Brain enlargement is associated with regression in
preschool-age boys with autism spectrum disorders
Christine Wu Nordahla, Nicholas Langeb, Deana D. Lia, Lou Ann Barnetta, Aaron Leea, Michael H. Buonocorec,
Tony J. Simona, Sally Rogersa, Sally Ozonoffa, and David G. Amarala,1
aMedical Investigation of Neurodevelopmental Disorders (M.I.N.D.) Institute and Department of Psychiatry and Behavioral Sciences, UC Davis School of
Medicine, University of California, Sacramento, CA 95817;bDepartments of Psychiatry and Biostatistics, Harvard University Schools of Medicine and Public
Health, McLean Hospital, Belmont, MA 02478; andcDepartment of Radiology, UC Davis School of Medicine, University of California, Sacramento, CA 95817
Edited by James L. McGaugh, University of California, Irvine, CA, and approved October 19, 2011 (received for review May 12, 2011)
Autism is a heterogeneous disorder with multiple behavioral and
biological phenotypes. Accelerated brain growth during early
childhood is a well-established biological feature of autism. Onset
pattern, i.e., early onset or regressive, is an intensely studied be-
havioral phenotype of autism. There is currently little known,
however, about whether, or how, onset status maps onto the
abnormal brain growth. We examined the relationship between
total brain volume and onset status in a large sample of 2- to 4-y-
old boys and girls with autism spectrum disorder (ASD) [n = 53, no
regression (nREG); n = 61, regression (REG)] and a comparison
group of age-matched typically developing controls (n = 66). We
also examined retrospective head circumference measurements
from birth through 18 mo of age. We found that abnormal brain
enlargement was most commonly found in boys with regressive
autism. Brain size in boys without regression did not differ from
controls. Retrospective head circumference measurements indicate
that head circumference in boys with regressive autism is normal
at birth but diverges from the other groups around 4–6 mo of age.
There were no differences in brain size in girls with autism (n = 22,
ASD; n = 24, controls). These results suggest that there may be
distinct neural phenotypes associated with different onsets of au-
tism. For boys with regressive autism, divergence in brain size
occurs well before loss of skills is commonly reported. Thus, rapid
head growth may be a risk factor for regressive autism.
icits in social interaction and communication, with restricted
interests and repetitive behaviors (1). It is a behaviorally defined
disorder that is typically diagnosed during early childhood. The
prevalence of autism spectrum disorders (ASD) in the United
States is estimated to be 1 in 110 children (2). Autism is di-
agnosed more frequently in males than females at a ratio of 4–1.
Current research suggests that autism is a heterogeneous disor-
der (3, 4), with a broad range of severity and intellectual ability
as well as a variety of comorbid conditions, such as epilepsy,
anxiety, and gastrointestinal conditions (5, 6). The heterogeneity
of this disorder is one of the major roadblocks to establishing
etiologies that could then lead to more effective prevention and
intervention. In the context of an ongoing, multidisciplinary ef-
fort to establish distinct autism phenotypes (the Autism Phe-
nome Project, APP), we have examined the relationship between
a behavioral feature of autism, onset status, and a commonly
reported biological feature of autism, accelerated head growth
and abnormal brain enlargement.
There is now ample evidence suggesting that brain growth in
children with autism is accelerated, leading to an abnormally en-
larged brain in early childhood (7). Studies using retrospective
that whereas children with autism are born with normal or slightly
smaller brain size, the trajectory of growth accelerates during the
first year of life (8–10).Several MRI studies ofvery young children
utism is a neurodevelopmental disorder with hallmark def-
with autism report a 5–10% abnormal enlargement in total brain
volume that persists into early childhood (11–13).
