new anthropometric risk index (ARI) by adding log hazard ratios from separate nonlinear regressions of the four indicators, height, BMI, ABSI, and HI, against NHANES III mortality hazard. ARI far outperforms any of the individual indicators as a linear mortality predictor in NHANES III. The superior performance of ARI also holds for predicting mortality hazard in the independent Atherosclerosis Risk in Communities (ARIC) cohort. Thus, HI, along with BMI and ABSI, can capture the risk profile associated with body size and shape. These can be combined in a risk indicator that utilizes complementary information from height, weight, and waist and hip circumference. The combined ARI is promising for further research and clinical applications.

Body mass index (BMI) (weight

BMI traces back to the pioneering 1800s statistician Quetelet, who postulated a power-law relationship between height and weight [

Hip circumference (HC) and derived measures such as waist to hip ratio (WC/HC, WHR) have also been studied extensively as risk factors [

In general, comparisons of various indices based on

Here, we propose a new approach to transform

We use nonlinear (penalized spline) regression with data from the Third National Health and Nutrition Examination Survey (NHANES III), a United States (USA) general population sample with some 20 years of follow-up for mortality, to estimate a functional relationship between each indicator and mortality hazard within the Cox proportional hazard framework. ARI is formed by summing the estimated logarithms of hazard ratios due to each of the independent indicators and constitutes a linear predictor for logarithm of mortality hazard. We demonstrate that ARI is transferable beyond the cohort in which it is developed by applying it to mortality outcomes of a different USA cohort study, Atherosclerosis Risk in Communities (ARIC). The ARI approach developed here could be applied to produce risk indices for various conditions that make maximum use of readily obtained body measurements for research and clinical decision-making.

We analyzed data from the NHANES III and ARIC studies. The NHANES III and ARIC protocols were approved by the NHANES Institutional Review Board and the University of North Carolina at Chapel Hill Office of Human Research Ethics, respectively, and all participants gave written informed consent [

NHANES III sampled the civilian noninstitutionalized USA population using a cluster approach, with some groups of public health interest (children, the elderly, and black and Mexican-American people) deliberately oversampled [

The ARIC cohort component sampled 4,000 adults (age 45–64) in each of the 4 USA communities during 1987–1989 to study correlates of heart disease risk [

Except where otherwise specified, we used the provided sample weights [

Cox proportional hazard modeling [

Correlations of body measures in NHANES III.

Height | Weight | BMI | WC | HC | ABSI | WHR | HI | |
---|---|---|---|---|---|---|---|---|

Height | 1 | 0.486 | −0.010 | 0.213 | 0.079 | 0.074 | 0.252 | −0.528 |

Weight | 0.360 | 1 | 0.863 | 0.872 | 0.821 | 0.115 | 0.413 | −0.251 |

BMI | −0.011 | 0.919 | 1 | 0.876 | 0.905 | 0.083 | 0.413 | 0.021 |

WC | 0.152 | 0.904 | 0.905 | 1 | 0.791 | 0.506 | 0.736 | −0.154 |

HC | 0.247 | 0.933 | 0.903 | 0.867 | 1 | 0.040 | 0.173 | 0.319 |

ABSI | 0.059 | 0.028 | 0.007 | 0.385 | 0.030 | 1 | 0.777 | −0.132 |

WHR | −0.056 | 0.415 | 0.468 | 0.699 | 0.260 | 0.717 | 1 | −0.599 |

HI | 0.016 | 0.034 | 0.031 | 0.028 | 0.356 | 0.030 | −0.459 | 1 |

Correlation coefficients for body measures among NHANES III nonpregnant adults. The upper-right triangle of the table shows correlations of the raw values, while the lower-left triangle shows correlations of the

Correlations of body measures in ARIC.

Height | Weight | BMI | WC | HC | ABSI | WHR | HI | |
---|---|---|---|---|---|---|---|---|

Height | 1 | 0.471 | −0.053 | 0.165 | 0.009 | 0.031 | 0.279 | −0.560 |

Weight | 0.322 | 1 | 0.851 | 0.862 | 0.793 | 0.048 | 0.525 | −0.308 |

BMI | −0.067 | 0.747 | 1 | 0.882 | 0.900 | 0.038 | 0.429 | −0.015 |

WC | 0.089 | 0.706 | 0.894 | 1 | 0.821 | 0.455 | 0.724 | −0.113 |

HC | 0.191 | 0.790 | 0.893 | 0.855 | 1 | 0.070 | 0.205 | 0.307 |

ABSI | 0.059 | −0.009 | 0.041 | 0.450 | 0.082 | 1 | 0.691 | 0.038 |

WHR | −0.057 | 0.287 | 0.493 | 0.733 | 0.284 | 0.724 | 1 | −0.571 |

HI | 0.010 | 0.009 | −0.049 | −0.009 | 0.317 | 0.088 | −0.442 | 1 |

The same as Table

Both linear and nonlinear associations with mortality hazard were modeled for each index for both NHANES III and ARIC and compared to a baseline model with only sex and race as predictors. In the linear proportional hazard models, death rate increases or decreases by a constant factor per standard deviation change in the index (unit change in

The main measure of relative model performance was AIC difference score,

Nonlinear modeling for mortality hazard associated with each anthropometric index yielded functions for the natural logarithm of the estimated hazard for different values of the

While the ARIC cohort was on average older than NHANES III or the national adult population, the groups had fairly similar body measurements on initial examination, with most individuals in the overweight or obese BMI ranges (Table

NHANES III and ARIC means.

