Cross-sectional and longitudinal assessment of cognitive development in Williams syndrome

Williamssyndrome(WS)isararegeneticsyndrome.Aswithallraresyndromes,obtain-ing adequately powered sample sizes is a challenge. Here we present legacy data from seven UK labs, enabling the characterisation of cross-sectional and longitudinal developmental trajectories of verbal and non-verbal development in the largest sample of individuals with WS to-date. In Study 1, we report cross-sectional data between N = 102and N = 209childrenandadultswithWSonmeasuresofverbalandnon-verbal ability.InStudy2,wereportlongitudinaldatafrom N = 17to N = 54childrenandadults with WS who had been tested on at least three timepoints on these measures. Data support theWS characteristic cognitive profile of stronger verbal thannon-verbal ability, and shallow developmental progression for both domains. Both cross-sectional and longitudinal data demonstrate steeper rates of development in the child participants than the adolescent and adults in our sample. Cross-sectional data indicate steeper development in verbal than non-verbal ability, and that individual differences in the discrepancy between verbal and non-verbal ability are largely accounted for by level of intellectual functioning. A diverging developmental discrepancy between verbal and non-verbal ability, whilst marginal, is not mirrored statistically in the longitudinal data. Cross-sectional and longitudinal data are discussed with reference to validating cross-sectional developmental patterns using longitudinal data and the importance of individual differences in understanding developmental progression


INTRODUCTION
Williams syndrome (WS) is a rare genetic syndrome with a prevalence of one in 7500 to one in 20,000 live births (Morris et al., 1998;Strømme et al., 2002) and mild to moderate intellectual disability. Despite a mean IQ between 50 and 60 (Martens et al., 2008), WS is associated with

Research Highlights
• Cross-sectional and longitudinal developmental trajectories of verbal and non-verbal development, in the largest sample of individuals with Williams syndrome (WS) todate, are presented. • This research is unique due to large sample sizes, independence between cross-sectional and longitudinal samples, and a reliance on minimum three timepoints for longitudinal trajectories.
• Data support the WS cognitive profile of stronger verbal than non-verbal ability and a developmental model of delayed onset and a delayed rate.
• Cross-sectional and longitudinal data are discussed with reference to validating cross-sectional developmental patterns using longitudinal data and the importance of individual differences in understanding development.
non-verbal ability, and the discrepancy in performance between these domains, in WS.
Most studies of WS have used cross-sectional data. While this is useful for determining cognitive profiles, it provides a snapshot of ability and fails to inform about developmental progression (Karmiloff-Smith, 1998). When cross-sectional data are used to plot developmental trajectories, it is not possible to differentiate individual differences from true change over time, and thus any developmental claims made using cross-sectional data ideally require validation from longitudinal data (Thomas et al., 2009). For rare genetic syndromes such as WS, sufficiently powered sample sizes of longitudinal data are difficult to obtain (Farran, 2021;Farran & Scerif, 2022). In the current study, we present cross-sectional and longitudinal data in the largest WS sample to-date, drawn from the WISDOM database (https://blogs.ucl.ac.uk/wisdom/). Below, we outline considerations related to reporting data from standardised measures, before reviewing existing longitudinal studies of the development of verbal and non-verbal ability in WS.

