Expansion or Contraction analysis

Selection of measure

As before we select from 37 pairs of measures which are:

4	36 #jaw motion
16	17
26	27
15	18
25	28
24	29
31	33
32	36
10	32 # crossface pairs
15	16
17	18
25	26
27	28
15	25
18	28
16	26
17	27 # 8 upper lip pairs
31	32
32	33 # lower lip pairs
24	21
29	22
24	14
29	19
24	25
29	28
24	34
29	38
24	31
29	33 # commissure pairs
9	15
11	18
8	14
12	19
8	13
12	20
13	23
20	30 # peripheral measures

We compute the relative change from rest in percentage terms for each marker pair. For each pair, we compute the maximum expansion and the maximum contraction. Thus there are 37*2=74 candidate measures. We now compute t-statistics for two comparisons:

For the first two visits, we compute the cleft - control difference.
For the revision group, we compute the before - after difference, where before averages the first two visits

These t-statistics are displayed in these 12 plots. The dotted lines are plotted at 2 and -2. Statistics outside these ranges are "statistically significant" (but note the t-test is only approximate here and we use this just for measure selection purposes).

For an expansion, negative values indicate marker pairs where a) the control expands more than the cleft or b) the expansion was greater after surgery. Thus for expansions, the ideal marker pair is in the lower left quadrant
For a contraction, positive values indicate marker pairs where a) the control contracted more than the cleft group or b) contraction was greater after surgery. Ideal marker pairs are in the upper right quadrant

On this basis, we select:

Both smiles: contraction average of 16-26 and 17-27
Lip purse and grimace: contraction of 25-28
Cheek puff: expansion average of 16-26 and 17-27
Mouth open: expansion average of 27-28 and 25-26

Note that the grimace, mouth open,cheek puff and lip purse measures are different from before - simpler and hopefully better. Note that there is no good candidate for a cheek puff measure. Also note that this selection of measures only uses 6 markers in total making it easier to use in practice.

Revision subjects

Now we display the before vs after scores for the revision subjects in these six plots. For the contaction measures, i.e. the smiles, lip purse and the grimace, subjects below the line improved in the sense they contracted more after surgery. For the expansion measures, i.e. cheek puff and mouth open, above the diagonal line cases showed more expansion after surgery.

Here the same plots except with rr34 included in red. It seems rr34 showed some improvement on the natural smile due to surgery but not too much difference on the other animations.

Now consider the three models. I had to measure jaw motion differently as we now have expansion or contraction (and both could occur during a single motion). I used the largest of the two as the measure.
Model 1 results
First two columns show the control and cleft mean effects adjusted for the other covariates. The next four columns show the effects of these four covariates (same as before). The p-vales for the effects follow.

	Control	Cleft	Jaw	Age	Gender	Angle	pCleft	pjaw	page	prace	pgender	pangle	
c	30.5	18.3	0.2	-0.4	-2.9	0.4	0	0	0.385	0.159	0.124	0.015	
g	-6.8	-3.5	-0.1	0	-0.7	0.1	0	0.024	0.588	0.85	0.436	0.182	
l	-20.1	-15.3	-0.2	-0.1	0.5	0	0	0	0.527	0.363	0.539	0.836	
m	32.1	24.8	0.3	0.1	-1.1	-0.1	0	0	0.825	0.226	0.449	0.269	
s	-26.9	-17.1	-0.1	-0.5	2.1	0.2	0	0.004	0.089	0.103	0.215	0.141	
n	-19	-13.4	-0.1	-0.3	1.9	0.2	0	0.038	0.284	0.243	0.193	0.176

As expected, there are strong control vs. cleft differences. The motion of the lower jaw also has a significant effect on the motion. Otherwise, the other predictors have little effect except for the angle measure on the cheek puff (which tends to increase the expansion with larger angles).
We can also extract estimates of the variation in the random effects. There is variation due to the subject not explained race, age, gender etc. There is variation from one visit to the next. There is also variation from one animation to the next within a visit, called the residual variation. A table of these SDs for this model is:

  subject visit residual
c     8.0   4.5      6.0
g     3.9   1.7      3.4
l     3.5   3.1      2.7
m     6.4   4.6      4.2
s     7.5   4.5      4.8
n     6.4   4.1      4.4

Of the three sources of variation, the visit effect is the smallest. For the subject effect, the scale of the variation is relatively large. For example, for the natural smile, the SD of 6.4 is about the same size as the difference between control and cleft (-19 vs. -13.4). In other words, the difference between one subject and the next is about the same size as the control vs. cleft difference. Furthermore, the variation within a single visit is quite large - just slightly smaller than the between subject variation. All this means that you need good replication to find statistical significance.

