2.1 Participants

Dyslexic and good readers were recruited in three countries (France, Poland and Germany). Reading accuracy and speed were assessed using different language-appropriate standardized reading tests (see Jednoróg et al., 2015; Płoński et al., 2017 for details). Participants came from diverse social backgrounds and had at least one and a half year of formal reading instruction to differentiate serious problems in reading acquisition from early delays that are not always persistent. They were recruited based on the following criteria: age was between 8.5 and 13.7 years old, intelligence quotient (IQ) higher than 85 or an age-appropriate scaled score of at least 7 on the Wechsler Intelligence Scale for Children (WISC) Block Design and 6 on the WISC Similarities, no spoken language disorders, no formal diagnosis of attention hyperactivity deficit disorder (ADHD), and no reported hearing, sight or other neurological problems.

Dyslexic readers were either identified in school, through clinics, or were specifically requesting a clinical assessment of their reading problems. Most of the studied children already had a clinical diagnosis of dyslexia, and all were screened for inattention/hyperactivity symptoms and language disorders. The inclusion criterion for dyslexic readers was defined as more than 1.5 SD below grade level on different appropriate standardized tests of reading, whereas good readers were less than 0.85 SD below grade level.

All studies were approved by local ethics committees (CPP Bicêtre in France; Medical University of Warsaw in Poland; Uniklinik RWTH Aachen in Germany) in compliance with the Code of Ethics of the World Medical Association—Declaration of Helsinki. The children and their parents gave informed written consent to participate in the study.

Together, 130 dyslexic (56 girls) and 106 good readers (55 girls) were included in the study.

2.2 Imaging procedure

High-resolution T1w images were acquired in five different studies:

2.3 Morphometric analysis

Image processing and analyses were carried out using SPM8 (http://ww.fil.ion.ucl.ac.uk/spm/) run in MATLAB7.11 (Mathworks, Sherborn, MA). T1w images were automatically segmented into different tissue classes (grey matter, white matter and nonbrain [cerebrospinal fluid, skull]), using the “New Segmentation” option in SPM8 (Ashburner & Friston, 2005). Tissue probability maps were taken from a customized paediatric brain generated using Template-O-Matic toolbox (http://dbm.neuro.uni-jena.de/software/tom/). The Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) algorithm was then used to create a study-specific template (Ashburner, 2007; Marchewka et al., 2014). This step was followed by an affine registration of the GM maps to the Montreal Neurological Institute (MNI) space, scaling the GM probability values with the Jacobian determinants to ensure that the total signal in each tissue class remained constant (i.e. “modulation”) (Ashburner & Friston, 2000). Binary masks for the main lobes (frontal, temporal, parietal, cerebellum, limbic and occipital) were derived from a cerebral lobe atlas defined in the MNI template space and published by Fonov et al. (Fonov et al., 2011).

2.4 Statistical analysis

Three different methodological approaches were used to investigate differences in allometric scaling and regional brain volume differences in dyslexic and good readers. The project was preregistered on OSF (https://osf.io/t2v5h/). All brain volumes were log-transformed because the relation between a regional volume and the total volume is not linear (de Jong et al., 2017).

2.5 ANOVA

First, we performed an ANOVA to examine the main effects of group (dyslexic and good readers), sex (girls and boys), hemisphere (left and right), tissue (grey matter and white matter), brain regions (frontal, temporal, parietal, cerebellum, limbic and occipital) and the interactions between group, sex and the other variables (hemisphere, tissue, lobe). Group and sex were between-subject variables, and hemisphere, tissue and lobe were within-subjects variables.

2.6 Linear regression models

Each regional brain volume was tested in separate models for differences in allometric scaling between groups (see Equation 1) (Mankiw et al., 2017).

(1)

RBV = Regional Brain Volume (e.g. right grey matter of the frontal lobe) and TBV = Total Brain Volume.

Linear regression models were performed using SAS 9.2 software (SAS Institute, Cary, NC). To reduce type 1 error inflation due to multiple testing, we set the alpha threshold at 0.002 [0.05/24, 24 being the number of observed brain regions]. We also tested the interaction between sex and group (dyslexic and good readers) in linear regression models. Moreover, we performed linear regression models in dyslexic versus good readers in girls and boys separately, to follow the same analytic plan as the MGCFA.