Reporting data from standardised assessments
Studies that have examined IQ or Standard Scores (SS) longitudinally (e.g., Fisher et al., 2016;Mervis & Pitts, 2015) ask questions related to stability over time. Stability in IQ or SSs of a WS group with increasing age reflects a similar relative position of the WS group compared to the general population over time (i.e., the gap remains stable), whilst a decrease in IQ or SS over time reflects that the gap between the WS group and the general population widens over time. Other studies have used age-equivalence or raw scores and compared change over time in these variables to change in chronological age, to determine whether the rate of developmental progression is typical, faster or slower than expected for chronological age (e.g., Jarrold et al., 2001;Porter & Dodd, 2011).
For IQ and SS, floor effects are common and thus can reduce the sensitivity of the measure. For example, Farran et al. (2019) report Tscores for the Matrices subtest of the British Ability Scales III (BAS-3) (Elliott & Smith, 2011) for a sample of N = 20 participants with WS, which range from 20 to 23. In fact, 18 of the 20 participants in this sample received a T-score of 20, despite a range of ability scores (the equivalent of raw scores) from 33 to 103. For longitudinal designs, floor performance means that a decline in SS is not possible to detect, and stability in SS might simply be an artefact of the individual remaining at floor.
In contrast to SSs, age equivalence scores provide a concrete indication of the absolute level of performance on a given measure, which can be directly compared across measures and time points. As noted by Jarrold et al. (2001), the underlying standardisation process that converts raw scores to age equivalent values necessarily also 'linearises' the resulting scores such that a year's developmental improvement is comparable at all ranges of the test.
Raw scores are the purest measure of performance. However, unlike age equivalence scores, raw scores are not directly comparable across tasks due to differences in scoring ranges. Furthermore, raw scores do not always progress linearly. For example, vocabulary development in younger children is much steeper than in older children. Thus, progression in raw scores in WS can be considered for single tasks only, and this must be within the context of the nature of the growth curve of the typical population (i.e., that it might not be linear). These considerations have been taken into account in the current studies.

