Autism spectrum disorders are a group of pervasive developmental anomalies characterized by impairments in verbal and nonverbal communication and social interaction, and a restricted repertoire of activities and interests combined with repetitive behavior and stereotypies. Autistic disorder (classical autism) involves profound deficits in all these areas, and is associated with a wide range of cognitive functioning (Tager-Flusberg, Joseph, & Folstein, 2001). According to latest estimates, it affects 1 in 1,000 individuals in the general population with the majority (4:1) being males (Fombonne, 2003). The reliance on behavioral features in identification means that the diagnosis of autism rarely occurs prior to 3 years of age, and is even later in children without associated intellectual disability. Thus, research efforts have aimed at pinpointing biological markers to facilitate early diagnosis and intervention. Identification of such markers also help to better understand the pathomechanisms leading to these developmental anomalies.

Neuropathologic and neuroimaging studies in autistic disorder have reported developmental changes in specific regions of the brain, including the cerebellum, mesial temporal structures, brainstem, basal ganglia, frontal and parietal regions, amygdala, and the corpus callosum, although these findings have not been replicated in all studies (see Acosta & Pearl, 2003; Gillberg & Coleman, 2001, for a review). One of the most consistent anatomical findings, which consolidates evidence for the biological basis of autism, is an enlarged head circumference, found across all age groups (e.g., Bailey et al., 1995; Courchesne, Carper, & Akshoomoff, 2003; Deutsch & Joseph, 2003; Fombonne, Roge, Claverie, Courty, & Fremolle, 1999; Lainhart, 2003; Lainhart et al., 1997; Woodhouse et al., 1996). Courchesne et al. (2003) used preexisting medical records of children with autism to chart growth in head circumference between birth and 14 months in comparison to infants from two normative databases. In keeping with the data from earlier cross sectional studies, they found that 59% of the target infants showed accelerated growth trajectories in comparison to only 6% of healthy infants from a longitudinal sample. Indeed, it has recently been shown that infantile macrocephaly (i.e., head circumference >97th percentile) is associated with an increased risk of developing an autism spectrum disorder (Bolton, Roobol, Allsopp, & Pickles, 2001). The frequency of enlarged head circumference is also increased in first-degree relatives, providing evidence that this characteristic may be a familial subclinical marker of autism (Fidler, Bailey, & Smalley, 2000).

The findings of an enlarged head circumference in autism are consistent with findings of increased brain size, using magnetic resonance imaging images (Aylward, Minshew, Field, Sparks, & Singh, 2002; Courchesne et al., 2001; Piven, Ardnt, Bailey, Havercamp, & Andreasen, 1996; Sparks et al., 2002). However, although a larger head circumference has been found across the life span, the increased brain size seems to only characterize young children with autism. Courchesne et al. (2001) found that children aged 2–4 years had larger brains than matched normal controls, whereas those aged between 5 and 16 years had slightly smaller brain volumes than the control children, suggesting that the early phases of excessive growth fail to be sustained. Aylward et al. (2002) found that although children with autism aged between 8 and 12 years had larger brains, there were no differences in brain size between the adolescents and adults with autism and the age matched controls. Despite some inconsistency in the data, it appears that autism is associated with acceleration in brain growth during early childhood. These changes clearly happen after birth, as head circumference at the time of birth is either within normal limits (Courchesne et al., 2001; Lainhart et al., 1997; Ostavik, Strmme, Ek, Torvik, & Skjeldal, 1997; Stevensen, Schroer, Skinner, Fender, & Simensen, 1997), or slightly smaller (Courchesne et al., 2003).