An altered trajectory of brain growth is now widely cited as
central to the neuropathology of autism (3). However, several
additional questions remain to be explored. Little is known about
how generalized the finding of brain enlargement is across all
individuals with autism. Both microcephaly and macrocephaly
have been reported in autism (14), and increased variability in
head size is also observed (15). Does brain enlargement occur in
the majority of individuals with autism or does it occur in just a
subset of individuals? Are there any clinical correlates to brain
enlargement? Also, studies of typical development have docu-
mented sex differences in the developing brain (16, 17). How-
ever, there is very little known about whether brain development
in children with autism is sexually dimorphic as well.
To address these issues, we initiated a large-scale, multidisci-
plinary study, the APP, to explore potential biological and be-
havioral phenotypes in autism. The goal of the APP is to enroll a
large sample of children and to carry out a comprehensive lon-
gitudinal analysis to begin to identify more homogeneous sub-
groups or phenotypes within the autism spectrum disorder
population. Extensive behavioral and biological data are col-
lected on all participants to correlate changes in brain growth
with other biological and behavioral facets of autism. One ex-
ample of a behavioral phenotype in autism is onset status.
Whereas some children exhibit symptoms of autism in the first
year of life, others experience a regression or loss of previously
acquired skills in language and/or social domains. Although
there are a number of complexities in determining onset status
(18), children with autism can be characterized as regression
(REG) or no regression (nREG), using parent report of early
development. The neural underpinnings of onset status remain
unclear because only one study has yet examined this question,
in a small sample (19).
We have studied the relationship between brain size and au-
tism onset status. We hypothesized that the classification of ei-
ther regression or no regression may map onto particular
trajectories of brain growth and brain size. Specifically, we
evaluated total cerebral volume (TCV) using magnetic reso-
nance imaging at age 3 y and retrospective head circumference
measurements from birth through 18 mo of age. These data
allowed us to produce brain growth trajectories in a large sample
of children with autism relative to age-matched typically de-
veloping controls. Our sample size of 180 subjects allowed us to
Author contributions: C.W.N., M.H.B., T.J.S., S.R., S.O., and D.G.A. designed research; C.W.N.,
D.D.L., L.A.B., A.L., T.J.S., and D.G.A. performed research; C.W.N., N.L., and D.D.L. analyzed
data; and C.W.N., N.L., S.O., and D.G.A. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1To whom correspondence should be addressed. E-mail: email@example.com.
| December 13, 2011
| vol. 108
| no. 50
analyze sex differences in brain size and growth trajectories re-
lated to onset status as well.
Participant characteristics are presented in Table 1. A total of
180 children, 2- to 4 y of age, participated in this study, 114 with
ASD (101, autistic disorder; 11, pervasive developmental disor-
der-not otherwise specified) (PDD-NOS) and 66 age-matched
typically developing (TD) controls. Of the children with ASD,
54% had ASD-REG and 46% ASD-nREG. There were no sig-
nificant differences in age between any of the groups. There were
also no sex differences in autism severity or developmental
quotient (DQ). As expected, DQ was significantly higher in TD
controls than children with ASD (P < 0.01). There was no sig-
nificant difference between the ASD-REG and ASD-nREG
groups on the Autism Diagnostic Observation Schedule-Generic
(ADOS-G) severity score, which allows for comparison of autism
severity across participants tested with different ADOS-G
modules (P > 0.10). There was a marginally significant difference
in DQ between the two groups of children with different onset
status (P = 0.05). Groups were matched on gestational age,
ethnicity, and socioeconomic status.
Total Cerebral Volume. Table 2 provides results and effect sizes
from our cross-sectional analysis of TCV. Fig. 1 depicts group
differences in TCV for males and females separately. Volumetric
differences between ASD-nREG, ASD-REG, and TD groups
were analyzed using ANCOVA for males and females separately,
as well as combined in a single model with sex as a covariate. The
models assign separable variability to each covariate to avoid
mistaking contributions from a secondary covariate (e.g., age) as
arising from the covariate of interest (group), thus providing
more accurate and precise estimates of true effects. Covariates
analyzed include age, body mass index (BMI), DQ, age × group,
and group × sex interactions (for the combined sex model). We
report effect sizes equal to the t statistics that provide the P
values, where each is equal to the magnitude of the effect divided
by its SE from the model. Roughly, any effect size greater than 2
may be considered large, because its significance value is P =
0.05 or smaller. In males, TCV increased by 8.6 cm3(0.8%) per
month. In females, TCV increased by 6.1 cm3(0.6%) per month.