Longitudinal development of verbal and non-verbal ability in Williams syndrome
We now review studies of longitudinal development of verbal and nonverbal ability in WS (for a comparative summary, see Table 1). Jarrold and colleagues used age equivalence scores to determine the rates of development of receptive vocabulary (British Picture Vocabulary Scale; BPVS, Dunn et al., 1982) and the Pattern Construction (PC) subtest of the Differential Ability Scales (Elliott, 1990) cross-sectionally and longitudinally in WS. Cross-sectional data (N = 16; 6-28 years) demonstrated significantly stronger verbal than non-verbal ability in WS at a group level (Jarrold et al., 1998). Longitudinal data were from N = 15 of the same sample (six timepoints over 40 months ;Jarrold et al., 2001) (note, Jarrold et al. (1998 also presented a two timepoint subset of this data, with timepoints spaced by 8 months; see Table 1).
In both cross-sectional and longitudinal datasets, the authors demonstrated shallower rates of development in age equivalence scores for non-verbal, relative to verbal ability. Thus, at a group level, the gap between verbal and non-verbal ability widened with increasing chronological age. Furthermore, using difference scores between verbal and non-verbal age equivalence scores, Jarrold et al. (1998)  this case using verbal ability as a proxy for intellectual functioning).
That is, individuals with stronger intellectual functioning, have a larger discrepancy between verbal and non-verbal ability.
The pattern of steeper verbal than non-verbal progression was mirrored in cross-sectional data from Thomas et al. (2009)  WAIS-III [Wechsler, 1997] (2011), and the discrepancy between verbal and non-verbal ability is consistent with Jarrold et al. (1998;2001). With the exception that longitudinal progression was observed for BPVS scores only, there was little evidence that this gap widens with increasing age. This is unsurprising because all participants in this study were adults, that is, the data did not capture the portion of the trajectory in which the verbal-nonverbal discrepancy emerged. Fisch et al. (2012) used the Stanford-Binet IV (Thorndike et al., 1986) (N = 17, 3-15 years of age at timepoint 1, two timepoints spaced by 2 years). They report a mean drop of 2.06 IQ points between timepoints (verbal and non-verbal IQ were not reported separately), and similarly to Porter and Dodd report the biggest longitudinal drop in IQ for the youngest participants. It should be noted, however, that there were large individual differences in difference scores between timepoints, with IQ differences ranging from −12 to +14 IQ points. Mervis et al. (2012) used the Kaufman Brief Intelligence Test-2 (KBIT2; Kaufman & Kaufman, 2004) longitudinally with children with WS (N = 40, 4-14 years at timepoint 1, 4-7 timepoints). They report no significant difference between verbal and nonverbal ability, and no significant change in SS over time for either verbal or non-verbal ability at a group level, that is, a lack of support for the WS cognitive profile. However, this might be explained by the substantial individual differences; large individual differences were reported for longitudinal intercepts for SS in both domains, and for rates of SS development (slopes) in the non-verbal domain. They also report a significant correlation between verbal and non-verbal SS intercepts at age 10 years (the age at which the model was centred), but not rates of development. This indicates that individuals with the lowest non-verbal ability at 10 years were also those with the lowest verbal ability at this age, whilst the lack of association for rate of development is likely due to the large individual differences in slopes for non-verbal ability only.
They also report a correlation between intercepts and slopes in the verbal domain, indicative of greater longitudinal progression in those individuals with higher intercepts at 10 years. Equivalent correlations are not reported for the non-verbal domain. This pattern for the verbal domain shows some parallel with Jarrold et al. (1998) who report that those with higher intellectual functioning show a larger verbalnonverbal discrepancy, suggestive of steeper verbal progression for those individuals. Thus, whilst at a group level Mervis et al. (2012) demonstrate a lack of support for the WS cognitive profile, associational evidence appears to show some evidence that verbal ability is differentiated from non-verbal ability in their WS sample. Mervis and Pitts (2015) report longitudinal development of vocabulary and IQ (Differential Ability Scales 2 nd edition [DAS-II; Elliott, 2007]) in WS (N = 76, 4-15 years at timepoint 1, two timepoints 3 years apart). At a group level, they report higher Verbal SS than Spatial SS, but that Non-verbal Reasoning SS was higher than both Verbal and Spatial SS. They also report a reduction in SS over time for vocabulary, Verbal SS and Non-verbal Reasoning SS (i.e., the gap between SS of the WS group and the normative sample increased), but not Spatial SS. This does not support the characteristic WS cognitive profile, or any developmental advantage for verbal development, and shows some similarity to Porter and Dodd (2011). The authors also report no relationship between chronological age and change in SS between individual with WS and their peers is increasing (Porter & Dodd, 2011;Fisch et al., 2012;Mervis & Pitts, 2015). This likely reflects the rapid neural and cognitive development in children, relative to adults. Saunaaho et al. (2019) is the only study to demonstrate a quadratic function between IQ and age. This is due to the wide age range of participants (their oldest participant was 86 years), which encompassed an age range in which cognitive decline would be expected in the typical population.
Our study is distinguished from the preceding literature due to its large sample sizes, its conservative approach in ensuring independence in cross-sectional and longitudinal samples, and its reliance on greater numbers of timepoints for longitudinal trajectories, to reduce estimation error. We report data from the BPVS (Dunn et al., 1997;Dunn & Dunn, 2009) as a measure of verbal ability, whilst two measures of non-verbal ability are included: Ravens Coloured Progressive Matri-ces (RCPM; Raven, 1993), and the Pattern Construction subtest of the British Ability Scales (PC; Elliott et al., 2007;Elliot & Smith, 2011).
It is important to note that, for the purposes of this study, our measures are used as proxy variables for verbal and non-verbal ability.
However, we recognise that the concepts of 'verbal ability' and 'nonverbal' ability are broad and that the measures used specifically measure receptive vocabulary (BPVS), pattern completion and abstract reasoning (RCPM), and visuo-spatial construction (PC). In Study 1, we report cross-sectional data from N = 209 individuals with WS for performance on BPVS, N = 102 individuals with WS on RCPM and N = 103 individuals with WS on PC. In Study 2, we report longitudinal data for individuals with WS who had been tested on at least three timepoints on BPVS (N = 54), RCPM (N = 41) and PC (N = 17).

