Main result
Demographic tables
Table 1
| Characteristic | Overall, N = 127 | Normal, N = 391 | Osteopenia, N = 571 | Osteoporosis, N = 311 | p-value2 |
|---|---|---|---|---|---|
| Age | 70 (9) | 69 (9) | 70 (9) | 72 (8) | 0.24 |
| Height | 160.0 (5.9) | 160.9 (5.4) | 159.3 (6.1) | 159.9 (6.0) | 0.43 |
| Weight | 73 (16) | 82 (17) | 72 (13) | 64 (14) | <0.001 |
| BMI | 28.6 (5.9) | 31.8 (6.0) | 28.3 (5.2) | 24.9 (4.6) | <0.001 |
|
1
Statistics presented: mean (SD)
2
Statistical tests performed: One-way ANOVA
|
|||||
Table 2 Measurements
| Characteristic | Overall, N = 127 | Normal, N = 391 | Osteopenia, N = 571 | Osteoporosis, N = 311 | p-value2 |
|---|---|---|---|---|---|
| viss_mean | 101 (23) | 100 (24) | 102 (21) | 101 (24) | 0.84 |
| trab_mean | 59 (24) | 71 (27) | 57 (19) | 50 (21) | <0.001 |
| cor_mean | 75 (30) | 84 (29) | 73 (30) | 68 (26) | 0.079 |
| baz_viss_mean | 67 (21) | 62 (20) | 72 (19) | 65 (23) | 0.074 |
| baz_trab_mean | 57 (24) | 60 (25) | 55 (25) | 56 (21) | 0.62 |
| baz_cor_mean | 62 (27) | 70 (27) | 61 (24) | 52 (30) | 0.035 |
|
1
Statistics presented: mean (SD)
2
Statistical tests performed: One-way ANOVA
|
|||||
Table 2 for reformat
| Characteristic | Normal, N = 391 | Osteopenia, N = 571 | Osteoporosis, N = 311 | p-value2 |
|---|---|---|---|---|
| md_vol_all | 21.2 (4.6) | 18.4 (3.6) | 18.0 (3.9) | <0.001 |
| md_vol_small | 9.27 (2.30) | 8.03 (1.67) | 8.18 (1.97) | 0.007 |
| md_vol_forame | 2.95 (1.41) | 2.44 (1.01) | 2.32 (1.22) | 0.057 |
| mx_vol | 4.70 (1.25) | 4.03 (1.40) | 3.94 (1.38) | 0.029 |
| x1_viss | 164 (41) | 148 (39) | 142 (38) | 0.042 |
| x1_trab | 71 (33) | 71 (29) | 71 (32) | >0.99 |
| x1_cor | 94 (24) | 77 (21) | 71 (21) | <0.001 |
| x1_baz_viss | 122 (17) | 107 (15) | 102 (15) | <0.001 |
| x1_baz_trab | 50 (13) | 51 (9) | 55 (12) | 0.35 |
| x1_baz_cor | 71 (21) | 56 (14) | 47 (15) | <0.001 |
| x1_cort_viss | 0.59 (0.14) | 0.54 (0.12) | 0.52 (0.16) | 0.074 |
| x2_viss | 151 (44) | 136 (39) | 130 (40) | 0.077 |
| x2_trab | 66 (37) | 65 (29) | 65 (33) | 0.98 |
| x2_cor | 84 (25) | 71 (20) | 65 (18) | <0.001 |
| x2_baz_viss | 117 (20) | 105 (15) | 103 (15) | 0.005 |
| x2_baz_trab | 51 (13) | 52 (11) | 54 (12) | 0.69 |
| x2_baz_cor | 65 (21) | 54 (14) | 49 (14) | 0.001 |
| x2_cor_viss | 0.58 (0.16) | 0.54 (0.14) | 0.52 (0.14) | 0.18 |
| x3_viss | 123 (49) | 114 (40) | 106 (40) | 0.24 |
| x3_trab | 65 (41) | 60 (32) | 55 (31) | 0.54 |
| x3_cor | 59 (22) | 54 (19) | 51 (18) | 0.21 |
| x3_baz_viss | 108 (15) | 97 (16) | 98 (16) | 0.039 |
| x3_baz_trab | 58 (14) | 55 (11) | 56 (8) | 0.51 |
| x3_baz_cor | 50 (13) | 43 (14) | 42 (13) | 0.14 |
| x3_cor_viss | 0.52 (0.17) | 0.50 (0.15) | 0.51 (0.17) | 0.84 |
| x4_viss | 121 (48) | 114 (43) | 108 (39) | 0.45 |
| x4_trab | 64 (38) | 62 (34) | 58 (34) | 0.81 |
| x4_cor | 57 (23) | 52 (19) | 50 (19) | 0.24 |
| x4_baz_viss | 109 (17) | 100 (16) | 97 (12) | 0.071 |
| x4_baz_trab | 60 (11) | 59 (11) | 61 (10) | 0.88 |
| x4_baz_cor | 49 (16) | 41 (13) | 37 (11) | 0.032 |
| x4_cor_viss | 0.50 (0.17) | 0.48 (0.15) | 0.49 (0.19) | 0.81 |
|
1
Statistics presented: mean (SD)
2
Statistical tests performed: One-way ANOVA
|
||||
IN this table, the comparison aren’t adjusted for any other variable, so please consider as an approximation in order to try to find the signal, that is the true effect or relationship between the bone measurements in CBCT and the DXA status
Now, we will to proceed to create a model that could isolate the signal (relation between measurements and DXA) from the noise (weight? height? age?) ## Measurements With the outliers
