Is It Possible to Differentiate the Impact of Pediatric Monophasic Demyelinating Disorders and Multiple Sclerosis After a First Episode of Demyelination? - Longitudinal Registration and Shape Modeling - page 39

To model the individual growth curves, we used mixed effect models that take repeat-
ed measures from the same individuals over time and accounts for the within-subject
correlation and for varying numbers of measurements for each subject [15]. The coeffi-
cients for fixed effects provide estimates of the average response in a group while sub-
ject-specific random effects account for heterogeneity among responses from different
individuals as well as a covariance pattern among responses within an individual [16].
We computed 3 different brain and normalized thalamus models: one with the pa-
tient group (included MS, ADEM and MONO subjects), one with the NC group and
one with the NIHPD group. The models were built using the nlme package [17] in R
software. In constructing the model, the fixed effects that were considered for inclu-
sion were sex and age. Because individual profiles suggest modeling brain growth as
a cubic function over time, an intercept and a linear, quadratic and cubic time effect
(age, age2, age3) were included in the fixed effects structure. The parameters of the
models were estimated with the maximum likelihood method, and evaluated using the
Akaike information criterion (AIC [17]).

Growth Rate Computation and Comparison
For each patient, each of the four metrics (brain volume, brain growth rate, normal-
ized thalamus and normalized thalamus growth rate) computed at the time of the first
attack were compared with the same metric computed on a subset of the NIHPD nor-
mal subjects that were of the same sex and age (+/- 6 months).
Z-scores were computed as follows:
Zscore

(1)

Where V is the subject metric for each patient, µ is the mean and σ the standard
deviation of the corresponding metric in the normal subjects (NIHPD group) of same
sex and age ± 6 months.
Z-scores were also computed to compare NC subjects (acquired on the same scan-
ner than the patients) to NIHPD subjects to exclude any scanner-related influence .

3 Results

3.1 Volume Computation and Individual Trajectory Model Creation

According to the AIC values, the following cubic mixed model with fixed and ran-
dom effects was defined as best for brain and normalized thalamus growth for the
NIHPD group:
Vol ij = ʲ 0 +ʳ 0 i + (ʲ 1 +ʳ 1 i ) Age + ʲ 2 .Age

² + ʲ 3 .Age 3 + ʲ 4 .Sex i +

ʲ 5 .Age*Sex i + ʲ 6 .Age 3 *Sex i + E ij
where Vol ij is the value of the structure volume (e.g., brain or thalamus) for time point
j of subject i , ʲ 0 is the intercept, ʲ 1 the linear term, ʲ 2 the quadratic term, ʲ 3 the cubic
term, ʲ 4 the coefficient of sex (multiplied by 1 if male, 0 if female), ʲ 5 the interaction
between age and sex, and ʲ 6 the interaction between age [3] and sex (multiplied by 1
if male, 0 if female), ʳ 0 i and ʳ 1i are the random effects coefficients specific for subject