An inferential study of the phenotype for the chromosome 15q24 microdeletion syndrome: a bootstrap analysis

In January 2012, a review of the cases of chromosome 15q24 microdeletion syndrome was published. However, this study did not include inferential statistics. The aims of the present study were to update the literature search and calculate confidence intervals for the prevalence of each phenotype using bootstrap methodology. Published case reports of patients with the syndrome that included detailed information about breakpoints and phenotype were sought and 36 were included. Deletions in megabase (Mb) pairs were determined to calculate the size of the interstitial deletion of the phenotypes studied in 2012. To determine confidence intervals for the prevalence of the phenotype and the interstitial loss, we used bootstrap methodology. Using the bootstrap percentiles method, we found wide variability in the prevalence of the different phenotypes (3–100%). The mean interstitial deletion size was 2.72 Mb (95% CI [2.35–3.10 Mb]). In comparison with our work, which expanded the literature search by 45 months, there were differences in the prevalence of 17% of the phenotypes, indicating that more studies are needed to analyze this rare disease.

As a result of these reports, in January 2012 Magoulas & El-Hattab (2012) conducted a comprehensive review of the cases reported up to that time (Magoulas & El-Hattab, 2012). In this review they descriptively analyzed the phenotypes of the patients with the syndrome, both in detail and in large groups. However, as this work did not include inferential statistics calculating the proportion of children with the different phenotypes with their Confidence Intervals (CI), we conducted a study to update the literature search and to determine the corresponding ranges for each phenotype using bootstrap methodology. The results provide a better understanding of this rare condition.

Study population
The population included all individuals with chromosome 15q24 microdeletion syndrome.

Study design and participants
This pooled analysis study examined MEDLINE and Google Scholar databases for reported cases of patients with the syndrome, using the keywords 15q24, deletion and microdeletion. The references in all the cases obtained were reviewed to detect possible studies not found in the databases analyzed, in order to collect all the papers that had been used as references to cases of the syndrome. This search was updated on September 29, 2015.
The source of information was the selected papers, i.e., those containing complete information on phenotype and genotype (Mb).

Sample size
The sample size was 40 patients, 4 of whom were excluded due to lack of the information required for this study (Mb and phenotype). The final sample consisted of 36 patients.

Statistical methods
The phenotype was described using absolute frequencies. One thousand bootstrap samples were obtained to determine the relative distribution frequency for the phenotypes and the mean loss size of the interstitial deletion of chromosome 15q24 (in Mb). Using these samples, we calculated a point estimate (median) and a CI (percentiles method) for these parameters (proportions and means). Thus we obtained a measurement of the uncertainty for the relative frequencies and for the mean, since with a small sample size we could not perform an asymptotic approximation of the normal distribution (n = 36). This bootstrap methodology was based on taking 1,000 simple random samples with replacement of the original sample. For each sample we calculated the statistic of interest (in our case proportions/means). At the end of the process we obtained 1,000 values for the statistic. In other words, we had a distribution of the statistic from which we could then calculate its estimation (median) with its CI (P2.5-P97.5). This method is very useful for obtaining the CI for statistics which are difficult to calculate (no closed form or with hypotheses which are not present). The computational cost is the only aspect of this method that is inadequate, but as our sample was small, this was not a problem. This methodology has already been applied with other rare diseases (Chiano & Yates, 1994). All analyses were performed with a significance level of 5%. The statistical software used was IBM SPSS Statistics 19. Table 1 shows the descriptive and analytical features of all the patients found in the literature search. We highlight the wide variability in the prevalence of the different phenotypes (3-100%). The phenotype with the lowest prevalence was myelomeningocele, which was only present in one case, whereas developmental delay was common in all cases (n = 36). The mean interstitial deletion loss was 2.72 Mb (95% CI [2.35-3.

DISCUSSION Summary
This study updates the descriptive analysis of the different phenotypes conducted in 2012 (Magoulas & El-Hattab, 2012), and provides inferential information on a range of values within which the true proportion of each phenotype in the study population can likely be found (95% CI).

Strengths and limitations of the study
The main strength of this study is that, for the first time, a measurement of the uncertainty of the proportion of each phenotype in the population has been obtained using inferential statistics (bootstrap samples). In addition, the descriptive data provided by Magoulas & El-Hattab (2012) have also been updated.
Concerning the limitations of this study, we have to assume a possible selection bias, since it is possible that not all incident cases of this syndrome have been published or that in our search strategy we may not have found all recently published cases, as we did not include the DECIPHER and ECARUCA databases. To minimize this bias as much as possible, we rigorously reviewed all the references for each of the articles. In terms of reporting bias, it is possible that not all the features have been specified in each of the cases. For example, MRI abnormalities: not all reported patients would have had an MRI scan done. In those cases the statistics for MRI abnormalities would be difficult to derive. Regarding obesity, the other authors used the Z-score for its assessment. In other words, the researchers took into account the age and gender of the patients. Other features are largely descriptive (thumb abnormalities, hypertelorism and brachydatyly) and thus subject to single clinical observer bias. Finally, the information was obtained through the publications instead of by contacting the authors. For obvious reasons, this information bias cannot be minimized. If we were analyzing associations between phenotypes and genotypes, this bias could give us incorrect information about the associations. However, we only obtained descriptive statistics with their confidence interval using the original sample through bootstrap methodology.

Comparison with the existing literature
To compare our results with those found by the 2012 study (Magoulas & El-Hattab, 2012), we determined whether the point estimate given by the previous study was within the CI we constructed for each phenotype. Such that if the estimate of the other study fell within that range, we had no evidence indicating that the proportion was different from that of our study (Magoulas & El-Hattab, 2012). However, if this estimate fell outside our CI, there was a difference compared with our study.
Overall we found agreement between both studies, as the previous estimate in nearly 83% of the phenotypes (38/46) was within our CI. The eight phenotypes that showed discrepancies with the previous study (Magoulas & El-Hattab, 2012) were facial asymmetry, high anterior hairline, hypertelorism, broad nasal base, hypospadias, microphallus, thumb abnormalities, and clynodactyly, all of which were approximately twice as prevalent in the earlier study (Magoulas & El-Hattab, 2012) than in our study. To assess the reasons for these discrepancies we need further studies on this syndrome, because they cannot be determined using our study design.

Implications for research and/or practice
The comparative analysis between our results and those of the review published in 2012 (Magoulas & El-Hattab, 2012) revealed differences in 17% of the phenotypes. Given that the previous article was accepted for publication in January 2012 (Magoulas & El-Hattab, 2012), and that our work expanded the literature analysis by approximately 45 months, it appears that the prevalence of the phenotypes in these patients is not fully known, which suggests the need for future studies in this rare syndrome. When there are more published cases of this rare syndrome, it would be very interesting to determine associations between the phenotypes and the size of the deletion. These associations were not studied in our paper because with 36 patients we would not have been able to obtain valid conclusions. Finally, it would be interesting to measure some phenotypes with facial recognition software (facial asymmetry, high anterior hairline, hypertelorism and broad nasal base).
Once we have this new knowledge, we can devise strategies to improve our decisions regarding these patients. For instance, we could attempt to determine where the breakpoint is using only the information about the phenotype.

CONCLUSIONS
The prevalence of the different phenotypes in patients with chromosome 15q24 microdeletion syndrome, published in early 2012 (Magoulas & El-Hattab, 2012), has been updated. The CI were calculated based on bootstrap samples for these proportions, providing a measurement of the uncertainty in the study population. Furthermore, differences between our study and the 2012 study were found in approximately one in six phenotypes, which suggests more studies are needed to analyze the characteristics of this rare syndrome.