2.7 Principal component analysis

The second method used to investigate differences in allometric scaling between groups was PCA. A PCA of the log-transformed regional brain volumes was performed separately in dyslexics and good readers. The loadings of the first principal components of the groups were considered as the coordinates of two vectors (Krzanowski, 1979). The angle between these two vectors served to test global differences in allometric scaling across groups (Jolicoeur, 1963). PCA and permutation tests (10,000 iterations) of the angle between vectors were performed by running the psych package in R software (Revelle, 2019). The statistical significance of the difference in angle was estimated by comparing it to a null distribution obtained from 10,000 random permutations. In each of these permutations, two groups of subjects were created with sample sizes corresponding to the number of dyslexic and control participants, independently of their diagnostic status. A p-value was estimated by counting the proportion of random permutations where the angle difference was more extreme than the one observed in the original groups (Toro et al., 2009). If the proportion was smaller than alpha = 0.05, then there was a significant group difference and follow-up analyses were conducted with a post hoc examination of the individual exponents. Differences in allometric scaling in dyslexic versus good readers in girls and boys were compared separately, and the interaction between sex and group (dyslexic and good readers) was tested.

2.8 Multiple-group confirmatory factor analysis

MGCFA is a popular method for measurement invariance which goes beyond the main limitations of linear regression and PCA. It is an extension of confirmatory factor analysis (CFA) (Davidov, Schmidt, Billiet, & Meuleman, 2018). In CFA, observed variables are considered to be indicators of an unobserved (latent) variable or construct (Davidov, Meuleman, Cieciuch, Schmidt, & Billiet, 2014). Systems of equations were thus used to describe the relationship between the observed variables (local regional volumes) and the latent construct (total brain volume) that these variables are supposed to measure. The observed variables log(RBV)_i were modelled as linear functions of the latent construct ξ (see the following Equation 2). The τ_i, λ_i and δ_i refer, respectively, to the intercept, the slope (factor loading), and the error term in these functions. The superscript (g) indicates the group (in our case: dyslexic and good readers).

(2)

The MGCFA starts with the determination of a well-fitting multi-group baseline model and continues by testing, in a hierarchical fashion, the metric invariance (i.e. equality of factor loadings) and the scalar invariance (i.e. equality of intercepts) between groups. To do this, some parameters are constrained to be the same across groups and this model is compared to a model that is unconstrained on these parameters, in terms of fit, by computing a chi-square difference test. Metric invariance is tested by constraining the loadings of the factor across groups (intercept being unconstrained) (Steenkamp & Baumgartner, 1998). If a global test (comparison of the fit of a model with all loadings constrained to be equal across groups to an unconstrained model) indicates that the metric invariance hypothesis is rejected, then each regional brain volume is examined one after the other (comparison of the fit of a model with all loadings constrained to be equal across groups with that of a model with the loading of one regional brain volume unconstrained). Similarly, scalar invariance is tested by constraining the intercepts across groups and comparing this model with an unconstrained model (loadings are also constrained if metric invariance was found in the previous step) (Davidov et al., 2014; Hong, Malik, & Lee, 2003; Steenkamp & Baumgartner, 1998). Again, if this global test indicates that the scalar invariance hypothesis is rejected, then each regional brain volume is examined one after the other (comparison of the fit of a model with all intercepts constrained to be equal across groups to a model with the intercept of one regional brain volume unconstrained).

MGCFA models were applied using procedures implemented in Mplus (Schnabel, Kelava, Vijver, & Seifert, 2015). The maximum likelihood estimation with robust standard errors (MLMV) estimator was used for parameter estimation (Asparouhov & Muthén, 2010). MGCFA models were also performed on four groups: dyslexic boys, dyslexic girls, non-dyslexic boys and non-dyslexic girls. We additionally compared dyslexic versus good readers in girls and boys separately and in non-dyslexic girls and dyslexic boys versus dyslexic girls and non-dyslexic boys to identify an interaction between sex and group (dyslexic and good readers). The sample sizes were sufficiently large to perform MGCFA on these subgroups (Mundfrom, Shaw, & Ke, 2005).

In order to evaluate the concordance between linear regression and MGCFA approaches, we estimated, using both methods, the slope and intercept differences between groups in the 24 regional brain volumes and then computed a Spearman rank order correlation.

3.1 ANOVA

The analysis of variance showed a main effect of group (F(1, 5,400) = 10.5, p-value = .001, η² = 0.1%; good > dyslexic readers), sex (F(1, 5,400) = 45.6, p-value < 0.001, η² = 0.4%; boys > girls), hemisphere (F(1, 5,400) = 5.5, p-value = .019, η² < 0.1%; left > right hemisphere), tissue (F(1, 5,400) = 27,832.7, p-value < 0.001, η² = 31.6%; grey > white matter) and brain regions (F(5, 5,400) = 10,542.5, p-value < 0.001, η² = 59.8%; frontal > temporal>parietal > occipital>cerebellum > limbic region). There was no significant interaction between group and sex and hemisphere, tissue and brain regions.

