Dental RCT ANCOVA
These sections are the results of the ANCOVA and the assessment of its assumption for each variable at 3, 6 and 12 months.
ANCOVA
Analysis: Account for mean PPD, number of PPD≥5 mm, OIDP, CS-OIDP, EQ-5D-5L, EQ-5D-VAS at BL, when calculating that for 3months and 12 months for each group
OIDP
ANCOVA Table OIDP
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 113.0800 | 1 | 4.135214 | 0.048670966249484 | 44.85507 | 1 | 0.6646520 | 0.4197504105872 | 19.77738 | 1 | 0.8535514 | 0.361089566356505 |
OIDP_BL | 1,528.7694 | 1 | 55.905471 | 0.000000004098281 | 2,522.74727 | 1 | 37.3814763 | 0.0000003267246 | 1,278.61712 | 1 | 55.1825064 | 0.000000004779914 |
TxAssign | 160.6565 | 2 | 2.937518 | 0.064516593768832 | 76.32941 | 2 | 0.5655157 | 0.5725426523423 | 109.66899 | 2 | 2.3665449 | 0.106812456646462 |
Residuals | 1,093.8246 | 40 | 2,699.46242 | 40 | 926.82787 | 40 |
Baseline OIDP was always associated with the score at later stages. Tx assignation, on the other hand, was not. There is some evidence of an association with OIDP at 3M, adjusting for baseline OIDP. Nevertheless, such there was no evidence for the association between tx assignation and OIDP at 6M and 12M, adjusting for baseline OIDP.
PPD
ANCOVA Table PPD
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 1.213837 | 1 | 11.350406 | 0.001679748708 | 0.368293 | 1 | 4.175988 | 0.04779751559531 | 0.1816511 | 1 | 1.701293 | 0.199393918233280 |
PostPPD_BL | 3.209132 | 1 | 30.008104 | 0.000002555712 | 4.041053 | 1 | 45.820547 | 0.00000004453723 | 5.9132648 | 1 | 55.381958 | 0.000000003946177 |
TxAssign | 2.106695 | 2 | 9.849694 | 0.000332508215 | 1.014916 | 2 | 5.753948 | 0.00646031991342 | 0.7640032 | 2 | 3.577719 | 0.036969179566590 |
Residuals | 4.277687 | 40 | 3.439528 | 39 | 4.3776685 | 41 |
Unlike OIDP, there was consistent evidence for an association between Post PPD and tx assignation over time, adjusting by baseline Post PPD.
Post No. PPD>5
ANCOVA Table Post PPD 5
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 221.3196 | 1 | 3.817408 | 0.05774039979 | 9.457231 | 1 | 0.1524205 | 0.6983043181100 | 2.668128 | 1 | 0.03221498 | 0.8584407586172 |
PostNoPPD.5_BL | 1,299.1343 | 1 | 22.407983 | 0.00002755032 | 2,481.702750 | 1 | 39.9971723 | 0.0000001654294 | 3,101.606964 | 1 | 37.44880233 | 0.0000002924603 |
TxAssign | 834.5364 | 2 | 7.197208 | 0.00213852130 | 638.907965 | 2 | 5.1485844 | 0.0102406859442 | 468.815008 | 2 | 2.83023619 | 0.0705686604807 |
Residuals | 2,319.0562 | 40 | 2,481.878202 | 40 | 3,395.726369 | 41 |
As for Post No. PPD>5 (PostPPD5), there is evidence of an association with tx assignation adjusted by baseline PostPPD5, however, the evidence for this association becomes weaker over time. Still, at the end of the analyzed period, there is some evidence of an association between PostPPD5 and tx assignation adjusted by baseline PostPPD5.
CS-OIDP
ANCOVA Table CSOIDP
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 1.688831 | 1 | 0.07077397 | 0.7915797028865 | 0.4653773 | 1 | 0.3515484 | 0.556660704959 | 8.371618 | 1 | 0.8138873 | 0.372374020443521 |
CSOIDP_BL | 1,031.200220 | 1 | 43.21458901 | 0.0000000738882 | 39.8613805 | 1 | 30.1114924 | 0.000002665295 | 636.553009 | 1 | 61.8855755 | 0.000000001199355 |
TxAssign | 21.386838 | 2 | 0.44812995 | 0.6419895844759 | 0.6304280 | 2 | 0.2381143 | 0.789249971767 | 26.877423 | 2 | 1.3065092 | 0.282068026125747 |
Residuals | 954.492679 | 40 | 51.6279238 | 39 | 411.438694 | 40 |
In the case of CSOIDP, there was no evidence for an association between tx assignation an the mentioned variable adjusted by its baseline levels at any point during the trial.