Seems to be a positive correlation, that is, more DXA, more mm. Now lets check divided by area and bone
This graph shows that the DXA measured in hip or lumbar vertebrae seems to be correlated to the measurements made in the cortical bone in the CBCT
Is there any association between the DXA values and the measurements? Continuos DXA values
Lets check the effect of the outliers
The outliers only add noise to the signal
Note that the outliers add noise to the signal, hence will be removed from any further analysis
Call:
glm(formula = value ~ dxa_worst, data = .)
Deviance Residuals:
Min 1Q Median 3Q Max
-79.842 -27.757 -7.546 24.216 111.524
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 83.7344 1.2788 65.478 < 2e-16 ***
dxa_worst 2.9702 0.6548 4.536 6.1e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for gaussian family taken to be 1366.118)
Null deviance: 2582750 on 1871 degrees of freedom
Residual deviance: 2554641 on 1870 degrees of freedom
(369 observations deleted due to missingness)
AIC: 18832
Number of Fisher Scoring iterations: 2MODEL INFO:
Observations: 1872 (369 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(1) = 28109.04, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.01
Pseudo-R² (McFadden) = 0.00
AIC = 18831.84, BIC = 18848.44
Standard errors: MLE
------------------------------------------------
Est. S.E. t val. p
----------------- ------- ------ -------- ------
(Intercept) 83.73 1.28 65.48 0.00
dxa_worst 2.97 0.65 4.54 0.00
------------------------------------------------
Estimated dispersion parameter = 1366.12 The baseline value for measurements is 84 and for every additional point in DXA, the measurement value increase in 2.97 (p<0.01)
This model explain very little of the variance of the measurements, only 1% (see R2), but there is a signal. We are interested in identify if this statistical significance is also clinically relevant.
But it could be that one group is bigger, or heavier, or older. Let’s identify if the difference is kept in check by other factors.
MODEL INFO:
Observations: 1854 (387 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 184133.61, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.07
Pseudo-R² (McFadden) = 0.01
AIC = 18547.07, BIC = 18585.75
Standard errors: MLE
------------------------------------------------
Est. S.E. t val. p
----------------- ------- ------ -------- ------
(Intercept) 34.51 8.66 3.99 0.00
dxa_worst 0.27 0.70 0.38 0.70
age -0.02 0.09 -0.20 0.84
md_vol_all 2.41 0.24 9.92 0.00
mx_vol -0.27 0.69 -0.39 0.70
ID 0.01 0.02 0.29 0.77
------------------------------------------------
Estimated dispersion parameter = 1289.01 Adjusting for all the variables seems that the signal disappear, but we haven’t yet adjusted by zone and clinical_variable_2 (basal, cort, all)
Now explore by zone and type of bone, maybe there are some interaction by zone and what is being measured (cortcal, trabeculae, etc). Let’s check
First, take a look at the graph:
and the regression model is:
MODEL INFO:
Observations: 1872 (369 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 187186.39, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.07
Pseudo-R² (McFadden) = 0.01
AIC = 18719.48, BIC = 18758.22
Standard errors: MLE
------------------------------------------------
Est. S.E. t val. p
----------------- ------- ------ -------- ------
(Intercept) 44.55 9.62 4.63 0.00
dxa_worst 0.75 0.75 1.00 0.32
age -0.02 0.09 -0.24 0.81
bmi -0.33 0.16 -2.04 0.04
md_vol_all 2.36 0.22 10.82 0.00
ID 0.01 0.02 0.40 0.69
------------------------------------------------
Estimated dispersion parameter = 1283.8 When adjusted for age and mannd/max volume, the signal is lost.
