## Introduction

## Method

### Participants

### Study procedures

### Statistical analyses

^{2}, women: ≤ 0.12, and ≥ 1.025 g/cm

^{2}]). All analyses were conducted in the statistical environment R, with distributional regression models conducted using the GAMLSS package [24].

## Results

### Reliability

Variable | Women (n = 116,688) | Men (n= 100,065) |
---|---|---|

Age (year) | 57.8 (8.3) | 58.7 (8.6) |

Mass (kg) | 71.0 (14.0) | 85.4 (14.2) |

Height (cm) | 162.5 (6.3) | 175.7 (6.8) |

BMI group (%) | ||

Under-weight | 0.9% | 0.3% |

Normal-weight | 40.6% | 26.8% |

Over-weight | 36.0% | 49.0% |

Obese | 22.5% | 23.9% |

Heel BMD (g/cm ^{2}) | 0.52 (0.12) | 0.58 (0.14) |

Heel BMD T score | −0.53 (1.08) | 0.02 (1.28) |

BMD | BMD T score | BMD Z score | ||||

Men Sd of difference | 0.12 | 1.10 | 0.78 | |||

Women Sd of difference | 0.07 | 0.64 | 0.57 | |||

Variable | Regression coefficient (standard error) | P value | Regression coefficient (standard error) | P value | Regression coefficient (standard error) | P value |

Intercept | −2.8 (0.002) | <0.001 | −0.54 (0.002) | <0.001 | −0.74 (0.002) | <0.001 |

Sex (men) | 0.46 (0.003) | <0.001 | 0.50 (0.003) | <0.001 | 0.38 (0.003) | <0.001 |

Mean value | 0.49 (0.003) | <0.001 | 0.41 (0.003) | <0.001 | 0.48 (0.003) | <0.001 |

Age | 0.00 (0.003) | 0.359 | 0.00 (0.003) | 0.243 | 0.01 (0.003) | 0.040 |

BMD | BMD T score | BMD Z score | |
---|---|---|---|

Concordance percentages | |||

Same quartile | 64.3% | 64.2% | 64.3% |

Adjacent quartile | 31.7% | 31.8% | 31.7% |

Opposite quartile (1st vs. 3rd, 2nd vs. 4th) | 3.0% | 3.0% | 3.0% |

Opposite quartile (1st vs. 4th) | 1.0% | 1.0% | 1.0% |

### Validity

Variable | Women (n = 2621) | Men (n= 2387) |
---|---|---|

Age (year) | 61.2 (7.5) | 62.7 (7.5) |

Mass (kg) | 69.6 (13.2) | 84.5 (14.0) |

Height (cm) | 162.5 (6.3) | 176.0 (6.6) |

BMI group (%) | ||

Under-weight | 1.3% | 0.1% |

Normal-weight | 43.9% | 29.3% |

Over-weight | 35.3% | 50.5% |

Obese | 19.5% | 20.1% |

DXA total body BMD (g/cm2) | 1.13 (0.13) | 1.30 (0.12) |

DXA Lumbar BMD (g/cm2) | 1.14 (0.18) | 1.26 (0.20) |

DXA Femur BMD (g/cm2) | 0.91 (0.14) | 0.99 (0.15) |

QUS BUA | 74.6 (15.8) | 85.7 (16.5) |

QUS SOS | 1550.7 (29.3) | 1564.3 (31.1) |

Heel BMD (g/cm2) | 0.53 (0.11) | 0.59 (0.12) |

Total BMD | Lumbar BMD | Femur BMD | |
---|---|---|---|

SOS (men) | r = 0.37 (0.33 to 0.42) n = 1250 | r = 0.31 (0.25 to 0.35) n = 1249 | r = 0.31 (0.26 to 0.36) n = 1261 |

SOS (women) | r = 0.44 (0.40 to 0.48) n = 1422 | r = 0.38 (0.33 to 0.42) n = 1413 | r = 0.37 (0.32 to 0.41) n = 1419 |

BUA (men) | r = 0.38 (0.33 to 0.43) n = 1250 | r = 0.29 (0.24 to 0.34) n = 1249 | r = 0.32 (0.27 to 0.37) n = 1261 |

BUA (women) | r = 0.40 (0.36 to 0.45) n = 1422 | r = 0.35 (0.31 to 0.40) n = 1413 | r = 0.35 (0.31 to 0.40) n = 1419 |

