## 3 Results  
Of the 41 DRF patients recruited to participate in this study, 20 were included. Twenty-one were excluded because they had received conservative therapy; had bilateral fractures, cognitive decline, severe postoperative pain, or excessive anxiety; or they did not participate in follow-up (Figure 3). Ten patients were assigned to each group, six patients who were discharged within 6 days or complained of pain were excluded before analysis. We planned to re-recruit patients to the control group, but this plan was abandoned due to the coronavirus disease 2019 pandemic. The characteristics of the participants are shown in Table 2. All participants were women. No statistically significant difference was observed inthe radiographical parameters between the groups. In terms of severity, 75% (3/4 patients) and 50% (5/10 patients) of the control and Ghost groups, respectively, were categorized as class C, the most severe category, according to the AO classification (Table 2). As a result of the therapy, improvements were observed in the arcs of motions in the Ghost and control groups during the treatment course (Supplementary File S1). The bootstrap data resampled from actual data are represented in Table 3. ANCOVA revealed a significant interaction between group and time course with the arc of motion as the dependent variable, stratified by age and BMI (F = 108.29, df = 6, \(p\) < 0.001, \(\eta^{2}\) = 0.003, Figure 4). The probability of recovery of wrist flexion-extension RoM from day 14 to 82 was greater in the Ghost group (75.8 \(\pm\) 3.9 to 136.2 \(\pm\) 6.1\({}^{\circ}\)) than in the control group (74.1 \(\pm\) 6.4 to 141.3 \(\pm\) 3.7\({}^{\circ}\), mean difference = 1.9 to 11.4\({}^{\circ}\), \(p_{Bonferroni}\) < 0.001, Table 4). In the stratified analysis, a larger likelihood of improvement was found in young patients than in old patients (F = 722.23, df = 3, \(p\) < 0.001, \(\eta^{2}\) = 0.002, Figure 5). The arc of motion of the Ghost group was larger than that in the control group in patients with normal and low BMI (\(p_{Bonferroni}\) < 0.001, Figure 6). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Characteristics**} & \multicolumn{2}{c}{**Ghost Group, \(n\) = 10**} & \multicolumn{1}{c}{**Control Group, \(n\) = 4**} \\  & \multicolumn{2}{c}{**(Vibration with Visualization)**} & \multicolumn{2}{c}{**(Vibration Alone)**} \\ \hline Sex & Female:Male & 10:0 & 4:0 \\ Age (years) & & 76 \(\pm\) 10 & 69 \(\pm\) 9 \\ BMI (kg/m\({}^{2}\)) & & 23.0 \(\pm\) 4.9 & 22.1 \(\pm\) 5.6 \\ Affected side & Right:Left & 6 (4) & 0 (4) \\ Handedness & Right:Left & 10:0 & 4.0 \\ AO classification & & A, 3; B, 2; C, 5 & A, 0; B, 1; C, 3 \\ \hline \multirow{3}{*}{Radiographic parameters (mm)} & Volar tilt & 14.7 \(\pm\) 2.1 & 15.5 \(\pm\) 1.4 \\  & Radial tilt & 8.2 \(\pm\) 3.1 & 9.1 \(\pm\) 1.9 \\ \cline{1-1}  & Radial inclination & 0.9 \(\pm\) 0.8 & 1.4 \(\pm\) 0.4 \\ \hline \hline \end{tabular} BMI: body mass index, AO classification: Arbeitsgemeinschaft für Osteonymthesfragen/Orthopaedic Trauma Association fracture and dislocation classification.  
\end{table} 
Table 2: Characteristics of patients with distal radius fracture. Figure 3: Recruitment procedure for patients with DRF. DRF: distal radius fracture.