Now, we will make 6 regression models - for every bone type separately.
1. Cortical Basal
MODEL INFO:
Observations: 260 (121 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 27062.44, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.32
Pseudo-R² (McFadden) = 0.04
AIC = 2153.90, BIC = 2178.82
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) 111.82 11.53 9.70 0.00
dxa_worst 4.64 0.85 5.44 0.00
age -0.78 0.11 -7.39 0.00
bmi -0.19 0.18 -1.04 0.30
md_vol_all 0.52 0.26 2.01 0.05
ID -0.01 0.03 -0.34 0.74
--------------------------------------------------
Estimated dispersion parameter = 224.94 2. Trabeculae Basal
MODEL INFO:
Observations: 260 (121 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 7408.24, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.22
Pseudo-R² (McFadden) = 0.03
AIC = 1958.39, BIC = 1983.32
Standard errors: MLE
------------------------------------------------
Est. S.E. t val. p
----------------- ------- ------ -------- ------
(Intercept) -9.30 7.92 -1.18 0.24
dxa_worst -1.83 0.59 -3.13 0.00
age 0.46 0.07 6.40 0.00
bmi 0.15 0.13 1.21 0.23
md_vol_all 1.05 0.18 5.96 0.00
ID 0.02 0.02 0.88 0.38
------------------------------------------------
Estimated dispersion parameter = 106.05 3. All Basal Bone
MODEL INFO:
Observations: 260 (121 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 23101.18, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.29
Pseudo-R² (McFadden) = 0.04
AIC = 2148.28, BIC = 2173.21
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) 102.51 11.41 8.99 0.00
dxa_worst 2.80 0.84 3.32 0.00
age -0.32 0.10 -3.03 0.00
bmi -0.04 0.18 -0.21 0.83
md_vol_all 1.56 0.25 6.17 0.00
ID 0.01 0.03 0.27 0.79
--------------------------------------------------
Estimated dispersion parameter = 220.14 4. Cortical
MODEL INFO:
Observations: 379 (2 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 78140.48, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.34
Pseudo-R² (McFadden) = 0.05
AIC = 3358.43, BIC = 3385.99
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) 109.15 11.66 9.36 0.00
dxa_worst 3.93 0.94 4.18 0.00
age -0.76 0.12 -6.50 0.00
bmi -0.94 0.20 -4.76 0.00
md_vol_all 2.39 0.27 8.99 0.00
ID 0.02 0.03 0.53 0.60
--------------------------------------------------
Estimated dispersion parameter = 404.41 5. Trabeculae
MODEL INFO:
Observations: 379 (2 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 173114.84, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.42
Pseudo-R² (McFadden) = 0.06
AIC = 3527.23, BIC = 3554.79
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) -96.46 14.57 -6.62 0.00
dxa_worst -4.54 1.17 -3.87 0.00
age 0.73 0.15 4.96 0.00
bmi 0.24 0.25 0.99 0.32
md_vol_all 5.20 0.33 15.70 0.00
ID -0.04 0.04 -1.17 0.24
--------------------------------------------------
Estimated dispersion parameter = 631.32 6. All Bone
MODEL INFO:
Observations: 334 (2 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 177606.12, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.43
Pseudo-R² (McFadden) = 0.06
AIC = 3146.98, BIC = 3173.66
Standard errors: MLE
-------------------------------------------------
Est. S.E. t val. p
----------------- ------- ------- -------- ------
(Intercept) 29.22 16.46 1.77 0.08
dxa_worst -0.36 1.34 -0.27 0.79
age 0.05 0.17 0.32 0.75
bmi -0.96 0.28 -3.45 0.00
md_vol_all 6.41 0.43 14.98 0.00
ID -0.00 0.04 -0.11 0.92
-------------------------------------------------
Estimated dispersion parameter = 706.58 And now lets see if all cortical could be better model:
MODEL INFO:
Observations: 639 (123 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 87049.28, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.25
Pseudo-R² (McFadden) = 0.03
AIC = 5670.54, BIC = 5701.76
Standard errors: MLE
-------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------ -------- ------
(Intercept) 115.23 9.34 12.33 0.00
dxa_worst 4.34 0.73 5.94 0.00
age -0.77 0.09 -8.53 0.00
bmi -0.62 0.15 -4.04 0.00
md_vol_all 1.33 0.21 6.38 0.00
ID 0.01 0.02 0.56 0.57
-------------------------------------------------
Estimated dispersion parameter = 413.12 Looking at graphs we would expect that all trabecular should be worse:
MODEL INFO:
Observations: 639 (123 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 120338.41, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.26
Pseudo-R² (McFadden) = 0.03
AIC = 5851.48, BIC = 5882.70
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) -61.27 10.76 -5.69 0.00
dxa_worst -3.46 0.84 -4.11 0.00
age 0.65 0.10 6.21 0.00
bmi 0.24 0.18 1.37 0.17
md_vol_all 3.29 0.24 13.69 0.00
ID -0.02 0.03 -0.61 0.54
--------------------------------------------------
Estimated dispersion parameter = 548.34 … but it is not true. So, the conclusion could be that the relation between DXA and measurements in CBCT in mandible is statistically significant, but maybe the relation is not clinically significant.
Maybe the models are better in some age group?
MODEL INFO:
Observations: 210 (42 missing obs. deleted)
Dependent Variable: value
Type: Linear regression
MODEL FIT:
χ²(5) = 27604.91, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.21
Pseudo-R² (McFadden) = 0.03
AIC = 1907.76, BIC = 1931.19
Standard errors: MLE
--------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------- -------- ------
(Intercept) 144.41 41.00 3.52 0.00
dxa_worst 8.98 1.44 6.25 0.00
age -0.56 0.57 -0.98 0.33
bmi -1.14 0.30 -3.77 0.00
md_vol_all 0.29 0.40 0.74 0.46
ID 0.03 0.04 0.81 0.42
--------------------------------------------------
Estimated dispersion parameter = 497.21 Grey Values
| Characteristic | Overall, N = 127 | Normal, N = 391 | Osteopenia, N = 571 | Osteoporosis, N = 311 | p-value2 |
|---|---|---|---|---|---|
| C1 Axial | 40 (105) | 86 (85) | 32 (112) | -6 (92) | <0.001 |
| C1 Sagital | 38 (99) | 72 (87) | 36 (108) | -0 (84) | 0.009 |
| C2 Axial | 140 (100) | 185 (86) | 129 (105) | 104 (90) | 0.001 |
| C2 Sagital | 132 (102) | 166 (99) | 126 (109) | 98 (78) | 0.017 |
|
1
Statistics presented: mean (SD)
2
Statistical tests performed: One-way ANOVA
|
|||||
Is there any association between the grey values and the measurements? Continuos DXA values
Visualise the overall correlation
Check the effect of the outliers
Plot without the outliers
MODEL INFO:
Observations: 506 (2 missing obs. deleted)
Dependent Variable: value_grey
Type: Linear regression
MODEL FIT:
χ²(1) = 529259.41, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.08
Pseudo-R² (McFadden) = 0.01
AIC = 6175.68, BIC = 6188.36
Standard errors: MLE
-------------------------------------------------
Est. S.E. t val. p
----------------- -------- ------ -------- ------
(Intercept) 123.20 7.16 17.21 0.00
dxa_worst 24.59 3.64 6.75 0.00
-------------------------------------------------
Estimated dispersion parameter = 11604.2 The baseline grey value is 123 and for each DXA point, the grey values increment +24
Is there any association between the grey values and the measurements? Ordinal Dx values (Normal, Osteopenia, Osteoporosis)