The larger head circumference and brain size in autism have been attributed to an excess of neurons, and/or reduced synaptic pruning (Keller & Persico, 2003). The finding that increased brain volumes in young children with autism was associated with hyperplasia in cerebral grey matter, and cerebral and cerebellar white matter (Courchesne et al., 2001), has led to the suggestion that a p27 gene, known to play a role in white matter development (Casaccia-Bonnefil et al., 1997), may be involved. At the biochemical level, the enlarged brain volume has been linked to the increased levels of neurotrophins (brain-derived neurotrophic factor, neurotrophin-4, and neuropeptides: vasoactive intestinal polypeptide [VIP], calcitonin gene-related protein [CGRP]; Akshoomoff, Pierce, & Courchesne, 2002; Courchesne et al., 2001). These were found in the neonatal blood spots of infants who later received a diagnosis of autism (Nelson et al., 2001). These factors have been known to increase neuronal survival (Lewin & Barde, 1996), and to play an important role in central synapse formation and maturation (Vicario-Abejon, Owens, McKay, & Segal, 2002).

There is evidence, however, that the neurotrophic factors noted above also play an important role in immunomodulation (Nassenstein et al., 2003), angiogenesis (Kraemer & Hempstead, 2003), and body metabolism (Chaldakov, Fiore, Hristove, & Aloe, 2003). Evidence for the significant role of neurotrophins and neuropeptides (CGRP and VIP) in bone metabolism and growth (Garcia-Castellano, Diaz-Herrera, & Morcuende, 2000) suggests that the increased levels of these factors in autism may affect both brain development and linear growth. However, to date, there has been no systematic study of physical growth in individuals with an autism spectrum disorder.

Three studies to date have reported data on stature in autism. In their study of 101 males and females with autism aged 2–7 years and of mixed intellectual ability, Campbell et al. (1980) found that the participants were shorter (and heavier) than their siblings and normally developing peers. Courchesne et al. (2003) compared body length (and weight) between birth and 14 months in male and female infants with an autism spectrum disorder and healthy infants, and found no differences between the groups. The third study (Davidovitch, Patterson, & Gartside, 1996) found that enlarged head circumference was strongly related to increased height (and weight) in a mixed ability, mixed gender group of young children with autism.

The aim in the present study was to explore the possibility of generalized growth dysregulation in autism by investigating growth in stature and head circumference between birth to 3 years of age, the period during which the behavioral features that characterize autism are becoming evident. We accessed repeated head circumference, length/height, and weight measurements from early health records of infants who later received a diagnosis of high-functioning autism (HFA; i.e., autism without intellectual delay) and Asperger disorder (AsD), and compared these to the records of a matched group of healthy infants. With one exception (i.e., Courchesne et al., 2003), the majority of studies of head circumference and brain volume have used cross sectional data. However, longitudinal data are essential for a full characterization of the developmental changes that occur in an individual.

AsD represents a milder form of autism spectrum disorder, with no delay in verbal communication, and it is only one-fourth as common as autistic disorder (Fombonne, 2003). The only study of head circumference in children with this disorder showed that these individuals were more likely to have an enlarged head circumference at birth and later in development than a group of lower functioning participants with autism and a group of children with attention-deficit/hyperactivity disorder (Gillberg & de Souza, 2002). Given the behavioral similarities between individuals with autistic disorder and AsD (DSM-IV, American Psychiatric Association, 1994; International Classification of Disorders—10, World Health Organisation [WHO], 1993; see review by Macintosh & Dissanayake, 2004), and the debate regarding the diagnostic distinctions between these conditions (Bishop, 1989; Gillberg, 1989; Klin, Volkmar, & Sparrow, 2000; Wing 1991), it was of interest in this study to investigate whether children with HFA and AsD are also similar in terms of their early growth patterns.

Growth in stature and head circumference were analyzed using the linear mixed-effects model (Laird & Ware, 1982). The growth parameters estimated in the two groups of children with HFA and AsD were compared with each other and with those from matched normal controls. If the results show accelerated growth in stature as well as in head size in the children with HFA and AsD relative to the normal controls, they will suggest that growth dysregulation in these clinical conditions is not limited to the brain. Although our primary interest was to chart skeletal growth, weight data were also examined. If similarities are found in the growth parameters for the children with HFA and AsD, this will lend additional support to the view that these conditions are not distinct diagnostic entities.

