Comorbidities

Traditionally, SLI, dyslexia, and dyscalculia have been described as relatively specific deficits in respective areas. Children with SLI typically have impaired lexical skills (word knowledge) including late development of first words [8], and slow naming [9]. In addition, grammatical and syntactic knowledge has been found to be impaired in this group with particular difficulty in acquiring verb morphology [10,11]. Indeed, tense marking [12], nonword repetition [13], and sentence repetition [14] have been suggested as clinical markers of the disorder. Children with dyslexia often have difficulty with letter or symbol knowledge including slow and error-prone word reading [15]. Deficits in letter-sound knowledge impair both phonetic reading and spelling of single words. In addition, sentence level reading may be slow and laborious leading to difficulties understanding what has been read [16]. Difficulty with mapping phonology to orthography, tapped by phonological awareness and decoding tasks, are considered hallmarks of dyslexia [17,18]. Children with developmental dyscalculia have difficulty with basic calculations [19]. One of the hallmarks of dyscalculia is the persistent use of effortful calculation strategies (such as using finger counting) when typically developing peers have shifted towards retrieving the solutions to calculation problems from memory [20]. More recently, studies have shown that children with dyscalculia may also have difficulties with number sense, the ability to quickly understand, approximate, and manipulate numerical quantities [21,22]. It has been found that dyscalculia is associated with difficulty estimating the number of objects in a group [23], and comparing quantities [24,25], particularly when represented in a symbolic format (e.g. Arabic numerals).

While pure forms of SLI, dyslexia, and dyscalculia occur, children identified with one of these learning disabilities often present with other co-morbid conditions. For example, SLI has been associated with high rates of speech production deficits [26], attentional difficulties [27], and motor discoordination [28]. Similarly, dyslexia often co-occurs with sensorimotor difficulties [29], attention deficits [30], and visual processing impairments [31]. Attentional difficulties have been reported also for dyscalculic groups [32,33], as have visuospatial processing deficits [34]. These significant and similar comorbidities have raised debate concerning whether these impairments stem from the same (e.g., [35]) or multiple deficits [36].

SLI and Dyslexia

These three childhood learning difficulties also tend to co-occur with each other, although appreciably less is known about such comorbidities. The co-occurrence of SLI and dyslexia has received considerable attention. In a review of studies, McArthur, Hogben, Edwards, Heath, and Mengler [37] reported high incidences of language impairment among those identified as dyslexic (19% to 63%) and reading impairment among those identified with SLI (12.5% to 85%). As well, in two twin studies, rates of reading impairment were significantly higher than matched control groups in children with SLI [38,39] and family members of children with SLI [39]. Given that both oral language and reading skills rely on an intact language system, one view of the overlap between SLI and dyslexia is that they both stem from a language impairment affecting reading only in its mild form, and oral language and reading in more severe cases. Consistent with this view are findings of shared genetic effects across SLI and dyslexia [40-42]. However, recent evidence including separable genetic effects [41] and subtle dissociations in the oral language profiles of the two populations [43,44] suggest that this single deficit/severity view is too simplistic.

Observations of the qualitative differences between SLI and dyslexic groups have led to the suggestion that both phonological and nonphonological dimensions of language must be considered in order to account for variations in language and reading development [45]. The prominent feature of the reading difficulty in classic dyslexia is a difficulty mapping between phonology and orthography stemming from a phonological processing deficit [46]. These children may struggle to decode unfamiliar words, but are able to comprehend those words once successful decoding has been achieved. Effortful decoding over many words, however, may lead to some breakdown in comprehension. While children with SLI often struggle with decoding, they also experience difficulty with reading comprehension even when they have accurately read a word [45,47]. It has been suggested that the oral language deficits in SLI impair comprehension of both spoken and written language [45]. Bishop and Snowling [45] have suggested a two-dimensional model to account for the unique and intersecting patterns of SLI and dyslexia including a common phonological deficit and an additional language-based (but nonphonological) impairment in SLI.

Dyslexia and Dyscalculia

Generally high rates of comorbidity have been reported for dyslexia and dyscalculia ranging from 17% [33] to approximately 60% [48,49]. As is the case for dyscalculia generally, research comparing dyscalculic groups with and without comorbid reading impairment is still in its early stages. Jordan and colleagues [50-52] found that children with comorbid dyscalculia and dyslexia performed more poorly than children with dyscalculia-only in exact calculation and solving story problems. No specific deficits were found for the dyscalculia-only group relative to the comorbid group. Consistent with these results are findings of similar patterns of impairment across a range of number processing tasks for dyscalculic groups with and without reading difficulties [24,53].

