Supplementary material to “Anatomical predictors of post stroke
aphasia recovery” by Forkel et al.
Individual dissections
dorsal view
left-lateral view
right-lateral view
dorsal view
01
09
02
02
10
03
12
04
13
05
15
06
17
07
18
08
19
left-lateral view
right-lateral view
Hierarchical regression analysis - power calculation
A sensitivity analysis was conducted using the software package, G*Power
β can be considered as the probability of failing to detect a genuine difference (type II
error). Hence, 1–β is the ability of a test to detect an effect of a particular size. This
value is referred to as power. Effect size is the standardised measure of the magnitude
of an observed effect.
Different measures can be used to estimate power and/or effect size. For regression
analyses Cohen’s 𝑓 2 is advisable. According to Cohen the probability of failing to
detect a given effect should be at least 0.20, meaning that the corresponding power
should be at least 1–β=1–.20=.80 (i.e. 80% chance of detecting an effect if one
genuinely exists; Cohen, 1990). By convention, for multiple and multiple partial
correlations and regressions, effect sizes (𝑓 2) of 0.02, 0.15, and 0.35 are considered
small, medium, and large, respectively (Cohen, 1992).
The results of the sensitivity analysis demonstrated that this study was able to detect
an effect size (𝑓 2) of 1.14 with a power of 1–β =.80 given its sample size of n=16 and
a specified α of 0.05. In other words, this is the minimum effect size to which the test
was sufficiently sensitive.
The effect size for regression models can be calculated with the equation (Cohen,
1992):
𝑅2
𝑓 =
1 − 𝑅2
2
Applied to our data, the effect size of our three-predictor model independent was
f2=0.388 (R2 was 0.28) and effect size of the four-predictor model independent was
f2=3 (R2 was 0.75).
With the added layer of complexity in two-level hierarchical regression models the
above equation needs to be adjusted to account for subsequent models. The effect size
for hierarchical regressions can be calculated using the equation:
𝑓2 =
2
𝑅𝐴𝐵
− 𝑅𝐴2
2
1 − 𝑅𝐴𝐵
where 𝑅𝐴2 is the explained variance of the first-stage
2
three-predictor model and 𝑅𝐴𝐵
is the variance
explained by the second-level four-predictor model.
From this we can conclude that the three-predictor model has an effect size of
𝑓 2 =0.388 (R2 was 0.28) and the four-predictor model has an effect size of 𝑓 2 =3 (R2
was 0.75). Both effect sizes can be considered as large effects. This two-level
hierarchical regression model (i.e. a stepwise analysis of the three-and four-predictor
model) has an effect size of 𝑓 2 =1.88. This effect size is larger than the critical value
( 𝑓 2=1.14) determined in the previous sensitivity analysis and we could therefor
assume that this analysis is sufficiently powered to detect a genuine effect with at
least an 80% chance.
Internal Validity of Regression Model
When calculating the expected data to compare to the observed data, the regression
equation was applied where patients’ longitudinal aphasia severity can be estimated
from socio-anatomical predictors based on the following regression equation:
𝑦 =∝ +𝛽1𝑖 𝑥1𝑖 + 𝛽2𝑖 𝑥2𝑖 + 𝛽3𝑖 𝑥3𝑖 + 𝛽4𝑖 𝑥4𝑖 + ℇ𝑖
Where y is the value of the dependent variable, α represents the constant of the model,
β is the coefficient of the predictor variable, i represents the observation, x1-4 is the
predictors (here: age, sex, lesion size, and right long segment index size), andε
represents the error associated with the model.
How apt the model fits the data can be appreciated when comparing the observed and
the expected recovery (mean 94.72, SD 1.69) (Table 1 and Figure 1). The model
would predict that eight patients should have recovered above an AQ of 93.8
(observed, three patients recovered).
Figure 1 Scatterplot between observed and expected Aphasia severity at six months
based on our model.
Table 1 Comparison of observed and expected aphasia severity (AQ). AQ expected
from model is calculating the expected values from within the model.
Patient
ID
1
2
3
4
AQ observed
95.2
96.2
81.4
91.9
AQ expected
from model
93.2
109.9
94.5
99.8
5
6
7
8
9
10
12
13
15
17
18
19
73.3
87.9
73.5
87.2
81
83.1
69.7
95.6
89.2
81.1
92.2
92.3
87.4
89.5
88.3
94.5
99.7
90.8
91.9
101.2
99.1
81.2
97.1
97.7
Thrombolysis – power calculation
A power calculation revealed that the critical t-value of t=1.654 would be reached for
a one-sided independent t-test with an effect size of 0.5, and a significance level of
α=0.05 with a sample size of 176 participants (88 in each group). Further inference on
the influence of thrombolysis can therefore not be undertaken within this study.