TCV was unrelated to BMI and DQ.
In males, relative to TD controls, the ASD-REG group had a
significant increase in TCV of 63.4 cm3(6.2%), whereas the
ASD-nREG group did not differ from TD controls (Fig. 1).
There were no age × group interactions. In females, there were
no group differences nor any age × group interactions (Fig. 1).
Results of the combined model confirmed those of sex-
As a secondary analysis, we also examined the rate of mega-
lencephaly in ASD-REG and ASD-nREG groups relative to the
TD controls in males. We defined megalencephaly as TCV
greater than 2 SDs above the TD mean (male TD control mean
984.7; SD 72). Out of 51 males in the ASD-REG group, 22% had
megalencephaly. Out of 41 males in the ASD-nREG group, 5%
Finally, we also explored the relationship between TCV and
autism severity. In children with ASD, there was no correlation
between TCV and ADOS severity score (r = 0.05).
Head Circumference, Birth Through 18 Mo. Cross-sectional analysis.
Retrospective head circumference measurements were avail-
able from a subset of 120 subjects (n = 42 TD, n = 34 ASD-
nREG, n = 44 ASD-REG). A total of 717 measurements were
obtained from birth through 18 mo of age. Head circumfer-
ence measurements from TD participants fell within the in-
terquartile ranges of the World Health Organization (WHO)
Child Growth Standards at each time point. Thus, this TD
sample is representative of the general population, and all ASD
group comparisons were evaluated relative to the current
Fig. 2 depicts cross-sectional head circumference measure-
ments at various age intervals from birth through 18 mo. Table 3
provides results and effect sizes from our cross-sectional
ANCOVA analyses including age, sex, and group as covariates at
2- to 3-mo increments. As anticipated, sex had a strong effect on
head circumference. Head circumference measurements in
males were, on average, between 2.4–3.7% larger than female
head circumference across this age span.
After isolating sex differences to focus on group and age
effects only, the model showed a pronounced increase in cross-
sectional head circumference in the ASD-REG group relative
to TD controls beginning at 4.0–5.9 mo of age that persisted
through 18.9 mo of age. The ASD-REG group had an average
head circumference enlargement of 2–3% above TD controls
from 4 to 18.9 mo (except during 13–15.9 mo), reaching a dif-
ference of 5.3% between 16 and 18.9 mo. Head circumference
in the ASD-nREG group did not differ from TD controls,
except a modest 1.5% difference during the 10- to 14-mo cross-
Longitudinal analysis. We examined individual longitudinal changes
in head circumference between birth and 18 mo of age in a subset
of children having at least three head circumference measure-
ments (n = 95; 77 male, 18 female). Due to the paucity of re-
peated measurements in females, we restricted these analyses to
males (ASD-nREG n = 26, ASD-REG n = 19, TD n = 32).
Fig. 3 depicts individual changes in head circumference over
time (shaded lines) and results from a piecewise linear longitu-
Table 1.Participant characteristics
ASD-nREG, autism with no regression; ASD-REG, regressive autism; TD,
typical development; ADOS, autism diagnostic observation schedule; DQ,
development quotient. Age, ADOS severity score, and DQ: mean (SD).
