nwr

Demographics

Year	Dx	N	Age (months)	Age (min-max)	Gender
7	DLD	38	86.47	74-96	F: 16, M: 22
7	TLD	45	86.60	76-98	F: 25, M: 20
8	DLD	33	99.00	87-111	F: 14, M: 19
8	TLD	42	98.14	84-109	F: 24, M: 18
9	DLD	32	110.38	100-121	F: 14, M: 18
9	TLD	41	112.29	103-138	F: 23, M: 18
10	DLD	33	122.18	112-133	F: 14, M: 19
10	TLD	41	122.93	114-133	F: 23, M: 18

Data Loss

Dx	Missing_Year	n
DLD	8	5
DLD	9	6
DLD	10	5
TLD	8	3
TLD	9	4
TLD	10	4

Reasons

stopped after year 1:

• 8
• 39
• 42
• 63
• 68
• 73
• 97
• 123

stopped after year 2:

• 44

missing only year 3

• 91

Subject	Dx	Gender	Missing_Year
8	TLD	M	8
8	TLD	M	9
8	TLD	M	10
39	DLD	M	8
39	DLD	M	9
39	DLD	M	10
42	TLD	F	8
42	TLD	F	9
42	TLD	F	10
44	TLD	F	9
44	TLD	F	10
63	DLD	M	8
63	DLD	M	9
63	DLD	M	10
68	DLD	F	8
68	DLD	F	9
68	DLD	F	10
73	TLD	M	8
73	TLD	M	9
73	TLD	M	10
91	DLD	M	9
97	DLD	F	8
97	DLD	F	9
97	DLD	F	10
123	DLD	M	8
123	DLD	M	9
123	DLD	M	10

Age-related changes

Plot

Dx_yr1	Year	N	NWR_prop	SD	SE
DLD	7	38	0.715	0.137	0.022
DLD	8	33	0.768	0.124	0.022
DLD	9	32	0.785	0.108	0.019
DLD	10	33	0.781	0.114	0.020
TLD	7	45	0.847	0.091	0.014
TLD	8	42	0.878	0.068	0.011
TLD	9	41	0.900	0.060	0.009
TLD	10	41	0.903	0.055	0.009

GCA models

m <- lmer(NWR_prop ~ (linear+quadratic)*Dx_yr1 + (linear+quadratic|Subject),data=d)

Anova(m,type=3,test='F')

## Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df)
## 
## Response: NWR_prop
##                          F Df Df.res                Pr(>F)    
## (Intercept)      7534.0824  1 80.789 < 0.00000000000000022 ***
## linear             37.7060  1 77.429         0.00000003290 ***
## quadratic          13.6756  1 74.003             0.0004145 ***
## Dx_yr1             37.9662  1 80.789         0.00000002667 ***
## linear:Dx_yr1       0.3477  1 77.429             0.5571247    
## quadratic:Dx_yr1    1.8869  1 74.003             0.1737035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

GCA fit

Plotting the model predictions - we can see that it does a good job fitting the data:

GCA results

## Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df)
## 
## Response: NWR_prop
##                          F Df Df.res                Pr(>F)    
## (Intercept)      7534.0824  1 80.789 < 0.00000000000000022 ***
## linear             37.7060  1 77.429         0.00000003290 ***
## quadratic          13.6756  1 74.003             0.0004145 ***
## Dx_yr1             37.9662  1 80.789         0.00000002667 ***
## linear:Dx_yr1       0.3477  1 77.429             0.5571247    
## quadratic:Dx_yr1    1.8869  1 74.003             0.1737035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Collapsing across groups, there was a significant effect of linear time, b=0.045, F(1,77.43)=37.71, p < .001. The proportion of phonemes children correctly repeated increased from year 1 (M=0.787, SD=0.131) to year 4 (M=0.849, SD=0.105).