EQ5D-5L
ANCOVA Table for EQ5
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 0.13370906 | 1 | 12.752853 | 0.0009634154 | 0.08008168 | 1 | 11.887603 | 0.0013436642 | 0.15871108 | 1 | 11.7267379 | 0.001411117 |
EQ5D5L_BL | 0.07992015 | 1 | 7.622595 | 0.0087406512 | 0.16333744 | 1 | 24.246378 | 0.0000150773 | 0.08357455 | 1 | 6.1751004 | 0.017128437 |
TxAssign | 0.06355121 | 2 | 3.030682 | 0.0597826715 | 0.04627754 | 2 | 3.434799 | 0.0420121667 | 0.01785969 | 2 | 0.6598025 | 0.522355485 |
Residuals | 0.40890092 | 39 | 0.26946283 | 40 | 0.55489892 | 41 |
There was some evidence for an association between tx assignation and EQ5 at 3M and 6M, adjusted by baseline EQ5. Nevertheless, no evidence for such association is seen at 12M.
EQ-5D-VAS
ANCOVA Table EQ5-VAS
Variable | 3M: Sum sq | 3M: Df | 3M: F | 3M: p-value | 6M: Sum sq | 6M: Df | 6M: F | 6M: p-value | 12M: Sum sq | 12M: Df | 12M: F | 12M: p-value |
(Intercept) | 174.3316 | 1 | 2.318475 | 0.1355216808995617 | 422.4377 | 1 | 5.804291 | 0.020682172521931 | 762.41277 | 1 | 14.2106240 | 0.0005160579898190 |
EQ5D_VAS_BL | 4,930.5795 | 1 | 65.572870 | 0.0000000004870385 | 4,046.4048 | 1 | 55.597578 | 0.000000004375166 | 3,558.57978 | 1 | 66.3284268 | 0.0000000004205145 |
TxAssign | 371.2873 | 2 | 2.468916 | 0.0971793209868985 | 200.7765 | 2 | 1.379334 | 0.263461105751919 | 79.86703 | 2 | 0.7443215 | 0.4813660106248442 |
Residuals | 3,082.8872 | 41 | 2,911.2094 | 40 | 2,199.68689 | 41 |
There was little evidence for an association between tx assignation and EQ5-VAS at 3M, adjusted by baseline EQ5-VAS. At 6M and 12M, there was no evidence for an association between tx assignation and EQ5-VAS, adjusted by its baseline level.
Overall: The ancova -used regardless of the distribution of the outcomes- showed an association between tx and the following outcomes -adjusted for baseline levels: Post PPD, Post No. PPD>5 (but weaker over time). For OIDP, CS-OIDP, EQ5 and EQ5-VAS, there was no little to no evidence for an association with tx, after adjusting for baseline levels. EQ5-VAS and CS-OIDP showed no evidence, EQ5 showed borderline evidence at 3 and 6M, and OIDP showed some evidence at 3M.
Assumptions
The assumptions of the used test -ancova- are assessed in this section
Linearity assumption
For OIDP, there seems to be a linear relationship between baseline level and OIDP at 3, 6 and 12 months. The slope by group differed
OIDP
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
PPD
For PPD, there seems to be a linear relationship between baseline PPD and PPD at 3, 6 and 12 months. However, the linear relationship is somewhat weaker for the RPFO group compared to the others.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Post PPD N5
There seems to be a linear association between the Post No.PPD>5 at baseline at its subsequents measurements. However, the linearity was weaker for the RPFO and SPPF group.