Table 2. ANCOVA results for total cerebral volume
TD volume (cm3) Difference (%)Effect SizeP value Difference (%) Effect sizeP value
See Table 1 legend for definitions. TD volume, mean (SD). Difference is cm3from TD mean. Covariates include
age, body mass index, and DQ.
| www.pnas.org/cgi/doi/10.1073/pnas.1107560108 Nordahl et al.
dinal model fit to each clinical group (bold lines). Table 4 pro-
vides the results of the comprehensive model including all
groups. On the basis of preceding cross-sectional analyses sug-
gesting that ASD-REG group divergence begins between 4 and 6
mo of age, we examined age- and group-dependent longitudinal
head circumference growth before and after 4.5 mo of age.
As indicated in Table 4, age is a highly significant predictor of
head circumference. Age acquires more predictive importance
when group differences are taken into account. We found an
average increase in head circumference of 1.80 cm per month in
all subjects during the first 4.5 mo of life (P < 0.001), followed by
more gradual increase of 0.44 cm per month thereafter (P <
0.001). Average head circumference in the ASD-REG group was
1.13 cm larger than that of the TD group (P < 0.001) across the
entire age range. We found that the rates of growth relative to
TD differed slightly between the ASD groups before 4.5 mo, with
0.21 cm/month in the ASD-nREG group (P = 0.003) and 0.14
cm per month in the ASD-REG group (P = 0.021). The age ×
group interaction was not significant after 4.5 mo of age.
The results presented in this report indicate that abnormal brain
enlargement is not generalized across all individuals with autism.
Accelerated head growth and brain enlargement was most con-
sistently observed in the subset of children who had regressive
autism. Specifically, total brain volume in 3-y-old males with
regressive autism was ∼6% larger than that of age-matched
typically developing controls. Indeed, 22% of boys with re-
gressive autism had megalencephaly, whereas only 5% of boys
without regression had megalencephaly. When did this abnormal
enlargement occur? Analysis of head circumference data, which
is a reliable proxy for total brain volume in young children (20),
indicates that the divergence in head size began around 4–6 mo
of age. Brain size and growth trajectory of children without
Total Cerebral Volume (cm )
Total Cerebral Volume (cm )
** p < .01
Fisher post hoc corrections). TCV in the autism without regression group (ASD-nREG) did not differ from TD. There were no group differences for the females.
Horizontal lines represent mean TCV for each group.
Total cerebral volume (TCV) is enlarged in males with regressive autism (ASD-REG) relative to typical development (TD) (ANCOVA with group, age and
Head Circumference (cm)
* p < .05
** p < .01
The ASD-REG group diverges from the ASD-nREG and TD groups around 4–6 mo of age.
Cross-sectional analysis of head circumference measurements from birth through 18 mo of life. Groups do not differ from birth through 4 mo of age.
Nordahl et al.PNAS
| December 13, 2011
| vol. 108
| no. 50
regression did not differ from typically developing controls.
Moreover, brain enlargement was not observed in girls with
ASD, regardless of autism onset status. These findings provide
suggestive evidence that the biological underpinnings of early
onset and regressive forms of autism are different.
Behavioral Correlates of Abnormal Brain Enlargement. Although
there is ample evidence for an altered trajectory of brain growth
during the first years of life (7), relatively little is known about
the behavioral correlates of this altered trajectory. There is some
evidence that increased head circumference is associated with
increased autism severity and that macrocephaly may be asso-
ciated with a delay in the onset of language (15), but clear and
consistent associations have not been reported. MRI studies of
brain enlargement in young children also have not shown any
clear correlations with autism severity (12).
In the current study, we found an association between brain
enlargement and regressive autism. The rate of regression in our
sample of children with autism was 54%, which is similar to that
of recent large-scale population-based studies (21, 22). Our head
circumference findings are consistent with the notion that ac-
celeration of head growth precedes onset of behavioral symp-
toms (10). We observed an increase in rate of head growth in
children with regressive autism as early as 4–6 mo of age. By 18
mo of age, head size was 5% larger in children with regressive
autism than typically developing controls. At age 3, total brain
volume remained about 6% larger. Thus, accelerated growth
appears to have taken place during the first 18 mo and thereafter
the rate of further growth came in line with that of typically
developing children. Importantly, these differences in brain size
were observed even after controlling for age, sex, body mass
index, and DQ.
