### INTRODUCTION

### METHODS

### 1. Participants

### 2. Reference material: European Spine Phantom (ESP)

^{2}, 0.990 g/cm

^{2}, and 1.499 g/cm

^{2}, respectively. The phantom's main body consisted of a water-equivalent resin and three inserts containing varying amounts of calcium hydroxyapatite to cover the full physiological range of spongious and cortical bone densities for all age groups. The container was 260 mm long, 180 mm wide, and 110 mm in height.[61011]

### 3. DXA

### 4. Improving traceability in the spine BMD measurement process

### 5. Measurement uncertainty

### 6. Modeling the measurement

##### (2)

${\scriptscriptstyle \mathit{u}\left({\mathit{X}}_{\mathit{i}}\right)\left\{\begin{array}{c}\mathit{u}\left({\mathit{X}}_{\mathit{\text{cal}}}\right),\\ \mathit{u}\left({\mathit{X}}_{\mathit{\text{ESP}}}\right),\\ \mathit{u}\left({\mathit{X}}_{\mathit{\text{IQC}}}\right),\\ \mathit{u}\left({\mathit{X}}_{\mathit{\text{IP}}}\right),\end{array}\right.}$*(Cal, calibration curve; ESP, European Spine Phantom; IQC, internal quality control; Res, resolution; IP, inspector precision)*

_{ESP}, X

_{IQC}, and X

_{IP}(2). Standard uncertainty and combined uncertainty of measurement were also calculated.

### 7. Measurements of standard uncertainty

### 8. Standard uncertainty of calibration curve

##### (3)

${\scriptscriptstyle {\mathit{U}}_{\mathit{c}}\left(\mathit{C}\mathrm{0}\right)=\frac{\mathit{s}}{{\mathit{B}}_{\mathrm{1}}}\sqrt{\frac{\mathrm{1}}{\mathit{P}}+\frac{1}{\mathit{n}}+\frac{{\left(\mathit{C}\mathrm{0}-\stackrel{-}{\mathit{C}}\right)}^{\mathrm{2}}}{{\mathit{S}}_{\mathit{\text{XX}}}}}}$*(Uc, standard uncertainty of calibration curve; C0, indicated value of equipment; s, standard deviation of residual; P, number of repeated measurements in BMD; n, number of repeated measurements in standard reference; Sxx, residual sum of squares of standard reference; C, mean of standard reference; B1, slope of calibration curve)*

### 9. Standard uncertainty of other uncertainty sources

##### (4)

${\scriptscriptstyle {\mathrm{U}}_{\mathrm{\text{ESP}}}=\mathrm{\text{accuracy of certified ESP value}}/\sqrt{\mathrm{3}}}$##### (6)

${\scriptscriptstyle {\mathrm{U}}_{\mathrm{\text{IP}}}=\sqrt{\left({\left(\mathit{\text{SD}}\left(\mathrm{1}\right)\right)}^{\mathrm{2}}+{\left(\mathit{\text{SD}}\left(\mathrm{2}\right)\right)}^{2}+\dots +{\left(\mathit{\text{SD}}\left(\mathrm{15}\right)\right)}^{\mathrm{2}}\right)/\mathrm{15}}}$### 10. Combined standard uncertainty

### 11. Coverage factor (k)

*V*, which was measured by using the Welch-Satterthwaite formula (9).[1516]

_{eff}