STUDY 1: CROSS-SECTIONAL ASSOCIATIONS
Using the largest WS sample of its kind to-date, we tested models of (cross-sectional) development. If the rate of development in WS is slow, this predicts a shallow gradient of broadly linear progression.
If development in WS is characterised by delayed onset followed by developmental catch-up, this predicts a similar (albeit developmentally shifted), non-linear trajectory to that observed in typical development of relatively rapid development followed by a plateau in adulthood. We predicted a combination of these two models, that verbal and nonverbal progression in WS would be characterised by delayed onset and a delayed rate, followed by a plateau in adulthood. This would be reflected by a non-linear relationship between performance and CA. We predicted a non-linear trajectory because of the large age range of our sample, which ranges from children to adults. The rate of change might differ for children compared to adults, as exemplified by Porter andDodd (2011), Fisch et al. (2012) and Mervis and Pitts (2015) because of differences in neural and cognitive development in children, relative to adults. In addition, we predicted that the effect size of this relationship would be negatively impacted by individual differences that are not wholly age-related, such as individual differences in intellectual functioning (Jarrold et al., 2001;Karmiloff-Smith, 1998;Mervis et al., 2012). We also investigated whether verbal abilities were superior to non-verbal abilities and, related to the point above, whether individual differences in the difference between verbal and non-verbal ability was associated with verbal ability (as a proxy for intellectual functioning), as observed by Jarrold et al. (1998). We predicted higher verbal than non-verbal ability and a larger magnitude of difference between verbal and non-verbal ability in those with higher verbal ability.

Participants
Data were obtained from the WiSDom database, a database of retrospectively shared cognitive and behavioural data across seven WS labs

Measures
The BPVS (Dunn et al., 1997;Dunn & Dunn, 2009)  the scoring procedure is such that raw scores are not meaningful without reference to the specific testing schedule in each testing session and this information was not available.

Cross-sectional trajectories
The cross-sectional developmental trajectories of BPVS, RCPM and PC were established by first removing scores at floor (0 participants for BPVS, 0 for RCPM, 18 for PC), and then curve-fitting against chronological age (CA), selecting from linear, logarithmic, power, and quadratic models. Raw scores were used for BPVS and RCPM, but age equivalence score was used for PC as discussed in the method.  We were also interested in individual differences in the magnitude of difference between verbal and non-verbal ability, and whether the magnitude of difference was associated with differences in intellectual functioning. Akin to Jarrold et al. (1998)  This suggests that verbal ability (specifically receptive vocabulary) progresses at a steeper rate than non-verbal ability in our sample. Notably, verbal ability explains a large amount of these individual differences in our sample, explaining 55% of the variance in raw score differences and 74%-80% of the variance in age equivalence score. Nevertheless, as discussed below, progression with increased chronological age also supports the suggestion of steeper verbal than non-verbal progression in the child participants in our sample, that is, many (but not all) of the more verbally able children are also older children. As shown in Figure 1 differences. This is consistent with our finding that the gap between verbal and non-verbal ability is stronger for those with higher verbal ability. However, the developmental pattern for RCPM differs from evidence of some developmental progression with age in our sample on the PC task, which is also a measure of non-verbal ability. Whilst error analysis of RCPM has demonstrated that it taps into similar non-verbal mechanisms in individuals with WS, compared to the typical population , PC performance is atypical in WS due to the construction demands, a particular weakness in WS (Farran & Jarrold, 2003). It is also a timed task (for all but the earliest items), which adds processing speed demands. Thus, although differences between RCPM and PC trajectories could reflect differences in the samples (participants for each measure were overlapping, but not identical), the difference is most likely related to differences in task approach. That is, construction draws on processes such as memory, executive functions, and fine motor skills. In contrast, factor analysis has determined that RCPM measures 'continuous and discrete pattern completion through closure' , 'closure and abstract reasoning' and 'simple pattern completion' (Carlson & Jensen, 1980). The construction demands of the PC task likely present a more uniform performance limitation in WS, particularly in young children, and thus represent a strong developmental contributor to progression on this task.