To our knowledge, onset status has not been investigated in
relationship to brain volume in previously published MRI studies
of autism. One head circumference study of 28 males with autism
(11 with regression) did not report an association between onset
status and rate of head growth in the first year of life (19). It is
likely that the substantially larger sample size and retrospective
longitudinal data in the present study provided greater statistical
power to detect differences in the pattern of head growth.
Brain Development in Girls with Autism. Very little is known about
the neuropathology of autism in females. There is some pre-
liminary evidence suggesting that girls have similar (23) and
possibly even more pronounced volumetric differences than boys
(13, 24, 25). However, sample sizes in these studies are quite
small, with fewer than 10 girls with autism in each study. The
sample size of girls in the current study is the largest reported to
date (n = 22 ASD, 24 TD). Interestingly, we found no
differences in growth trajectory or brain size from birth to 3 y of
age regardless of onset status. Clearly, additional studies with
even larger sample sizes are needed to elucidate the neuropa-
thology of autism in females. On the basis of available literature
and results from the current study, it is likely that the pattern of
pathology is different in females than in males.
Limitations. One limitation of the present study is the sole re-
liance on parent report for establishing onset status. Recent
papers have pointed out significant complexities in defining and
measuring the onset of autism symptoms (18). Studies have
demonstrated relatively low correspondence between parent
report of onset and home videotape evidence of symptom tra-
jectories (26), with one study showing that 45% of participants
clearly demonstrated a regression on videotape that was not
reported by parents (27). Similarly, a recent prospective study
found that regression was evident in many infants who were
developing autism but was reported by only a minority of parents
(28). It may be, therefore, that some of the children character-
ized in the no-regression group in the current study may more
appropriately be considered to be in the regressive group. Thus,
we must be cautious in our interpretations of the current data,
0 3 6 9 12 15 18
Head Circumference (cm)
represent the growth trajectories of the brains of individuals in this study.
Bold lines indicate the piecewise linear longitudinal model fit to each clinical
group separately. Results from the longitudinal analysis confirm that the
ASD-REG group is larger than the TD and ASD-nREG groups.
Longitudinal head circumference growth in males. Lighter lines
adjusted for age, group, and sex
Cross-sectional differences in head circumference (cm) from typical development
Age, mo 0.0–1.9 2.0–3.9 4.0–5.9 6.0–7.9 8.0–9.9 10.0–12.9 13.0–15.9 16.0–18.9
Sample size TD
ASD-EO, early onset autism. For other definitions, see Table 1 legend. *Uncorrected, two-sided; **NS, P > 0.20.
| www.pnas.org/cgi/doi/10.1073/pnas.1107560108Nordahl et al.
and replication, preferably using prospective direct observational
methods of classifying onset, is needed. Nevertheless, parent
report remains the most practical method of defining autism
onset at the present time. Moreover, our strategy of using both
the Autism Diagnostic Interview- Revised (ADI-R) and Early
Development Questionnaire (EDQ) with additional parent
interviewing to reconcile differences hopefully increased the
reliability of parent report in the current study. The robust dif-
ferences in brain growth trajectory of the different onset groups
suggest there may well be an association between onset and
neurobiological underpinnings that has emerged despite poten-
tial noise in the assays.
In addition, further exploration of head growth trajectories in
the first 2 y of life is needed. The sample sizes for the head
circumference analyses in the current study cover the first 2 mo
of life predominantly. A more comprehensive study of longitu-
dinal head circumference measurements would be informative.