Nevertheless, some researchers have reported qualitative differences between groups with dyscalculia with or without dyslexia. Fuchs and Fuchs [54] replicated Jordan and Hanich’s [50] findings of poorer performance of dyscalculic groups with reading impairment than those without on untimed math facts and simple story problems. However, Fuchs and Fuchs did observe a disproportionate impairment for their dyscalculia-only group relative to the comorbid group on complex mathematical operations involved in story problems and real world problem solving. These results were interpreted as suggesting that the children with dyscalculia-only had more serious deficits in math procedures. Naming speed [55] and phonological and magnitude processing [56] have been examined in dyslexic-only, dyscalculic-only, and dyslexia/dyscalculia groups. These researchers found phonology-based impairments in the dyslexic groups irrespective of arithmetic status, and magnitude processing deficits in the dyscalculic groups irrespective of reading status. The deficits in the dyslexia/dyscalculia groups were considered additive in that they were equivalent to the impairments characterizing each respective specific group. The researchers hypothesized that dyslexia and dyscalculia have separable cognitive profiles that may co-occur.

The high rate of comorbidity between dyslexia and dyscalculia may appear to undermine a strictly separable but co-occurring account of these disorders. An alternative view is that verbally based deficits may give rise to both reading and math impairments whereas a more domain-specific impairment related to number processing may underpin pure dyscalculia. Rourke and colleagues [57-59] have provided evidence consistent with this view. Children with comorbid dyslexia and dyscalculia had more difficulty with verbal than visuospatial neuropsychological tests whereas children with dyscalculia-only were more likely to struggle with visuospatial than verbal materials. Also in broad agreement are suggestions of subtypes of children with dyscalculia [20,60] including those with impairments in primary verbal working memory and conceptual knowledge, retrieval of facts from long-term memory, or visuospatial abilities. It should be noted, however, that there is a lack of evidence replicating the group differences [61] or supporting Geary’s subtyping (but see 54). Part of the problem across these research studies may be that consistency is lacking both in the criteria employed for identifying dyscalculia and dyslexia, and in the range of numerical, reading, and cognitive tasks investigated.

SLI and Dyscalculia

To our knowledge, no studies have investigated the comorbidity of dyscalculia and SLI. Nevertheless, a relationship may be expected. According to Dehaene et al.’s [62] Triple Code Model, three distinct systems may be recruited during mathematical processing including the quantity system (nonverbal), the visual system, and verbal representations (lexical, phonological, syntactic). Verbal representations are tapped, for example, during tasks involving fact retrieval or sentence-level processing. The reliance on verbal representations during some mathematical operations would lead to the prediction that children with SLI may experience difficulties in mathematical learning, and indeed, such a relationship has been reported. Children with SLI have difficulty acquiring early verbal numeracy skills such as logical operations and numerical representations but score at age appropriate levels on early nonverbal numeracy tasks such as numeral estimations [63-67]. Indeed, Kleemans et al. [67] found that phonological awareness, grammatical ability, and naming speed were significant predictors of early numeracy skills in children with SLI. It is clear that a systematic investigation of oral language, and verbal and nonverbal numeracy skills is needed to further our understanding of the relationships between developmental language and math impairments.

The Present Study

The findings reviewed above provide strong evidence for the presence of important relationships between SLI, dyslexia, and dyscalculia. Nevertheless, work in this area has been hindered by inconsistencies in the criteria applied to define each learning disability, and in the tasks and analyses employed to investigate group differences. In addition, most studies have investigated the overlap between these disorders by focusing on small groups exhibiting only one or two of these disabilities. While informative, these studies cannot describe the overall pattern of variance and covariance in learning language, reading, and mathematics present in children generally, and in those struggling to learn specifically. It was the purpose of the present study to provide this crucial population perspective concerning SLI, dyslexia, and dyscalculia. In particular, this study is the first to consider learning patterns and challenges in language, reading, and math within subjects in a large developmental sample. The emerging patterns from this work can then form the basis for future research questions aimed at understanding corresponding deficits.

A large, unselected group of school age children completed measures of language, reading, and math. One aim of the study was to examine the patterns of performance across measures using cluster analysis in which sets of observations are created using the dimensions of interest such that sets are more similar to each other within clusters than between clusters. We anticipated that general ability (i.e., performance across all tasks of interest) would yield several clusters reflecting ability levels (e.g., clusters identifying children who generally score in the low, average and high ranges across all tasks). Nevertheless, we were interested in differentiating patterns of performance, and so the analysis aimed to reveal additional clusters with unique profiles if they do in fact exist. Findings of clusters identifying solely language, reading or math weaknesses would be suggestive of specific and separable underlying mechanisms with comorbidity due to artifacts in the data. The presence of clusters with weaknesses in multiple areas would be reflective of potentially meaningful comorbidity perhaps suggesting a different pattern of core deficits. We also examined whether the same pattern of learning profiles would be found for those performing at the low end of the distribution. Findings of similar distributions would suggest that our cluster rates might be applicable to learning disabilities.