NHANES III | NHANES III (weighted) | ARIC | |
---|---|---|---|

Number | 16034 | 14917 | |

Deaths | 4897 | 4829 | |

% female | 52 | 51 | 51 |

% black | 28 | 11 | 24 |

Age (y) | 43 (30–63) | 41 (30–57) | 54 (49–59) |

Height (cm) | 166 (159–174) | 168 (161–176) | 168 (161–176) |

Weight (kg) | 73 (63–85) | 73 (62–85) | 78 (67–89) |

BMI (kg m^{−2}) | 26 (23–30) | 25 (22–29) | 27 (24–30) |

WC (cm) | 92 (82–102) | 90 (80–101) | 96 (88–105) |

HC (cm) | 99 (93–106) | 99 (93–106) | 103 (98–109) |

WHR | 0.92 (0.85–0.98) | 0.91 (0.84–0.97) | 0.94 (0.88–0.98) |

ABSI ( | 0.0803 (0.0764–0.0841) | 0.0798 (0.0761–0.0834) | 0.0823 (0.0792–0.0852) |

HI (cm) | 100 (96–105) | 100 (96–105) | 102 (98–106) |

Comparison of demography and body measurements in the NHANES III and ARIC cohorts. For age and for body measurements, medians and interquartile ranges are given. For NHANES III, frequencies and quantiles were also calculated with the sample weights given to better represent the national population.

Mortality hazard association with body measures in NHANES III.

Predictor | Hazard ratio per SD increase | | | |
---|---|---|---|---|

ARI (linear) | 1.46 (1.41–1.52) | 0 | 0.065 | 0.615 |

BMI (nonlinear) | 187.2 | 0.046 | 0.591 | |

ABSI (nonlinear) | 247.3 | 0.036 | 0.585 | |

ABSI (linear) | 1.16 (1.12–1.20) | 256.4 | 0.034 | 0.584 |

HI (nonlinear) | 314.6 | 0.028 | 0.567 | |

BMI (linear) | 1.07 (1.04–1.10) | 326.4 | 0.025 | 0.570 |

| 327.5 | 0.027 | 0.569 | |

| 0.96 (0.93–0.99) | 336.4 | 0.024 | 0.562 |

None | 342.8 | 0.023 | 0.555 | |

HI (linear) | 0.99 (0.96–1.02) | 343.9 | 0.023 | 0.558 |

Results of Cox proportional hazard modeling for mortality risk in NHANES III with

SD: standard deviation;

Mortality hazard association with body measures in ARIC.

Predictor | Hazard ratio per SD increase | | | |
---|---|---|---|---|

ARI (linear) | 1.43 (1.38–1.49) | 0 | 0.103 | 0.622 |

ABSI (linear) | 1.26 (1.22–1.30) | 86.0 | 0.093 | 0.616 |

ABSI (nonlinear) | 86.4 | 0.093 | 0.616 | |

BMI (nonlinear) | 121.9 | 0.090 | 0.613 | |

HI (nonlinear) | 221.5 | 0.078 | 0.606 | |

BMI (linear) | 1.11 (1.08–1.15) | 277.3 | 0.070 | 0.601 |

HI (linear) | 0.92 (0.89–0.95) | 294.4 | 0.067 | 0.602 |

| 0.96 (0.93–0.99) | 312.0 | 0.065 | 0.596 |

None | 317.4 | 0.064 | 0.593 | |

| 318.8 | 0.066 | 0.597 |

The same as Table

In nonlinear (penalized spline) regression models, BMI and HI showed asymmetric U-shaped associations with mortality in both cohorts, while associations with

Estimated mortality hazard ratios in NHANES III and ARIC as nonlinear (penalized spline) functions of normalized (a) height, (b) BMI, (c) ABSI, and (d) HI. Dashed lines indicate 95% confidence intervals. Percentiles and

In NHANES III, ARI was a significantly better linear predictor than any of the (linear or nonlinear) models based on individual indicators (

The difference in optimum BMI found between the NHANES III and ARIC cohorts, on the one hand, and the more recently enrolled NHANES 1999–2004 cohort, on the other hand [

Previously, anthropometric indices have not included all four of the measurements

Although our ARI is a substantially better predictor of mortality risk than any of the individual anthropometric indices tested, its absolute predictive value is modest for the cohorts and follow-up periods tested: the measure of explained variation

Commonly, WC but not HC is measured. In such cases, ARI could be modified to sum only risk due to the indicators

One potential drawback of ARI as calculated from cohorts such as NHANES III is that it is not a simple function of

The work presented here has several limitations that could be addressed in future studies. The quality of the mortality follow-up information from NHANES III and ARIC has not been, to our knowledge, rigorously verified, raising the possibility of some bias in the estimated risks, although the consistency across the two cohorts of the associations of mortality with initially measured anthropometric variables is reassuring. The data we use here is only from USA. It is likely that the NHANES III derived ARI should be modified for application to non-USA populations [

The approach used to compute ARI here for hazard of all-cause mortality could also be extended to derive risk indices customized for specific causes of death and morbidity outcomes such as heart disease, stroke, or diabetes, which could facilitate individualized cost-benefit consideration in deciding what medical interventions to undertake [

We derived and tested a combined anthropometric risk index that takes into account multiple body measurements to arrive at a risk score that outperforms the individual indices previously used. The allometry-inspired methodology used to arrive at the components of this index can potentially be applied to define mutually independent indices from a broad range of biometric and other variables and has the potential to help elucidate the findings from association and observational studies.

The authors declare that they have no competing interests.

This work was partly supported by PSC-CUNY Award 68346-00 46 to Nir Y. Krakauer.