Implications and Future Directions. This study highlights the com-
plexity and heterogeneity of autism. We have found that a com-
monly reported biological feature of autism, abnormal brain
enlargement, is mainly present in a subset of male children with
regressive autism. Investigations of how different genetic under-
pinnings or immunological profiles may map onto our findings are
important next steps. In fact, the overarching goal of this research
is to identify more homogeneous subgroups of individuals with
autism to facilitate analysis of the etiology of each type. Ongoing
aspects of brain structure and function, such as white matter mi-
crostructure and connectivity, will very likely shed light on addi-
tional neural phenotypes that may relate to other behavioral or
biological aspects of autism. Thus, whereas the children with early
autism onset did not differ from typically developing controls with
respect to brain growth trajectory and total brain volume at age 3,
this does not imply that these children have normal brain de-
velopment, but rather that changes are likely more subtle than
what is detectable with these relatively gross volumetric measures.
Similarly, females with autism did not exhibit abnormal brain en-
largement or trajectory of growth, but another aspect of brain
development or function must be altered.
The major finding of this study is that a subset of boys with
regressive autism have normal head circumference at birth,
which diverges from normality around 4–6 mo of age, well before
any loss of skills were documented. Thus, rapid head growth
beginning around 4–6 mo of age may be a risk factor for future
loss of skills. Furthermore, whereas behavioral regression in
autism usually occurs between 12 and 24 mo of age, we found
that the brain changes that are associated with this form of au-
tism begin as early as 4 mo of age. This calls into question the
association of pediatric vaccinations, in particular the measles,
mumps, and rubella (MMR) vaccine, administered close to the
time of regression as a causal factor in the disorder. Clearly,
additional studies need to be conducted to elucidate the precise
neural underpinnings of this rapid head growth that precedes the
behavioral onset of regressive autism.
Materials and Methods
Participants. Subjects were enrolled in the Autism Phenome Project. At study
entry, height, weight, and occipitofrontal circumference were measured by
trained study personnel.Diagnostic instruments included theADOS-G(29, 30)
and the ADI-R (31). Diagnostic criteria for ASD were based on the Collabo-
rative Programs of Excellence in Autism network. Participants met ADOS
cutoff scores for either autism or ASD. In addition, the participants were
over the ADI-R cutoff score for autism on either the social or communication
subscale and within two points of this criterion on the other subscale. An
ADOS severity score was calculated (32), which allows for comparison of
autism severity across participants tested with different ADOS-G modules.
Developmental ability was obtained for all participants using the Mullen
Scales of Early Development (MSEL) (33). A DQ was calculated as the average
of the age equivalent scores on the visual reception, fine motor, receptive
language, and expressive language scales, divided by chronological age,
multiplied by 100.
For TD controls, inclusion criteria were developmental scores within two
SDs on all scales of the MSEL. In addition, TD children were screened and
excluded for autism using the Social Communication Questionnaire (SCQ-
Lifetime Edition) (scores > 11).
All children were native English speakers, ambulatory, and had no sus-
pected vision or hearing problems or known genetic disorders, and/or other
neurological conditions. In the ASD group, one child with fragile X syndrome
and five with a history of abnormal EEGs were excluded. Additional exclu-
sionary criteria included physical contraindications to MRI. This study was
approved by the University of California (UC) Davis Institutional Review
Board, and informed consent was obtained by the parent or guardian of
Onset Status. Onset classification was determined using the ADI-R (18). To
be classified in the ASD-REG group, parents had to indicate that their child
had acquired and then lost at least five words and/or demonstrated losses
in social engagement, social responsiveness, and social interest. Parents of
children classified as ASD-nREG, indicated that their child had not lost such
language and social abilities. For validation purposes, the EDQ (34), a set
of 70 questions that detail development and regression over the first 18
mo of life, was also administered. If parents gave inconsistent responses
across the two measures, further parent interviewing was done to resolve
Imaging. Scans were acquired during natural, nocturnal sleep (35) at the UC
Davis Imaging Research Center on a 3T Total Imaging Matrix (TIM) Trio
whole-body MRI system (Siemens Medical Solutions) using an eight-channel
head coil. Success rate in acquiring images during natural sleep was 85%.