Model 2 results
The second model considered which factors might effect the motion within clefts as a group. The first three columns show the magnitude of the effects (only variables which have at least some significant effects shown). The first column shows the effect of the revision group relative to the non-revision i.e for the cheek puff the revision expands 4.8% less than the non-revision. For the third column, the effect of a unilateral compared to a bilateral is shown i.e for cheek puff, unilateral expand 5.5% more. These are followed by the p-values.

	rev	jaw	lip	pRev	pJaw	pAge	pPalate	pLip	pMaxexp	pBone	
c	-4.8	0.2	5.5	0.002	0	0.068	0.415	0.011	0.015	0.493	
g	0.6	-0.1	-0.1	0.545	0.008	0.543	0.347	0.974	0.981	0.229	
l	-0.5	-0.1	-2.5	0.706	0	0.763	0.652	0.1	0.618	0.614	
m	-3.4	0.3	0.9	0.053	0	0.068	0.917	0.446	0.256	0.557	
s	2.5	-0.1	-5	0.069	0.002	0.383	0.604	0.014	0.071	0.494	
n	1.4	0	-5.7	0.273	0.285	0.485	0.356	0.003	0.826	0.444

The lower jaw motion has an effect on most of the animations (which we expect). Otherwise, we see that the cleft lip type (uni vs. bi) has an effect on three of the motions.
Here is corresponding table of SDs:

  subject visit residual
c     5.7   4.5      5.4
g     3.1   1.3      2.7
l     3.5   3.1      2.4
m     5.4   4.0      4.0
s     5.7   4.6      4.5
n     4.8   3.8      4.1

These follow a similar pattern to the previous SD table. These use only the cleft subjects so you may not want to present this table.

Model 3 results These are the longitudinal effects. The first three columns are p-values. The second three columns are covariate-adjusted means at the three time points. The last two columns are the sizes of the jaw and uni/bilateral effect.

	Visit	Jaw	Lip	Pre	3mos	12mos	Jaw	Lip	
c	0.1	0	0	18.3	16.1	17.9	0.1	-7.9	
g	0.058	0.014	0.627	-3.1	-2.3	-3.6	-0.1	-0.6	
l	0.702	0	0.083	-15	-14.5	-15.4	-0.1	3.2	
m	0.038	0	0.597	21.5	23	25.1	0.3	-1.2	
s	0.037	0.231	0.01	-15	-15.7	-17.5	0	7.9	
n	0.27	0.533	0.017	-11.7	-12.6	-13.2	0	6

Significant longitudinal effects for the forced smile and mouth open with motion improving in the direction of the controls. Grimace not quite significant but moving in the right direction. Natural smile and lip purse not significant but moving in the right direction. Cheek puff not significant and getting slightly worse. Lower jaw motion effects significant as expected as well as uni vs. bi effect as expected from Model 2.

Here is the table of SDs:

    subject visit residual
c     3.1   4.5      4.5
g     2.5   1.9      2.3
l     3.8   3.1      2.6
m     4.6   4.6      4.2
s     6.2   4.2      3.7
n     5.1   4.1      3.7

Again, this is a different subset of the data than before. First table is sufficient to get the idea across.

Scores for individual files

There is seperate file for each animation. The columns in each file are, respectively:

The subject
The replicate number
The visit number
The group (nc, rr or nr)
The score computed on the basis of the selected maximal distortion of a few marker pairs
The score normalized by the controls (i.e. control mean subtracted and then divided by control SD)

Note that the sign of normalized score must be interpreted relative to whether the control motion is an expansion. For example,for an expansion, a positive score would indicate even more of an expansion for that motion. In contrast, for a smile, where the motion is a contraction, a positive score would mean less of a contraction.

Animations

Animations may be found here

Grimace

The grimace calculations were repeated using an alternative measure based on the average of the 4-9 and 4-11 distances. The distances 9-10 and 10-11 were considered but were found to move relatively little. The results for the corresponding models above were:

Model 1

  	Control	Cleft	Jaw	Age	Gender	Angle	pCleft	pjaw	page	prace	pgender	pangle	
g	-19.5	-17.4	0.2	0.1	0.2	0.1	0.008	0	0.448	0.44	0.869	0.384

Model 2

	rev	jaw	lip	pRev	pJaw	pAge	pPalate	pLip	pMaxexp	pBone	
g	1.5	0.1	-0.4	0.309	0	0.866	0.98	0.665	0.403	0.151

Model 3

  	Visit	Jaw	Lip	Pre	3mos	12mos	Jaw	Lip	
g	0.099	0	0.157	-16.6	-18.1	-17.7	0.1	3.7

We see that the controls show somewhat more contraction on this measure than the clefts with no other significant covariate besides the jaw motion. Looking at the cleft patients only, the jaw motion was again the only significant predictor. Looking at the longitudinal effect on the revision subjects, we find that there is some improvment (in the sense of their being more contraction) but that the effect is only significant at the 10% level. The plot shows the before and after scores shows that subject rr16 showed the most dramatic improvement.

Last modified: Wed Apr 18 15:52:58 BST 2007