Method

The sample and data collection

The health records of 16 children with HFA, 12 children with AsD, and 19 normally developing children (NC) were obtained from the relevant Maternal and Child Health (MCH) Centers following parental consent. None of the children had been premature at birth, and all were male and physically healthy.

Head circumference and body length/height and weight had been repeatedly measured and recorded in each participant's health charts by trained MCH nurses at routine developmental checkups between birth and 3 years of age. These measurements are taken in a standard fashion, using a measuring tape for head circumference, standard scales for weight, and a reclining measuring board for body length. Height measurements from 2 years of age were taken using a free-standing anthropometer.¹

In accessing retrospective data, which was collected prior to the children being diagnosed, the possibility of bias in taking the physical measurements was eliminated. Moreover, as the measurements were taken by different nurses, the possibility of any systematic error in measurement is also unlikely. Thus, there are clear advantages in the use of such data (Courchesne et al., 2003).

Given the nature of real-world data, a different number of measurements were available for each child in each group across the 3-year period (see Table 1). Given the retrospective nature of this data, no reliability measures are available.

Number of data points for each group of participants for head circumference, body length/height, and weight

The children in each group had participated in another study at the Child Development Unit at La Trobe University on social understanding and social responsiveness (Dissanayake & Macintosh, 2003), at which time they were aged between 4 and 11 years. The children had been recruited via advertisements placed in the publications of various autism-related organizations. All families who participated in the original study (HFA = 20, AsD = 19, NC = 20) consented to the release of their children's MCH records. Unfortunately, only a subset of records was available for use in the current study. Some records could not be located and others could not be accessed as a result of some infants being born interstate or in another country. Data were extracted from all available records, with the exception of the data from one normal child who was premature.

The children in the clinical groups had been diagnosed by experienced clinical psychologists/psychiatrists using DSM-IV (American Psychiatric Association, 1994) criteria. Clinical records and developmental histories were examined closely to confirm the diagnoses. All participants had a full-scale IQ above 70 (assessed with the short form of the Stanford–Binet Intelligence Scales, 4th edition; Thorndike, Hagen, & Sattler, 1986) at the time of their participation in the social abilities study, so that none met criteria for an intellectual disability. No participant had any known comorbid conditions.

Sample characteristics at the time of the original study are presented in Table 2. The three groups were matched on overall mental age, F (2, 46) = 0.947, p = 0.395, but not on chronological age, F (2, 46) = 3.552, p = 0.037, or verbal mental age, F (2, 46) = 3.339, p = .045. Post hoc analyses indicated that the NC children were significantly younger than the children with HFA (p = 0.021) and AsD (p = 0.045) and had a higher verbal mental age than those with HFA (p = 0.014). The remaining pairwise comparisons were not significant (p > 0.1). The two clinical groups were matched on each of the developmental variables.

Sample characteristics for the three groups (HFA, AsD, and NC) in the study

Growth models

Longitudinal designs are the most appropriate for describing physical growth patterns and the variety of factors likely to influence this growth. In the balanced longitudinal design, the repeated measurements are recorded at fixed time points, and an equal number of measurements are observed for all individuals. However, incomplete and irregularly spaced observations are a common feature of growth data, usually due to early withdrawal or failure to meet scheduled appointments. Statistical methods such as repeated-measures analysis of variance or multivariate regression are unsuitable for this type of data. The linear mixed-effects model of Laird and Ware (1982) used in the current study takes advantage of the fact that the mean function of longitudinal data can often be approximated by linear or nonlinear functions, and is therefore flexible to accommodate unbalanced longitudinal data. The model consists of an overall fixed effects component and a random effects component. The fixed effects component contains population-specific parameters describing average profiles, whereas the random effects component contains subject-specific parameters, describing how the individual subject's profile deviates from the average profiles.