For each participant, a 3D T1-weighted magnetization prepared rapid
acquisition gradient echo (MPRAGE) scan (TR 2170 ms; TE 4.86 ms; matrix
256 × 256; 192 sagittal slices, 1-mm isotropic voxels) was obtained. A T2-
weighted scan was also obtained for clinical evaluation when possible (i.e.,
when the child remained asleep). All MPRAGE and available T2 scans were
reviewed by a pediatric neuroradiologist and screened for significant, un-
expected clinical findings. A calibration phantom (Magpham Alzheimer’s
Disease Neuroimaging Initiative; Phantom Laboratory) was scanned at the
end of each MRI session using an MPRAGE pulse sequence matched to the
study sequence. The phantom was used to derive a 3D image distortion map
for each child’s MRI scan. Distortion correction was then carried out on each
participant’s images (Image Owl). This distortion correction step ensures
accuracy in volumetric measurements of TCV by removing any distortion
associated with scanner hardware or head placement.
Total Cerebral Volume. Image preprocessing included removing nonbrain
tissue (36), and correcting inhomogeneity (37). TCV was measured using a
template-based automated method. Each participant image was warped
to a study-specific template. A mask, with the brainstem and cerebellum
removed, was created on the template by carrying out a manual tracing of
the cerebrum (38). The mask was applied to all participant images. Images
were transformed back to native space and TCV was calculated. This auto-
mated protocol was validated by carrying out reliability checks with 10
manually defined volumes. Intraclass correlation coefficient was 0.98.
Results of longitudinal mixed-effects model for male
TD (mean ± SD) cm
34.6 ± 1.8
At 4.0–5.0 mo
42.8 ± 1.4
Age < 4.5 mo (cm/mo)
Age ≥ 4.5 mo (cm/mo)
ASD-nREG x age (<4.5 mo)
ASD-REG x age (<4.5 mo)
See Table 1 legend for definitions.
Nordahl et al.PNAS
| December 13, 2011
| vol. 108
| no. 50
Head Circumference. Retrospective head circumference measurements were Download full-text
obtained from pediatric medical records (i.e., well-baby visits) obtained
through the APP. Birth head circumference measurements were obtained
from labor and delivery records. Occipitofrontal measurements were ab-
stracted from the medical records.
Biostatistical Analysis.Cross-sectional analysesof TCV andheadcircumference
were performed by using multiple linear regression (ANCOVA) that included
age, sex, BMI, DQ, and group as covariates. Longitudinal time series of in-
dividual head circumference growth in males from birth through 18 mo
were analyzed using a piecewise linear longitudinal random-effects model
(39). Our model set a change point at 4.5 mo, consistent with the initial
cross-sectional analysis and verified in the longitudinal data. The piecewise
linear model yielded a better and more interpretable fit than did a quadratic
age model of equal complexity (having an equal number of model param-
eters) or higher-order polynomials with change points. An additional
advantage of the piecewise linear model was that a quadratic fit was not
forced at age extremes (birth and 18 mo), thus avoiding potential bias at the
endpoints. For all analyses, a uniform application of the Akaike information
criterion (40) determined the inclusion and exclusion of covariates to yield
the simplest, best-fitting models among all other choices.
ACKNOWLEDGMENTS. The authors acknowledge the following individuals
for their help in the logistics of family visits and data collection: L. Deprey,
K. Harrington, J. Nguyen, K. Ross, S. Rumberg, P. Shoja, and A. Stark. We thank
E. Fletcher for technical assistance and K. Camilleri, C. Green, C. McCormick,
S. Subramanian, R. Scholz, S. Sepehri, M. Shen, and C. Rossi for invaluable
assistance in acquiring MRI data; and we especially thank all of the families
and children who participated in the Autism Phenome Project study.
Funding for this study was provided by the National Institute of Mental
Health (1R01MH089626, U24MH081810, and 1K99MH085099) and the
University of California Davis Medical Investigation of Neurodevelopmental
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