There was also a significant effect of quadratic time, b=-0.021, F(1,74)=13.68, p < .001. This year-to-year increase plateaued between year 3 (M=0.849, SD=0.101) and year 4 (M=0.849, SD=0.105).

There was a significant effect of diagnostic group, b=0.117, F(1,80.79)=37.97, p < .001. Averaging across all 4 years, children in the DLD group (M=0.76, SD=0.124) were less accurate in NWR than children in the TLD group (M=0.881, SD=0.073).

The interaction between diagnostic group and linear time was not significant, b=-0.009, F(1,77.43)=0.35, p = .557. This suggests that both groups experience similar average growth each year.

The interaction between diagnostic group and quadratic time was not significant, b=0.016, F(1,74)=1.89, p = .174. This suggests that both groups experience a similar plateau between years 3 and 4.

GCA subset

Limiting the analyses to just children with data in all 4 years, we find a similar pattern of results:

Dx_yr1	Year	n	NWR_prop
DLD	7	32	0.7122396
DLD	8	32	0.7646063
DLD	9	32	0.7846351
DLD	10	32	0.7784358
TLD	7	41	0.8544207
TLD	8	41	0.8785512
TLD	9	41	0.8995957
TLD	10	41	0.9029920

##  Groups   Name        Std.Dev. Corr          
##  Subject  (Intercept) 0.078636               
##           linear      0.040479 -0.528        
##           quadratic   0.011334  0.408  0.560 
##  Residual             0.046925

## Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df)
## 
## Response: NWR_prop
##                          F Df Df.res                Pr(>F)    
## (Intercept)      7212.1957  1     71 < 0.00000000000000022 ***
## linear             34.7499  1     71         0.00000011555 ***
## quadratic          12.1243  1     71             0.0008558 ***
## Dx_yr1             40.9780  1     71         0.00000001441 ***
## linear:Dx_yr1       0.6293  1     71             0.4302666    
## quadratic:Dx_yr1    2.7595  1     71             0.1010906    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Simplifying random effects to remove the quadratic slope:

## Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df)
## 
## Response: NWR_prop
##                          F Df Df.res                Pr(>F)    
## (Intercept)      7212.3447  1     71 < 0.00000000000000022 ***
## linear             34.8603  1     71         0.00000011123 ***
## quadratic          12.4381  1    144             0.0005647 ***
## Dx_yr1             40.9788  1     71         0.00000001441 ***
## linear:Dx_yr1       0.6313  1     71             0.4295382    
## quadratic:Dx_yr1    2.8309  1    144             0.0946338 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The only difference from the full model is that the interaction between quadratic time and diagnostic group is marginally significant where it was not significant before. This needs to be interpreted with caution, however, not only because it is marginally significant, but also because the full model random effect structure yielded a singular fit and the random slope for the interaction between quadratic time and diagnostic group was removed to address this problem.

The change change to a marginal effect with the subset of participants suggests less of a plateauing effect for the TLD group.

Cross-year comparison

Let’s focus on NWR for the DLD group in year 4 and the TLD group in year 1:

We have year 1 NWR scores for 45 children in the TLD group. We are missing NWR scores for 0 children. And we are missing vocabulary scores for 0 children.

We have year 4 NWR scores for 33 children in the DLD group. We are missing NWR scores for 5 children (68, 97, 39, 63, 123). And we are missing vocabulary scores for 7 children (68, 81, 97, 39, 63, 123, 139).

Age

All

Here are the average ages for children with NWR scores:

Dx	N	Age	Age.YM	SD
DLD	33	122.182	10;2	5.763
TLD	45	86.600	7;2	4.580

Subset

Here are the average ages for children with Vocab scores:

Dx	N	Age	Age.YM	SD
DLD	31	122.161	10;2	5.71
TLD	45	86.600	7;2	4.58

Vocabulary

Here are the uncorrected standard scores on the NIH Picture Vocabulary Test from year 1 for children in the TLD group and from year 4 for children in the DLD group.