Discussion
In summary, in line with predictions, we have demonstrated the characteristic profile of stronger verbal than non-verbal ability in WS and shown evidence of developmental progression in raw scores for both domains, with steeper development in verbal than non-verbal ability, particularly at the younger end of the range of ages in our sample. It is important to note, however, that whilst cross-sectional designs are useful for gathering large samples thus invoking sufficient statistical power and representativeness, conclusions related to change with age are confounded by between-participant individual differences and are of most value when considered in tandem with longitudinal data.

STUDY 2. LONGITUDINAL TRAJECTORIES
In Study 2, we investigated the longitudinal trajectories of verbal ability and non-verbal ability, using the same three tasks: BPVS, RCPM and PC. In contrast to previous studies, we classified longitudinal data as a minimum of three timepoints. Three timepoints provide a more interpretable insight into longitudinal trajectories. With just two timepoints one is unable to index the reliability of the rate of change seen between these points (as two datapoints are necessarily connected by a straight line), which can introduce larger estimation error of gradients than when more timepoints are included. Furthermore, with more than two timepoints one can examine whether the rate of change remains constant over two or more intervals, with some consequent indication of the reliability of that rate of change. For BPVS and RCPM, crosssectional datapoints from Study 1 were excluded from Study 2, in order that the two datasets were independent. This enabled comparison of cross-sectional and longitudinal findings, whilst avoiding the confound of overlapping datasets. These two elements of the design drastically reduced our longitudinal sample size but increased scientific rigour.
We were interested in the developmental patterns of verbal and non-verbal ability, predicting that the longitudinal data would validate the cross-sectional data, that is, that group level and within-participant longitudinal rates of development would be shallower for non-verbal ability than for verbal ability. We were also interested in whether participants' changes in score over time (i.e., the gradient of their longitudinal trajectory) would be related to chronological age. This was carried out for replication purposes (e.g., for comparison with Porter &Dodd, 2011 andPitts, 2015) and for comparison with study 1. We predicted that chronological age would not account for a large amount of variance in this analysis. However, in line with study 1 data and our hypothesis of developmental catch-up in WS, we predicted that, broadly, we would observe a model of delayed onset and delayed rate, and larger developmental change (steeper gradients) for children, compared to adults due to faster neural and cognitive changes in children compared to adults.

Method
The same measures were used as in Study 1. Longitudinal data were collated for BPVS and RCPM for the subsets of the Study 1 samples of individuals with at least three testing records ∼6 months apart or more, with resulting subsamples of 41 and 53 individuals, respectively.
In addition, cross-sectional data from the analyses in Study 1 were excluded in order that the two studies consisted of independent samples. For PC, there were very few repeat testing records across individuals; there were 17 individuals with at least three testing records, but data common with the cross-sectional analyses were used for the first time-point.

Results
To test for any inconsistency of gradients between T1-T2 and T2-T3 although note that this applies to norms data for 3 years 9 months to 15 years 9 months only).

RCPM
For RCPM, a model was constructed that was identical in structure to that above, with RCPM raw score instead of BPVS. Fifteen individuals (37%) had negative coefficients, 26 (63%) had positive ones. To better interpret the negative coefficients, we determined how many of these were likely to be statistical error versus true decline. Of the fifteen individuals, seven had scores with overlapping confidence intervals between the highest and lowest scores (the RCPM manual states that ±2 raw score points are within the 97.5 Confidence Interval) and thus are not considered to represent true decline. The remaining eight individuals had a broader range of scores; however, even for this subgroup, not all showed consistent decline across their set of scores. Coefficients for these eight individuals ranged from −0.0051 (almost flat, with the score differential presumably reflecting poor test-retest consistency rather than a meaningful decline) to −0.14. Such latter cases may reflect a meaningful decline in score over time. The overall model fit was evaluated by deriving a pseudo-R-square value from the correlation between the fitted and the observed values, resulting in a figure of 0.74 using the MuMin package (Bartoń, 2022). There was a modest but significant increase of 0.008 raw score points with each month of CA, t(196) = 2.105, p = 0.036 (95% CI = 0.00052, 0.016). This compares to an increase of 0.27 points per month in the typical population (based on a linear line-of-best-fit for RCPM age equivalence norms, although note that this applies to norms data for 5 years 6 months to 11 years 6 months only).