A second goal of the study was to provide a preliminary validation of our clusters, and to explore cognitive performance differences across clusters using data available for a subset of the large, unselected sample. Findings that a particular cognitive profile characterizes both unitary and comorbid clusters would implicate similar underlying processes whereas different cognitive deficits for unitary and comorbid clusters might suggest separate underlying cognitive constraints.

Participants

A total of 34 schools (including 5 rural schools) in the southwest region of Ontario, Canada were recruited to the study. All children in senior kindergarten through grade 4 in each of the schools were invited to participate in October of the school year, corresponding to an age range of 4 years;10 months to 10;10. Approximately 5967 consent forms were distributed of which 1605 were returned, signed by parents. Of these, 1387 children participated in the study (the remainder were either outside the age range, n = 61, or could not be screened within the time frame of the study, n = 157). Complete data sets were obtained for 1120 children aged 6;0 to 9;11 (Epidemiological Sample). Children under 6;0 were not included in the present study because they did not complete the reading screening measure (n = 178). Of those meeting the age criteria for the present study, 14 did not have complete data sets. By parent report, approximately 86% of the children were right handed, 85% spoke English as their first language, and 82% of mothers had at least some college or university education. It should be noted that these proportions did not differ from that of the full sample (n = 1605). Additional data were available for a subset of the Epidemiological Sample who participated in further studies with our research group (referred to as the Standardized Test Subsample, see below; n = 383).

Procedure

All participants in the Epidemiological Sample completed a 10-minute screening protocol consisting of four tasks, Sentence Recall, Math Fluency, Sight Word Reading Efficiency, and Phonemic Decoding Efficiency. The Standardized Test Subsample completed a battery of standardized language, reading, math, phonological awareness, intelligence, and working memory tests (and other measures not reported here) in three visits occurring one week apart and within 6 months of the original screening. All tasks were administered individually in a quiet room in the child’s school by a trained research assistant.

Screening Measures

All participants completed the screening measures described below.

Standardized Test Battery

The Standardized Test Subsample was comprised of monolingual English speakers, and was selected based on criteria motivated by other studies focusing on children with impairments and on practical constraints. Briefly, standard score cutoffs equivalent to -1.3 SD (19.5 standard score points) below the full sample mean were set separately for each of the sentence recall (M = 103; SD = 18), phonemic decoding efficiency (M = 106, SD = 13), and math fluency tasks (M = 93, SD = 14), or for a pattern of low performance equivalent to -1.0 SD (15 standard score points) on more than one of these tasks. The cutoff point of -1.3 SD was based on previous findings of high agreement between clinician judgments of SLI and test scores of at least -1.25 SD below the standardized mean [72]. The cutoff for a pattern of low performance across tasks was narrowed to -1.0 SD due to practical limitations related to testing all the children meeting the corresponding criteria. For the applied criteria, standard scores were based on the present sample for the sentence recall, and on the published test norms for the remaining tests. No cutoff was set for the sight word efficiency test.

The Standardized Test Subsample comprised all low performers, that is, all who scored below the cutoffs and who could be tested (186/255), and children who scored within the average range on all screening tasks and attended the same schools as the low performers (n = 193). Although the composition differs from that of the Epidemiological sample, the performance of the Standardized Test Subsample provides some indication of the characteristics of relevant learners when interpreted with caution. The information may be especially relevant to those with learning challenges because low and average scorers on the screening tasks were represented in roughly equivalent proportions in this Subsample. All participants in the Standardized Test Subsample completed the measures described below.

Data Analysis

In order to compare performance across our screening tasks, we created our own normative scores based on our large, unselected Epidemiological Sample. To do this, raw scores from the screening measures were converted to z-scores within four age bands (6;0-6;11; 7;0-7;11; 8;0-8;11; 9;0-9;11) and then transformed to a standard score scale with a mean of 100 and a SD of 15. Standard scores for all of the tests completed by the Standardized Test Subsample were based on the respective published test norms.

In order to explore the patterns of unique learning profiles in our Epidemiological Sample, we completed a two-step cluster analysis appropriate for large samples (SPSS v. 17). The cluster analysis technique groups cases of observations into discrete subgroups based on their similarity across a set of chosen dimensions. The clustering procedure proceeds hierarchically so that smaller subgroups (clusters) are merged iteratively into increasingly larger clusters. We planned to explore the number of unique learning profiles by systematically increasing the number of clusters to be found by the solution until no further unique learning profiles were established. Additional tests available for the Standardized Test Subsample allowed us to examine performance on related cognitive measures for each profile group.