## `geom_smooth()` using formula 'y ~ x'
## [1] 24 30 29 38 59 31 20 33 14 13 16 30 14 26 38 14 21 40 30 28 43 31 30 18 24
## [26] 36 35 14 40 21 38 20 50 10 17 32 8 34 4 16 2 30 42 26 30 NA NA NA## `geom_smooth()` using formula 'y ~ x'
## [1] 24 30 29 38 59 31 20 33 14 13 16 30 14 26 38 14 21 40 30 28 43 31 30 18 24
## [26] 36 35 14 40 21 38 20 50 10 17 32 8 34 4 16 2 30 42 26 30 NA NA NA## `geom_smooth()` using formula 'y ~ x'
CS-OIDP
For CS-OIDP, there seems to be a linear relationship between baseline PPD and PPD at 3, 6 and 12 months. However, the linear relationship is somewhat weaker for the RPFO group compared to the others. Similar to PPD.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
EQ5 D5L
In this variable the plots suggests some violation of the linearity assumption. Very small slopes can be seen in these graphs.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
EQ5D VAS
Unlike the previous variable, EQ5D-VAS does not violate the linearity assumption between baseline and subsequent levels of the outcome.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Homogeneity of regression slopes
This assumption checks that there is no significant interaction between the covariate and the grouping variable. Based on the previous graphs, there seems to be an interaction by group, but we can formally test it.
OIDP
There is strong and consistent evidence of a significant interaction between OIDP at baseline and group of treatment.
Tables assessing interaction between baseline OIDP and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()PPD
As for PPD, there is moderate evidence of an interaction between baseline levels and treatment group at 6M, but no evidence for such interaction can be seen at 3M and 12M.
Tables assessing interaction between baseline PPD and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()POST PPD N5
For POST PPD N5, there’s evidence of a violation of this assumption at 3 and 6 months, but not at 12 months.
Tables assessing interaction between baseline POST PPD N5 and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()CS-OIDP
In the case of CS-OIDP, there is evidence of violation of the homogeneity of regression slopes at 3 and 12 months, but no evidence for such violation at 6 months.
Tables assessing interaction between baseline CS-OIDP and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()EQ5 D5L
For EQ5, there was no evidence of an interaction between baseline levels of these variables and treatment group at any point in time.
Tables assessing interaction between baseline EQ5 and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()EQ5D VAS
Similarly, for EQ5-VAS there was no evidence of an interaction between baseline levels of these variables and treatment group at any point in time.
Tables assessing interaction between baseline EQ5-VAS and treatment group.
## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()## Coefficient covariances computed by hccm()Normality of residuals
OIDP
Residuals not normally distributed for OIDP
PPD
Normal distribution of residuals
Post PPD N5
Normally distributed at 3m, not normally distributed at 6 and 12m
CS-OIDP
Residuals not normally distributed
EQ5 D5L
The residuals of EQ5 are not normally distributed at any point in time.
EQ5D VAS
There is no evidence of violation of the assumption of normality of residuals for EQ5-VAS.
Homogeneity of variances
OIDP
The levene’s test provide evidence to assume homogeneity of residual variance by group for OIDP at all points in time.
PPD
The levene’s test provide evidence to assume homogeneity of residual variance by group for PPD at all points in time.
Post PPD N5
The levene’s test provide evidence to assume homogeneity of residual variance by group for Post PPD N5 at all points in time.
CS-OIDP
The levene’s test provide evidence to assume homogeneity of residual variance by group for CS-OIDP at all points in time.
EQ5
There is some evidence of a violation of the homogeneity of variance for EQ5 at 3 months, but not in subsequent points in time.
EQ5-VAS
There is some evidence of violation of the assumption of homogeneity of variances across groups for EQ5-VAS at 3 and 6 months, but no evidence for such violation at 12 months.Outliers
Observations whose standardized residuals are greater than 3 in absolute value are possible outliers.
OIDP
3M:Row 39 standardized residuals of -3.8
6M: row 22 and 36, standardized residuals of 5.5 and -3.5, respectively.
12M: row 36 and 39, standardized residuals of 3.7 and -3.5, respectively.PPD
3M: No std res higher than 3
6M: No std res higher than 3
12M: 1 std res of 3.2
POST PPD N5
3M: No std res higher than 3
6M: row 5 and 6, std res of 3.16 and 3.4, respectively
12M: 1 std res of 3.7
CS-OIDP
3M:row 36 and 39, std res of 4.8 and -3.4, respectively
6M: row 23 and 33, std res of 4.4 and 3.9, respectively
12M:row 36 and 39, std res of 5.4 and -3.9, respectively
EQ5
3M: row 2 -3.8
6M: No std res higher than 3
12M: 1 participant with std res of -4.6
EQ5-VAS
No std res higher than 3 at any point in time.