These standard scores (M = 100; SD = 15) represent an individual’s performance compared to the average U.S. population - that is they are not adjusted based on the individual’s age, gender, race/ethnicity, or level of education. This is necessary to make cross-age comparisons between 7-year-old children with TLD and 10-year-old children with DLD.

Dx	N	Vocab	SD
DLD	31	77.742	6.033
TLD	45	76.044	6.194

## 
## Call:
## lm(formula = Vocab ~ Dx, data = stat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.0444  -5.7419   0.1068   4.0312  14.2581 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  76.8932     0.7153 107.499 <0.0000000000000002 ***
## Dx           -1.6975     1.4306  -1.187               0.239    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.129 on 74 degrees of freedom
## Multiple R-squared:  0.01867,    Adjusted R-squared:  0.00541 
## F-statistic: 1.408 on 1 and 74 DF,  p-value: 0.2392

The effect of vocabulary was not significant, b = -1.7, t(74) = -1.19, p = .239. Children in the TLD group (n = 45) had similar vocabulary scores (M = 76.04, SD = 6.19) than children in the DLD group (n = 31, M = 77.74, SD = 6.03).

NWR

Here are the proportion of correct phonemes produced in the Nonword repetition task from year 1 for children in the TLD group and from year 4 for children in the DLD group.

Full

Including every child with a NWR score:

Dx	N	NWR	SD
DLD	33	0.781	0.114
TLD	45	0.847	0.091

## 
## Call:
## lm(formula = NWR ~ Dx, data = stat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.34386 -0.06461  0.01418  0.07014  0.16655 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  0.81394    0.01157  70.327 <0.0000000000000002 ***
## Dx           0.06517    0.02315   2.815              0.0062 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.101 on 76 degrees of freedom
## Multiple R-squared:  0.09444,    Adjusted R-squared:  0.08252 
## F-statistic: 7.926 on 1 and 76 DF,  p-value: 0.006204

The effect of NWR was statistically significant, b = 0.07, t(76) = 2.82, p = .006. Children in the TLD group (n = 45) had higher NWR accuracy (M = 0.85, SD = 0.09) than children in the DLD group (n = 33, M = 0.78, SD = 0.11).

Subset

Including only children with a Vocab score:

Dx	N	NWR	SD
DLD	31	0.775	0.114
TLD	45	0.847	0.091

## 
## Call:
## lm(formula = NWR ~ Dx, data = stat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33748 -0.06528  0.01668  0.07014  0.17293 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  0.81076    0.01177  68.863 < 0.0000000000000002 ***
## Dx           0.07154    0.02355   3.038              0.00329 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1009 on 74 degrees of freedom
## Multiple R-squared:  0.1109, Adjusted R-squared:  0.0989 
## F-statistic: 9.231 on 1 and 74 DF,  p-value: 0.003286

The effect of NWR was statistically significant, b = 0.07, t(74) = 3.04, p = .003. Children in the TLD group (n = 45) had higher NWR accuracy (M = 0.85, SD = 0.09) than children in the DLD group (n = 31, M = 0.77, SD = 0.11).

Reading

TOSREC

Some research demonstrates that older children (e.g., 10 years old) with DLD catch up with their TLD peers in NWR performance if they have no literacy problems, while children with DLD who do have literacy problems will not catch up in NWR performance (Bishop, McDonald, Bird, & Hayiou-Thomas, 2009). There are, however, conflicting results which find that older children (8 years old) with DLD who have no literacy problems do not catch up (Vandewalle, Boets, Ghesquière & Zink, 2012).

Wagner et al. (2010) recommend a dichotomized TOSREC score, where standard scores of less than 90 are considered below average and scores of 90 or above are considered average or above average. Johnson et al. (2011) partially validate this, demonstrating that the dichotomoized TOSREC score has high sensitivity and specificity in predicting which children will subsequently not meet grade-level performance on the ISAT (Idaho Student Achievement Test)

This cut-off score, however, has not been validated for a sample of children who have DLD. We plan to conduct a sensitivity analysis and examine the impact of different cut-off scores.