The growth of infants less than 3 years of age is typified by a high initial growth rate, which then continuously decreases. This pattern is apparent in the scatterplot in Figure 1, where body height (cm) is plotted against age (weeks) for the three groups of infants. This relationship can be conveniently simplified by applying square root transformation of age, which yields an approximate linear relationship between the variables as shown in Figure 2. This enables us to apply a simple linear model of the form

where the intercept parameter α is the measurements of infants at age 0, β is the growth rate,²

For untransformed covariate the growth rate would initially equal λβ, then would decrease proportionally to 1/age^λ−1 as age increases, and would be equal to λβ/age^λ−1 at a specific age.

and ε_ij are random errors. The response random variable y_ij denotes either height, head circumference, or weight for the ith subject measured at age j (i = 1, … , m; j = 1, … , n_i), and t_ij = age_ij^λ, where λ(constant) = 0.5 for height and weight and 0.2 for head circumference.

A plot of the body length/height versus age for all infants (nontransformed data).

A plot of the body length/height versus the square root of age for all infants.

After group factor and random effects are incorporated, the linear mixed-effects model may be expressed as

Alternatively, this may be written as

where AU_i and AS_i are binary indicator variables with the value of 1 if the participant belongs to the HFA group or the AsD group, respectively, and zero otherwise. In this parsimonious model, the parameters have a ready interpretation. The intercept parameter α₀₀ is the average height, head circumference, or weight for the typical infant at age 0, whereas the parameters α₀₁ and α₀₂ are the average difference in the intercept between the NC children and the children in the HFA and AsD groups, respectively. The parameter b_0i describes deviation of intercept of ith subject from the average intercept. The slope parameter β₀₀ is the average age effects for the normal group, whereas β₀₁ and β₀₂ are the average differences in the slope between the NC group and the HFA and AsD groups, respectively. The parameter b_1i describes deviation of slope of ith subject from the average slope. Comparison of average growth between all three groups, was conducted by comparing the average slopes for the respective groups.

Model 1 presented in matrix form is described in Equation A.1 in Appendix A. The assumptions of random effects and within-subject error are also described in the appendix. Equation A.2 in Appendix A describes a general functional form for within-subject error ε_ij. Figures were plotted using the statistical package STATA (STATA Statistical Software, 1997). The extended linear mixed-effects Model 1 was fitted to the data using restricted maximum likelihood (REML) estimation method in the lme function in S-Plus software (S-Plus, 2001).

Results

The results for the fixed effects component from fitting the extended model to the data on head circumference, body length/height, and weight across all ages for the HFA and AsD groups are presented in Table 3. Because there were no differences between these two groups on the intercept or slope estimates for either of the measures, the groups were combined for comparison with the NC group.³

The results reported below for the combined group are consistent with the results for each clinical group compared separately with the control group.

Results from fitting the model to head circumference and body length/height data using restricted maximum likelihood estimation across all ages

The average fitted values of head circumference for the NC and the combined HFA/AsD groups plotted against age over the first 3 years of life are presented in Figure 3a. The results of fitting the model to the data for these groups (using REML estimation) are presented in Table 3. It is apparent from Figure 3a and Table 3 that there is a trend (p = .08, two-tailed test) for the children in the combined HFA/AsD group to have a smaller head circumference initially in comparison to the NC children. Considering the previous findings of enlarged head circumference in young individuals with an autism spectrum disorder, we tested the hypothesis that head circumference growth rates are elevated using a one-tailed test. There was an average higher growth rate across the 3-year period in the HFA/AsD group than in the NC group; this is most evident between 2 and 3 years of age (p = .031; see Figure 3c), where the two curves separate at approximately 52 weeks (see Figure 3b).

A plot of the average fitted values of the head circumference for normal and combined high-functioning autism/Asperger disorder groups versus age (weeks) using a fixed effects component for periods of (a) 0–156, (b) 52–104, and (c) 104–156 weeks.

