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Table 2 Treatment effects in terms of the difference in change using linear multilevel models to account for 15 subjects and 120 teeth, and relative treatment effects of the change in terms of the odds ratio of the body segment referred to the gingival segment using ordinal multilevel models

From: Assessing the effect of multibracket appliance treatment on tooth color by using electronic measurement

   Linear multilevel model (mixed model) Ordinal multilevel model
Change within gingival segment (S1) Change within body segment (S2) Treatment effect (difference in change) Relative treatment effect
Time points (95% CI) Change (95% CI) Coefficient (95% CI) P value Odds ratio (95% CI) P value
3D system
 Lightness T0 – T1 0.09 (−0.10–0.28) 0.12 (− 0.07–0.31) 0.025 (− 0.11–0.16) 0.716 1.08 (0.62–1.90) 0.780
 Lightness T1 – T2 0.04 (− 0.15–0.23) 0.02 (− 0.17–0.22) − 0.017 (− 0.15–0.12) 0.807 0.95 (0.54–1.66) 0.860
 Lightness T0 – T2 0.13 (0.02–0.25) 0.14 (0.02–0.26) 0.008 (− 0.11–0.12) 0.885 1.05 (0.57–1.94) 0.870
 Chroma T0 – T1 0.03 (−0.05–0.11) 0.01 (− 0.07–0.09) − 0.017 (− 0.09–0.06) 0.668 0.87 (0.51–1.49) 0.608
 Chroma T1 – T2 0.07 (−0.01–0.15) 0.08 (0.004–0.16) 0.017 (− 0.06–0.09) 0.648 1.16 (0.68–1.98) 0.587
 Chroma T0 – T2 0.10 (0.01–0.19) 0.10 (0.01–0.19) 0.000 (−0.7–0.07) 1.000 0.97 (0.56–1.69) 0.911
L* T0 – T1 0.34 (− 0.27–0.94) 0.40 (− 0.20–1.00) 0.066 (−0.41–0.54) 0.786 1.04 (0.65–1.66) 0.879
L* T1 – T2 0.03 (− 0.65–0.70) −0.004 (− 0.68–0.67) −0.033 (− 0.51–0.44) 0.889 0.83 (0.52–1.33) 0.436
L* T0 – T2 0.37 (− 0.001–0.73) 0.40 (0.03–0.77) 0.032 (−0.37–0.43) 0.873 0.92 (0.57–1.47) 0.726
C*ab T0 – T1 0.19 (− 0.43–0.81) 0.18 (− 0.44–0.80) −0.008 (− 0.48–0.47) 0.972 1.06 (0.66–1.69) 0.809
C*ab T1 – T2 0.42 (− 0.13–0.96) 0.29 (− 0.26–0.83) −0.129 (− 0.55–0.29) 0.543 0.85 (0.53–1.36) 0.498
C*ab T0 – T2 0.61 (0.19–1.03) 0.47 (0.05–0.89) −0.138 (− 0.51–0.23) 0.464 0.78 (0.49–1.25) 0.302
 ΔE T0 – T1 2.10 (1.50–2.69) 2.46 (1.86–3.05) 0.360 (− 0.16–0.89) 0.176 1.43 (0.88–2.33) 0.154
 ΔE T1 – T2 2.15 (1.64–2.66) 2.35 (1.84–2.86) 0.197 (−0.33–0.72) 0.460 1.23 (0.77–1.97) 0.392
 ΔE T0 – T2 1.80 (1.39–2.22) 1.86 (1.45–2.28) 0.062 (− 0.37–0.49) 0.777 1.11 (0.68–1.81) 0.688
 d(OM1) T0 – T1 0.38 (− 0.46–1.22) 0.42 (−0.41–1.26) 0.043 (− 0.56–0.65) 0.889 1.01 (0.63–1.61) 0.979
 d(OM1) T1 – T2 0.32 (− 0.48–1.12) 0.21 (−0.59–1.01) −0.11 (− 0.66–0.44) 0.691 0.92 (0.58–1.47) 0.739
 d(OM1) T0 – T2 0.70 (0.22–1.18) 0.63 (0.15–1.11) −0.068 (− 0.55–0.41) 0.781 0.96 (0.60–1.54) 0.882
2D system
L* T0 – T1 0.31 (− 0.17–0.80) 0.30 (− 0.19–0.78) −0.016 (− 0.35–0.32) 0.926 1.01 (0.63–1.60) 0.975
L* T1 – T2 0.06 (− 0.37–0.50) 0.05 (− 0.39–0.49) −0.012 (− 0.31–0.29) 0.936 0.91 (0.57–1.46) 0.704
L* T0 – T2 0.38 (− 0.03–0.78) 0.33 (− 0.06–0.75) −0.028 (− 0.31–0.26) 0.847 0.93 (0.58–1.48) 0.748
C*ab T0 – T1 0.23 (− 0.29–0.75) 0.17 (− 0.35–0.69) −0.053 (− 0.36–0.26) 0.738 0.84 (0.53–1.33) 0.449
C*ab T1 – T2 0.20 (− 0.25–0.66) 0.17 (− 0.28–0.62) −0.034 (− 0.31–0.24) 0.805 0.90 (0.56–1.44) 0.668
C*ab T0 – T2 0.43 (0.05–0.82) 0.34 (− 0.04–0.73) −0.087 (− 0.33–0.15) 0.471 0.77 (0.49–1.23) 0.279
 ΔE T0 – T1 1.63 (1.17–2.10) 1.74 (1.28–2.21) 0.111 (− 0.26–0.48) 0.552 1.33 (0.83–2.14) 0.239
 ΔE T1 – T2 1.45 (1.03–1.87) 1.65 (1.22–2.07) 0.199 (−0.16–0.56) 0.271 1.32 (0.82–2.13) 0.260
 ΔE T0 – T2 1.61 (1.24–1.97) 1.39 (1.03–1.76) −0.214 (− 0.51–0.08) 0.155 0.80 (0.49–1.28) 0.346