Note we are missing TOSREC scores for the following11participants:

Subject	Dx_yr1
59	DLD
68	DLD
82	DLD
97	DLD
39	DLD
63	DLD
123	DLD
42	TLD
44	TLD
8	TLD
73	TLD

This is mostly, because 9participants did not complete all 4 years of data collection (TOSREC was administered during the final, 4th year):

Subject	Dx_yr1	NWR_raw_yr1	NWR_raw_yr2	NWR_raw_yr3	NWR_raw_yr4
68	DLD	72	NA	NA	NA
97	DLD	74	NA	NA	NA
39	DLD	78	NA	NA	NA
63	DLD	80	NA	NA	NA
123	DLD	38	NA	NA	NA
42	TLD	72	NA	NA	NA
44	TLD	54	82	NA	NA
8	TLD	88	NA	NA	NA
73	TLD	80	NA	NA	NA

Cut-off

Using the Wagner et al.(2010) recommend cut-off of 90, where standard scores of less than 90 are considered below average and scores of 90 or above are considered average or above average.

Here are the numbers of participants in the DLD and TLD group split by their reading ability:

Dx_yr1	Reading	Year	N
DLD	average	7	7
DLD	average	8	7
DLD	average	9	7
DLD	average	10	7
DLD	below	7	24
DLD	below	8	24
DLD	below	9	23
DLD	below	10	24
TLD	average	7	33
TLD	average	8	33
TLD	average	9	33
TLD	average	10	33
TLD	below	7	8
TLD	below	8	8
TLD	below	9	8
TLD	below	10	8

Reading	Dx_yr1	Year	N	NWR_prop	SD	SE
average	DLD	7	7	0.725	0.205	0.078
average	DLD	8	7	0.775	0.167	0.063
average	DLD	9	7	0.792	0.152	0.058
average	DLD	10	7	0.802	0.119	0.045
below	DLD	7	24	0.720	0.106	0.022
below	DLD	8	24	0.778	0.109	0.022
below	DLD	9	23	0.783	0.100	0.021
below	DLD	10	24	0.779	0.118	0.024
average	TLD	7	33	0.866	0.074	0.013
average	TLD	8	33	0.890	0.057	0.010
average	TLD	9	33	0.913	0.052	0.009
average	TLD	10	33	0.911	0.052	0.009
below	TLD	7	8	0.809	0.096	0.034
below	TLD	8	8	0.831	0.095	0.033
below	TLD	9	8	0.842	0.058	0.020
below	TLD	10	8	0.871	0.056	0.020

NWR accuracy for children with DLD does not vary based on their reading proficiency. For children with TLD, however, those with below average reading proficiency are less accurate in NWR than their peers with average reading proficiency. Note: this latter comparison is lacking in previous research (e.g., Bishop et al., 2009) because the control/comparison group for the DLD group was selected to not have dyslexia (i.e., a true TLD group). In the current project, however, the control/comparison group allowed children with reading difficulties (hence TLD rather than TD).

There is, therefore, no need to re-analyze the results because DLD with below average reading and DLD with average reading will be the same distance from the TLD group with average reading.