QUS BMD (men) | r = 0.39 (0.34 to 0.44) n = 1249 | r = 0.31 (0.26 to 0.36) n = 1248 | r = 0.33 (0.28 to 0.37) n = 1260 |

QUS BMD (women) | r = 0.43 (0.39 to 0.47) n = 1422 | r = 0.37 (0.33 to 0.42) n = 1413 | r = 0.37 (0.33 to 0.42) n = 1422 |

Total BMD vs. heel BMD Z scores | Lumbar BMD vs. heel BMD Z scores | Femur BMD vs. heel BMD Z scores | ||||

Men Sd of difference | 1.03 | 1.15 | 1.12 | |||

Women Sd of difference | 0.97 | 1.05 | 1.07 | |||

Variable | Regression coefficient (standard error) | P value | Regression coefficient (standard error) | P value | Regression coefficient (standard error) | P value |

Intercept | −0.17 (0.014) | <0.001 | −0.13 (0.014) | <0.001 | −0.11 (0.014) | <0.001 |

Sex (men) | 0.04 (0.020) | 0.076 | 0.06 (0.020) | 0.004 | 0.03 (0.020) | 0.134 |

Mean value | 0.13 (0.021) | <0.001 | 0.14 (0.020) | <0.001 | 0.02 (0.021) | 0.266 |

Age | −0.01 | 0.704 | −0.02 (0.020 | 0.270 | −0.01 (0.021) | 0.609 |

Diagnosis: total BMD | Diagnosis: lumbar BMD | Diagnosis: femur BMD | |
---|---|---|---|

Osteoporosis proportion diagnosed | 0.004 | 0.049 | 0.024 |

Osteoporosis sensitivity | 0.23 | 0.04 | 0.05 |

Osteoporosis specificity | 0.99 | 0.99 | 0.99 |

Osteoporosis PPV | 0.14 | 0.26 | 0.13 |

Osteoporosis NPV | 1.0 | 1.0 | 1.0 |

Osteopenia proportion diagnosed | 0.08 | 0.23 | 0.34 |

Osteopenia sensitivity | 0.62 | 0.40 | 0.37 |

Osteopenia specificity | 0.81 | 0.83 | 0.85 |

Osteopenia PPV | 0.21 | 0.42 | 0.57 |

Osteopenia NPV | 0.98 | 0.94 | 0.92 |

## Discussion

^{−2}for men and 0.07 g·cm

^{−2}for women indicating relatively small variation given central values of approximately 0.70 g·cm

^{−2}and maximum values of approximately 1.5 g·cm

^{−2}. In contrast, differences between left and right heel appeared large and potentially unsuitable when expressed in standardised units. When expressed as a Z score, the standard deviation of differences was equal to 0.78 for men and 0.57 for women. From these initial values, we should expect 95% of QUS BMD Z scores obtained from the left and right heel to vary between ± 1.1 (e.g., 1.96·√2

^{−1}·0.78) for men and ± 0.79 (e.g., 1.96·√2

^{−1}·0.57) for women [25]. However, results from distributional regression analyses identified the existence of heteroscedasticity, such that variation in all QUS BMD variables between the left and right heel were influenced by both sex and average value, with greater variation for men and participants with larger BMD values. Similarly, concordance analysis casted doubt upon the reliability of QUS BMD measurements when considering participants on standardised scales. The analyses identified that a substantive proportion of individuals (~35%) should be expected to change quartile ranking based upon measurement of the left and right heel. Collectively, these results indicate that, whilst the change in absolute measurement between the left and right heel may be reasonable, BMD measurements from a relatively homogenous middle-aged population are tight enough such that variation can induce substantive differences in any ranking type of assessment.

^{−1}·1.1). The upper bounds of this interval represent a large difference in the placement of a participant within a population, thus demonstrating poor criterion agreement. Additionally, analyses identified the presence of heteroscedasticity, such that those with higher DXA BMD values would experience greater variation in their QUS BMD Z scores. For example, a man with a DXA BMD Z score of 1.5 should expect standard deviation of difference scores of approximately 1.4 for total body or lumbar spine (Table 6) leading to QUS BMD Z scores expected to range between −0.4 and 3.4, further demonstrating poor agreement.