The results for body length/height across the 3-year period in the combined HFA/AsD sample and in the NC sample, and the comparison between these two samples are shown in Figure 4a and Table 3, respectively. The increase in growth in the HFA/AsD group relative to the NC group is, again, most evident between 2 to 3 years of age (Figure 4c), with the curves beginning to separate at 52 weeks (Figure 4b). This increase is significant, with the p value (two-tailed test) for the difference between the HFA/AsD and NC slopes across all ages equal to .0035 (Table 3). The difference in growth rates in body length/height was also significant when each of the clinical groups (HFA and AsD) was individually compared to the NC group (HFA/NC: p = .002; AsD/NC: p = .025). There was no difference between the combined HFA/AsD group and the NC group in the estimated intercept values. The results for weight mirror those obtained for height, although the difference is less striking than for height (see Table 3). This may be attributed to the fact that, in infants, weight is highly volatile, as it is subject to alterations in feeding patterns as a result of illness and other anomalies, resulting in greater variability.

A plot of the average fitted values of body length/height for normal and for combined high-functioning autism/Asperger disorder groups versus age (weeks) using fixed effects component for period of (a) 0–156, (b) 52–104, and (c) 104–156 weeks.

Appendix A

Linear mixed-effects model

Letting y_i be the n_i-dimensional vector of measurements for the ith subject, that is, y_i = (y_i1, y_i2, … y_ni)^t, the linear mixed-effects model proposed by Laird and Ware (1982) takes the form:

where β is the p-dimensional vector of fixed effects, b_i is the q-dimensional vector of random effects, X_i is the (n_i × p) matrix of known fixed-effects, Z_i is the (n_i × q) matrix of known random-effects, and ε_i is the n_i-dimensional within-subject errors. In Model A.1 we assume b_i = (b_0i, b_1i)^t ∼ N(0, Ψ) and ε_i ∼ N(0, σ²Λ_i), where Ψ is a general (q × q) covariance matrix and assumed to be positive definite, and Λ_i is a (n_i × n_i) covariance matrix parametrized by a fixed set of parameters, and depend on i only through its dimension n_i. The random effects vector and within-subject vector are assumed to be independent of each other within each subject and to be independent between different subjects.

Covariance structure for within-subject error

Initially we assumed within-subject errors in the linear mixed-effects model are independent, normally distributed random variables with mean zero and constant variance, that is, Λ_i = I_ni. This assumption may not be realistic for growth data, where repeated measurements within subjects are often correlated, and the within-group errors have unequal variances. The extended linear mixed-effects model relaxes this assumption by allowing heteroscedactic and correlated within-group errors. Following Pinheiro and Bates (2000), the matrices Λ_i can decompose into two simpler matrices: one contains the variance and the other contains the correlation, that is, Λ_i = V_i C_i V_i, where V_i is a diagonal matrix and describes the variance structure, C_i is a positive-definite matrix with all diagonal elements equal to one and describes the correlation structure. The general variance function structure of V_i can be computed approximately by

, where

, where x_ij and z_ij denote the jth rows of X_i and Z_i, v_ij is a vector of variance covariates, δ is a vector of variance parameters, and g(.) is the variance function and assume continuous in δ. The general correlation structure of C_i is expressed as cor(ε_ij,ρ_ik) = [C_i]_jk = [h(|t_ij − t_ik|, ρ)] for j < k, where ρ is a vector of correlation parameters, and h(.) is a correlation function taking values between −1 and 1. The function h(.) is usually a decreasing function such that h(0, ρ) = 1 and that correlation between ε_ij and ε_ik depends only on the time interval between y_ij and y_ik and decreases as the length of this interval increases.

Initially, we fitted the simple linear mixed-effects model, using S-Plus software (S-Plus, 2001), where observations on the same individual were assumed independent. Next, we fitted the extended linear mixed-effects with various covariance and correlation functions. Here, the observations are no longer assumed to be independent. Several models for covariance and correlation were then considered. The final model was chosen based on smallest value of Akaike information criterion (Akaike, 1973) and the Bayesian information criterion (Schwarz, 1978), was found with variance function taking the exponential form var(ε_ij) = σ²exp(2δ_Sij t_ij) where δ_Sij are the variance parameters with different variances per group, and correlation function cor(ε_ij,ε_ik) = ρ_ij^{|t_ij−t_ik|} for j < k, the continuous time AR(1) correlation function (Jones & Boadi-Boateng, 1991).