Cluster Analysis

The four screening variables, Sentence Recall, Math Fluency, Sight Word Efficiency, and Phonemic Decoding Efficiency, were entered into a two-step cluster analysis with noise handling set to the 25% default and using the log-likelihood distance measure. The autoclustering statistics include the Schwarz’s Bayesian Information Criterion (BIC), BIC changes, ratio of BIC changes, and ratio of distance measures. Smaller BICs and BIC changes reflect better models and are used to find an initial estimation for the number of clusters. The initial estimate is refined by taking into account the ratio of distance measure, which reflects the greatest change in distance between the two closest clusters in each hierarchical clustering stage (SPSS, 2001). In the current analysis, the absolute value of the BIC declined to five clusters although the ratio of distance measures indicated that the complexity beyond three clusters is not necessary. Given our interest in identifying the largest number of unique clusters that would fit our data, we repeated the two-step cluster analysis requesting increasing numbers of clusters from three until profiles were duplicated. It should be noted that the order of case entry can influence cluster formation in these analyses. We validated our clustering by repeating the analyses with four additional uniquely randomized case orders and found no additional unique profiles.

Results of the cluster analyses are displayed in Figure 1, which presents the percent of participants included in each cluster and the Student’s t statistics reflecting each variable’s importance to each cluster. In comparison to the critical value line, the t-values provide a guideline as to how each variable contributes to the formation of the cluster and how individual clusters differ from the overall average. As can be seen in Figure 1, the model with 3-clusters selected by the autoclustering procedure included clusters of children distinguished by below average performance overall (34%), above average performance overall (32%), and largely average performance with above average sentence recall and below average math fluency scores (average with language strength; 34%). Analyses were discontinued at 7 clusters due to the presence of two clusters with the same profile: positive and significant t-values on all four measures. The most complex solution of unique clusters, then, was the 6-cluster model, which included both overall below (cluster 1) and above average profiles (cluster 6), as well as separable profiles for below average reading efficiency (both sight word and phonemic decoding efficiency; cluster 3), below average math fluency (cluster 5), below average math fluency and reading efficiency (cluster 4), and below average sentence recall and reading efficiency (cluster 2).

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Figure 1. Attribute importance for possible cluster solutions (Language – sentence recall; Sight Word – sight word efficiency; Decoding – phonemic decoding efficiency).

Dashed lines represent critical t-values at the .05 level.

https://doi.org/10.1371/journal.pone.0077463.g001

Descriptive Statistics for Clusters

Table 1 presents descriptive statistics for the 6-cluster solution including cluster size, sex distribution, age, screening measure centroids and standard deviations, and cluster descriptors. The mean ages across clusters varied by five months with cluster 5 (below average math fluency) and cluster 6 (above average overall) tending to be comprised of older children. While significant age differences did occur in this large sample, effect sizes did not exceed 0.02 indicating a very small effect of chronological age on the clustering. There were no significant sex differences in the 6-cluster model, X²(5) = 9.7, p = .082. In the 3-cluster model selected by the autoclustering solution (see Figure 1), however, more males comprised the below average overall cluster while more females comprised the average with language strength cluster, X²(2) = 8.6, p = .014.

The boxplot presented in Figure 2 compares performance on all screening measures for the 6-cluster model. The number of outliers was greatest for the sentence recall measure. Clusters 1, 2, and 6 have a pattern of low sentence recall compared to stronger and similar word and nonword reading efficiency and math fluency. These clusters (1,2,6) are distinguished by overall performance (low, average, high, respectively). Clusters 3 and 4 show the opposite pattern with stronger sentence recall performance compared to reading and math performance. Finally, cluster 5 is characterized by lower math than sentence recall or reading scores.

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Figure 2. Boxplot for screening measures for each cluster in the 6-cluster solution (Language – sentence recall; Sight Word – sight word efficiency; Decoding – phonemic decoding efficiency).

