Anxiety Disorders in Williams Syndrome Contrasted with Intellectual Disability and the General Population: A Systematic Review and Meta-Analysis

Individuals with specific genetic syndromes associated with intellectual disability (ID), such as Williams syndrome (WS), are at increased risk for developing anxiety disorders. A systematic literature review identified sixteen WS papers that could generate pooled prevalence estimates of anxiety disorders for WS. A meta-analysis compared these estimates with prevalence estimates for the heterogeneous ID population and the general population. Estimated rates of anxiety disorders in WS were high. WS individuals were four times more likely to experience anxiety than individuals with ID, and the risk was also heightened compared to the general population. The results provide further evidence of an unusual profile of high anxiety in WS. Electronic supplementary material The online version of this article (doi:10.1007/s10803-016-2909-z) contains supplementary material, which is available to authorized users.

Single restricted or non-random sample e.g., a specialist clinic or previous research study a Single regional sample e.g., a regional parent support group Multiple restricted or non-random samples e.g., multi-region specialist clinics National non-random sampling e.g., national parent support groups Random or total population sample Screening instrument e.g. PAS-ADD Clinician judgement against specified diagnostic criteria e.g., DSM-IV or ICD-10 Diagnostic instrument/interviews e.g., K-SADS, ADIS Consensus from multiple assessments, including at least one diagnostic instrument a For individuals recruited as part of a larger ongoing study, if the recruitment strategy is described, it is coded. If not, it is coded as 1, indicating the sample has come from one source (i.e., the larger ongoing study). b Studies can only be classified into a category if all of the participants were tested using the outlined method. For instance, if only 50% of participants were FISH tested, the study cannot receive a score of 3 and will receive a score of 2. For heterogeneous ID studies, a score of 1 is given to studies which include an IQ or adaptive behaviour assessment as part of the study design.

Online Resource C Statistical Meta-Analytical models
There are various statistical meta-analytical models which can be used to estimate effect sizes. Each model makes different inferences and assumptions regarding the data in question (Hedges and Vevea 2000). The three models referenced in the study are the fixed-effects model, the random-effects model and the quality-effects model. Explanations of the models and justifications for the models used are provided below.

The Fixed Effects (FE) model
The FE model generates effect sizes based on the assumption that studies are homogenous and share common effect sizes (Hedges & Vevea 2000). This model only accounts for within study variability; however it is considered probable that there will also be some level of variation between studies that this model fails to consider. Variability may result from study methodological differences, as well as moderating variables which may act to influence outcomes (Hunter and Schmidt 2000). As a result, Type 1 bias may increase and inaccurate conclusions may be drawn using this model (Field 2003;Overton 1998).

The Random Effects (RE) Model
The RE model accounts for between study variance and is described as providing a more applicable model for real-world data (Borenstein, Hedges, Higgins and Rothstein 2010). The model assumes that effect sizes will vary due to random error and true variation between the studies and redistributes study weightings to account for this (Erez, Bloom and Wells 1996). As a result of the additional sources of variation, the confidence intervals generated in the RE model tend to be larger than those in the FE model (Egger, Smith and Phillips 1997) Even so, the RE model was considered a more appropriate alternative to the FE model for this review, as it considers both within and between study variability.

The Quality Effects (QE) Model
The QE model is a newer method which accounts for methodological differences between studies. This model provides more weight to studies which are of higher quality when estimating effect sizes and this is indicated to be more clinically relevant than the RE model (Doi and Thalib 2008). The redistribution of mathematical weightings corresponds to the parameters '0'indicating low quality and '1' indicating high quality (Barendregt, Doi, Lee, Norman and Vos 2013). Quality assessment for this model is required and according to Doi and Thalib (2008), any criteria can be used, providing a Qi score (Quality of the ith score) is derived by dividing individual study quality scores by the maximum score.

The Review
Both a RE model and a QE model were used in this review. These models were chosen for the metaanalysis as they were deemed the most suitable and appropriate for the study's aims. Both models redistribute mathematical weight to prevent outliers from interfering with the effect size; with the RE model based on statistical heterogeneity and the QE model considering quality (Doi and Thalib, 2008), Usage of both models enabled us to demonstrate the utility of weighting the quality of studies when estimating effect sizes. It also provided some indication as to whether the model's assumptions had an effect on the prevalence rates estimated.
Models were generated using the statistical package MetaXL 2.0 (Barendregt and Doi 2011). Online Resource E Pooled prevalence estimates, random effects forest plots and quality effects forest plots for anxiety disorders in individuals with intellectual disability of heterogeneous aetiology Supplemental Table 2. Total number of included ID studies and participants, mean quality weightings; and random-effects/quality effects models with 95% confidence intervals. Data from Reardon, Gray and Melvin (2015).

(CI)
Any   Figure 27. Pooled prevalence estimates for social anxiety disorder using the random effects model. Figure 28. Pooled prevalence estimates for social anxiety disorder using the quality effects model.