PC
Finally, a corresponding model was constructed for PC. Age equivalence score was used as the dependent variable, for the same reasons as in Study 1. All 17 participants had positive coefficients (Pseudo-Rsquare model fit was 0.71). There was a significant increase of 0.12 age equivalence score points with each month of CA, t(52) = 5.027, p < 0.001 (95% CI = 0.069, 0.16) (compared to one age equivalence month for each month of CA in the typical population).

Comparison of verbal and non-verbal longitudinal gradients
We compared longitudinal gradients for BPVS and RCPM using a partially overlapping samples t-test, that is, each data point was coded as repeated measures or independent, with reference to the two variables. This allows one to use data from the full longitudinal sample. In order to compare like-for-like between tests we used age equivalence scores for this analysis; gradients were extracted from the relationship

3.2.3
Relationships between chronological age and cognitive change To determine whether the patterns of longitudinal development above were associated with the age of the participants, we investigated the

Discussion
Study 2 (2011), who report improvement over time in raw scores for their sample of children and adults, but no specific advantage for verbal subtests.
We were also interested in whether participants' changes in score over time would be related to chronological age. Based on the literature, we predicted larger developmental change for children than for adults. This was largely supported; the relationship between chronological age and developmental progression in BPVS and RCPM was best explained by a quadratic function. Observation of Figure 4 indicates that the steepest gradients on these measures were amongst the youngest participants, and that developmental progression then reduced with age until early adulthood when rates of progression reached a plateau, that is, adults showed consistent rates of relatively shallow progression over time. No significant relationship was observed for PC, but this likely reflects a lack of power. This supports our hypothesis of a period of developmental catch-up in the children in our sample. This could be an impact of the late onset of many verbal and non-verbal competencies (e.g., Laing et al., 2002), which would be observed as steeper developmental progression in younger participants as their neural and cognitive capabilities are progressing at speed, relative to older participants. This pattern is consistent with Our cross-sectional data demonstrated support for the WS cognitive profile of stronger verbal than nonverbal abilities and support a developmental model of non-linear development in WS, rather than linearly slow development. This is also mirrored in the analyses of the relationship between longitudinal change over time and chronological age. This suggests that development in WS is characterised by delayed onset followed by a delayed rate of developmental catch-up, that is, a non-linear trajectory of relatively rapid development followed by a plateau in adulthood, similar to that observed in typical development (albeit developmentally shifted and shallower). These findings inform parents and educators of predicted developmental patterns in WS, thus enabling them to broadly determine developmental potential and tailor approaches accordingly. For example, focussing more support on weaker areas of cognition in early development, and focussing more support on compensation strategies, by drawing on relative strengths, in later development are potential strategies afforded by the non-linear trajectories reported here (see also Van Herwegen et al., 2019).
The cross-sectional data suggest that individual differences in intellectual functioning largely explain the discrepancy between verbal and non-verbal ability, whilst the longitudinal data suggest that the discrepancy between verbal and non-verbal ability remains constant with increasing age for the age range in our sample. For the longitudinal data, although not significant, there was a trend towards diverging developmental trajectories. It could be that the time windows available across timepoints for the longitudinal data analysis were not spread over a sufficiently long time to capture the process of developmen-tal divergence. Also, the first timepoint of longitudinal data were used for study 1 and not included in study 2. Thus, the study 2 longitudinal data do not include the timepoint where development is likely at its fastest. These arguments could explain why there was not significant evidence that the discrepancy increased with increasing age for the range of developmental timelines, abilities and ages of our sample.
Future research which includes larger samples and longer timelines, and which start at earlier points in development is needed to fully answer questions of developmental divergence.
In summary, our data support the WS cognitive profile of stronger verbal than non-verbal ability, but also demonstrate that for both domains, when compared to TD norms, longitudinal developmental progression is delayed and shallower than in the typical population.
This suggests that the gap between individuals with WS and their typ-