Solid line marks standard score of 100, and dashed line marks standard score of 85.

https://doi.org/10.1371/journal.pone.0077463.g002

Cluster Validation

In order to validate our clusters, the same pattern of performance across clusters would need to be demonstrated for additional measures of language, reading, and math such as those available for our Standardized Test Subsample. Thus, we compared the standardized test performance of our Standardized Test Subsample in a multivariate ANOVA with the Composite Language Score (language), reading fluency, and calculations scores entered as multivariates. The between group factor in this ANOVA was the cluster (6 levels) to which each child had been assigned in our cluster analysis. All effects were significant, F (5, 316) > 11.5, p < .001, η²_p > 0.155. Descriptive statistics and results of pairwise comparisons with Bonferroni correction are presented in Table 2. Clusters 1 and 6 (overall below and above average) were readily distinguished in these comparisons by their low vs. high scores, respectively. There was reasonable agreement for two of the other clusters: Cluster 2 (below average sentence recall) was associated with lower language than reading fluency scores and cluster 4 (below average math fluency and reading efficiency) was associated with higher language than reading fluency and calculations scores. Numerically, results corresponded for cluster 5 (below average math fluency) with the math calculations score lower than scores on the language or reading fluency measures for this group, however this difference was not significant. The pattern for the remaining cluster, cluster 3 (below average reading efficiency), did not match the cluster profile in that the reading fluency score was not disproportionately lower. On these additional tests, cluster 3 presented with average test scores on all measures (average overall).

Associations with Related Measures

Given the reasonable validation of our clusters in the Standardized Test Subsample as described above, we next explored differences in performance on our cognitive measures across clusters. To do this, we completed a multivariate ANOVA with cluster (6 levels) as the between group factor, and the data related to short-term memory, working memory, intelligence, and phonological awareness from our Standardized Test Subsample entered as multivariates. All effects were significant, F (5, 300) > 5.9, p < .001, η²_p > 0.09, all cases. Descriptive statistics and results of pairwise comparisons with Bonferroni correction are presented in Table 3. Cluster 1 (below average overall) was consistently distinguished (relative to at least three other clusters) by a significantly below average pattern of performance on all of the measures except block recall (visuospatial short-term memory). Cluster 2 (below average sentence recall) was differentiated by significantly lower phonological short-term memory in the context of average performance on the remaining measures. Cluster 4 (below average reading and math) was associated with lower phonological awareness but average phonological short-term memory. Clusters 5 (above average except math) and 6 (above average overall) were characterized by higher performance IQ. Cluster 3 was not distinguished by any of the test scores. Cluster 3 was identified as ‘below average reading efficiency’ in the cluster analysis, but had average overall performance in the cluster validation. This latter pattern is consistent with the finding that this cluster was not distinguished by any of the related measures. Nevertheless, this group did show high variability on a task closely related to reading, the phonological awareness task with a standard deviation of 6.5, more than 2.5 times that of any of the remaining groups (range of SD for remaining groups: 2.4 to 2.6).

Profiles of Children with Impaired Performance on Screening Measures

The distribution of cluster membership across the epidemiological sample is shown in Table 4. Approximately equal proportions (16-18%) of children were included in clusters 2 (below average sentence recall), 3 (below average reading efficiency), and 5 (below average math fluency) with lower proportions (10-11%) included in clusters 1 (below average overall) and 4 (below average reading and math), and a higher proportion in cluster 6 (above average overall: 28%). Thus, 38% of the sample had a general learning profile with largely equivalent performance across measures (clusters 1 or 6), and 62%, a more specific learning profile with marked differences in performance on at least one measure (clusters 2, 3, 4, and 5).

A final descriptive analysis considered whether the learning profile distributions of children with a potential learning disability differed from that of the Epidemiological Sample. To do this, we compared the cluster membership distribution (see Table 4) in the Epidemiological Sample to that of children for whom we had some evidence of a learning disability as reflected by performance of at least 1 SD below the mean on at least one screening measure (Sentence Recall, Sight Word Reading Efficiency, Phonemic Decoding Efficiency, Math Fluency). The cutoff criterion of -1 SD, conventionally considered to reflect a large effect size (Cohen, 1988), was chosen to capture all children who performed poorly on at least one screening measure. Note that this cutoff criterion differs from that described for the Standardizd Test Subsample, which was motivated by other studies and not suited to the research question being addressed in this analysis. The proportions of children with a general learning profile was smaller for the potential learning disability group (clusters 1 and 6: 30 vs. 38%, for the potential learning disability and Epidemiological Samples, respectively), and included a higher proportion of below average profiles (cluster 1: 27% vs. 10%). A higher proportion of the potential learning disability group had a specific learning profile (clusters 2, 4, and 5: 70% vs. 58%). Comparatively high proportions characterized the potential learning disability group for clusters 2 (below average sentence recall: 24 vs. 17%) and 4 (below average reading and math 4: 27 vs. 11%) whereas smaller proportions were found for clusters 3 (below average reading efficiency: 12% vs. 18%) and 5 (below average math fluency: 7% vs. 16%).