3.2 Linear regression

In linear regression models, we found no difference in allometric scaling (Table 1) nor in regional brain volume (Table 2) between dyslexic and good readers, even in the subsamples of boys and girls or when the interaction between sex and group was considered. In Figure S1, we present, as an example, the relationship between the left temporal lobe grey matter and the total brain volumes in dyslexic and good readers. Together, these results indicate no differences in allometric scaling nor regional brain volumes between dyslexic and good readers.

3.3 PCA

In PCA models, we found no differences in allometric scaling (Table 3) between dyslexic and good readers, even in the subsamples of boys and girls or when the interactions between sex and group were considered.

3.4 MGCFA

Group differences were reported with Cohen's d and uncorrected p-values. Differences in total brain volume between good and readers were 0.39 in the whole sample, 0.34 in girls, and 0.43 in boys. Differences in total brain volume between girls and boys were −0.88 in the whole sample, −0.94 in good readers, and −0.72 in dyslexic readers. No differences between dyslexic and good readers were found with the test of equality of all loadings (metric invariance), in the entire sample and each subgroup (dyslexic boys, dyslexic girls, non-dyslexic boys and non-dyslexic girls; Table 4). No differences between dyslexic and good readers were reported from the test of equality of all intercepts (scalar invariance) in the entire sample. Interestingly, the test of equality of all intercepts in the four groups was significant (p-value = 0.004; Table 5). Further analyses revealed scalar invariance in boys (good readers and dyslexic readers; p-value = 0.3), girls (p-value = 0.7), and when the interaction between sex and group was considered (p-value = 0.5). A supplementary test was performed to confirm that scalar invariance between the four groups was rejected because of sex (p-value < 0.001). These results indicated sex differences in regional brain volumes) between girls and boys, after the proper adjustment (in log–log scale) of total brain volume differences (see Figure 1). Girls had larger frontal grey and white matter (d = 0.1) volumes and a smaller cerebellar grey matter (d = −0.2) volume than boys, relative to total brain volume.

3.5 Comparison of the three methodological approaches

Results of the three methodological approaches (linear regression, PCA and MGCFA) were largely consistent. The ranking of Δ slopes (good readers – dyslexic readers) and Δ intercepts (good readers - dyslexic readers) between linear regression and MGCFA methods in the 24 regional brain volumes using Spearman's correlation coefficients was 0.96 and 0.97, respectively. Moreover, the PCA method was concordant with the two other approaches since it did not detect differences in allometric scaling between dyslexic and good readers (even in the subsamples of boys and girls or when the interaction between sex and group was considered).

4.1 Strengths and limitations

The two major strengths of this study are the large sample of female and male dyslexic and good readers and the comparison of three methods (linear regression, PCA and MGCFA) used to examine volumetric group differences. However, the current study also has several limitations that must be considered when evaluating the results. First, total brain volume estimates were not identical across methods. While it remains a measured variable in the linear regressions, total brain volume is a latent variable estimated by the shared variance of lobar volumes in the MGCFA and corresponds to the first principal component in PCA, which reflects the component with the most shared and unshared variance of the lobar volumes. While estimates may differ across methods, the consistency of our findings suggests that the MGCFA and PCA are nonetheless advantageous methods to investigate overall neuroanatomical group differences in future studies.

Second, our total sample gathered participants from 5 studies conducted in 3 different countries with different languages and different school systems, although good and dyslexic readers were recruited in comparable proportions in each of these studies. Since the PCA and MGCFA cannot simultaneously examine the effect of group, sex, scanner site and language, we were not able to correct for the non-independency of data collected per scanning site nor could we investigate how different languages influence the present findings (Table 6). Future large-scale studies should nevertheless investigate the impact of different cultures and languages to obtain a more precise estimate of volumetric group differences in dyslexia.

Third, in theory, the relationship between total brain volume and each lobar volume could correspond to a more complex equation than the power function we employ. However, there is an extensive literature on brain allometry, and the power equation is widely considered as a sufficiently good fit and is the current state of the art (Sanchis-Segura et al., 2019).

Finally, the brain region segmentations used in this study were quite coarse. It remains entirely possible that allometric scaling and regional brain volume differences between dyslexic and good readers might emerge when considering smaller brain regions (e.g. superior temporal gyrus of the left temporal lobe). Of course, the smaller the brain regions considered, the more numerous they are, the higher the risk of false-positive results and the more stringent corrections for multiple tests should be. We suggest that MGCFA is a powerful approach to the study general group differences across a large number of brain regions since it allows for a global test of allometric differences, which does not necessitate correction for multiple comparisons. Our study therefore paves the way for more fine-grain investigations of regional brain volume differences in dyslexia, by taking allometry into account.