Stability

Dx_yr1	cor_yr7_yr8	cor_yr8_yr9	cor_yr9_yr10
DLD	0.824	0.688	0.672
TLD	0.615	0.654	0.718

rank order

Dx Accuracy

across years

	year	threshold	sensitivity	specificity
7	7	0.755	0.605	0.844
8	8	0.828	0.636	0.810
9	9	0.862	0.781	0.805
10	10	0.870	0.788	0.829

year 7

threshold	sensitivity	specificity
0.755	0.605	0.844

sensitivity is 0.605

15 in the DLD group (n=38) score above the cut-off of 0.755:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
97	F	DLD	7	90	0.771
91	M	DLD	7	94	0.771
74	M	DLD	7	80	0.781
26	M	DLD	7	85	0.812
104	M	DLD	7	94	0.823
127	M	DLD	7	93	0.823
141	M	DLD	7	74	0.823
63	M	DLD	7	89	0.833
81	F	DLD	7	81	0.844
98	M	DLD	7	86	0.854
21	F	DLD	7	86	0.865
139	M	DLD	7	94	0.865
93	M	DLD	7	85	0.875
39	M	DLD	7	95	0.876
55	F	DLD	7	86	0.917

specificity is 0.844

7 in the TLD group (n=45) score below the cut-off of 0.755:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
44	F	TLD	7	84	0.562
3	F	TLD	7	82	0.688
19	F	TLD	7	92	0.708
18	M	TLD	7	85	0.719
35	M	TLD	7	82	0.729
77	M	TLD	7	83	0.740
42	F	TLD	7	85	0.750

year 8

threshold	sensitivity	specificity
0.828	0.636	0.81

sensitivity is 0.636

13 in the DLD group (n=38) score above the cut-off of 0.828:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
139	M	DLD	8	105	0.844
21	F	DLD	8	98	0.854
72	M	DLD	8	91	0.854
127	M	DLD	8	105	0.865
141	M	DLD	8	87	0.865
75	M	DLD	8	96	0.875
91	M	DLD	8	109	0.875
104	M	DLD	8	107	0.896
26	M	DLD	8	97	0.917
103	F	DLD	8	111	0.925
55	F	DLD	8	99	0.938
93	M	DLD	8	97	0.944

specificity is 0.81

9 in the TLD group (n=45) score below the cut-off of 0.828:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
80	M	TLD	8	90	0.698
25	F	TLD	8	94	0.708
27	F	TLD	8	103	0.740
18	M	TLD	8	98	0.760
35	M	TLD	8	95	0.792
77	M	TLD	8	94	0.802
3	F	TLD	8	94	0.812
32	M	TLD	8	104	0.823

year 9

threshold	sensitivity	specificity
0.862	0.781	0.805

sensitivity is 0.781

8 in the DLD group (n=38) score above the cut-off of 0.862:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
21	F	DLD	9	111	0.865
26	M	DLD	9	112	0.885
81	F	DLD	9	105	0.896
13	F	DLD	9	111	0.906
93	M	DLD	9	110	0.938
55	F	DLD	9	110	0.948
104	M	DLD	9	119	0.990

specificity is 0.805

9 in the TLD group (n=45) score below the cut-off of 0.862:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
27	F	TLD	9	115	0.771
18	M	TLD	9	110	0.771
19	F	TLD	9	117	0.802
77	M	TLD	9	106	0.802
92	F	TLD	9	108	0.812
80	M	TLD	9	138	0.812
31	F	TLD	9	110	0.823
35	M	TLD	9	107	0.823

year 10

threshold	sensitivity	specificity
0.87	0.788	0.829

sensitivity is 0.788

8 in the DLD group (n=38) score above the cut-off of 0.87:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
91	M	DLD	10	126	0.875
104	M	DLD	10	132	0.885
26	M	DLD	10	121	0.896
93	M	DLD	10	122	0.896
81	F	DLD	10	116	0.906
55	F	DLD	10	123	0.927
141	M	DLD	10	112	0.948

specificity is 0.829

8 in the TLD group (n=45) score below the cut-off of 0.87:

Subject	Gender	Dx_yr1	Year	Age_in_months	NWR_prop
77	M	TLD	10	118	0.771
25	F	TLD	10	118	0.781
27	F	TLD	10	127	0.789
35	M	TLD	10	119	0.796
18	M	TLD	10	121	0.802
3	F	TLD	10	118	0.833
31	F	TLD	10	119	0.844