The sphenoidal emissary foramina prevalence: a meta-analysis of 6,369 subjects

Search strategy

A systematic literature search was conducted by two independent assessors in August 2022 using Publish or Perish software [15]. Through this application, all available databases except for the Web of Science (Crossref, GoogleScholar, OpenAlex, PubMed, Scopus, and Semantic Scholar) were scanned using combinations of the following keywords: [“foramen Vesalius”, “sphenoidal emissary foramen”, “presence”, “occurrence”, “prevalence”, “incidence”)]. Notably, in Semantic Scholar and OpenAlex, only single keywords were used since both databases’ application programming interfaces did not support the use of Boolean operators. After duplicates’ removal, each publication’s reference list was manually scanned for potentially non-identified studies. The systematic literature search flowchart (Fig. 1) is based on the PRISMA 2020 Statement [29].

Fig. 1figure 1

Flow chart depicting the systematic search results from the relevant studies' identification and selection

Criteria for study selection and data inclusion and extraction

All original studies reporting data regarding SEF prevalence were included with no restriction on language or publication date. Case reports, review articles, letters to the editor, conference abstracts, doctoral thesis, studies with no full-text or detailed abstracts available, and articles that could not be cross-verified by multiple secondary sources were excluded. Out of each publication, the extracted data included the authors, year of publication, continent of origin (Europe, Asia, and America), type of data (dried skulls and imaging), probing for evaluating SEF patency (yes or no), instrument used for probing (bristle, wire, and other), total sample, reported SEF frequency (total, bilateral, and unilateral), type of dominance (bilateral: when the bilateral to unilateral foramina ratio was greater than 1, otherwise, unilateral), morphometric data (SEF diameter, SEF–FO, and SEF–FS distances), and the methodology used for the morphometric measurements (caliper, DICOM Viewer, image analysis software). In publications not mentioning the continent of origin, the country where the study originated from, was eventually recorded and in case of an article written in a non-Latin language (e.g., Russian), the full paper was downloaded and translated using the Google Translate website (https://translate.google.com). Additionally, in manuscripts where only the bilateral or unilateral percentages were reported, the respective frequencies (bilateral and unilateral frequency) were calculated by converting each percentage to integers with no decimal approximation.

Quality assessment

The quality assessment was performed according to the Anatomical Quality Assessment (AQUA) tool [16], a tool consisting of 25 questions and dividing into 5 areas: 1. Objectives and Subject Characteristics, 2. Study Design, 3. Methodology Description, 4. Descriptive Anatomy, and 5. Results Reporting. For each domain, where all questions were replied affirmatively, the risk of bias was rated as 'low', otherwise as 'high'. Study quality was defined as ‘high’ if at low risk of bias in all five domains, ‘moderate’ if at low risk of bias at least in three domains, and otherwise as ‘low’.

Statistical analysis

Statistical analysis was carried out using RStudio (version: 2022.7.1.554) software (RStudio Team (2022)). RStudio: Integrated Development for R. RStudio, PBC, Boston, MA for MacOS. The DerSimonian and Laird random-effects model was used to estimate the pooled prevalence and its respective 95% confidence intervals (CI). No logit or double arcsine transformation were made since the observed proportions identified across studies were between 0.2 and 0.8 [21, 37]. Heterogeneity presence across studies was estimated by constructing a forest plot and tested using the Cochran’s Q statistic and its respective p value. The Higgins I2 statistic and its respective 95% CI were used for quantifying the magnitude of true heterogeneity in effect sizes. An I2 value of 25%, 50%, and 75% indicated low, moderate, and high heterogeneity. To detect studies that overly contributed to the heterogeneity, a Baujat plot [2] was created. To determine if the potential outlying studies, as evaluated in this plot, were also influential, screening for externally studentized residuals with z-values larger than two in absolute value and leave-one-out diagnostics were performed [38]. With the outlying and influential studies removed, the pooled prevalence, its’ respective 95% CI, and the substantial heterogeneity were re-evaluated through moderator analyses. In the conducted subgroup analyses, the following covariates were evaluated: continent of origin, type of data, probing, sample size, dominance, study quality, and measurements. As per the sample size, all manuscripts were divided into two categories (small and large studies) based on the median sample size (n = 239 subjects). In the performed univariable regression analyses, except of the aforementioned covariates, the SEF diameter, as well as the SEF–FO and SEF–FS distances were assessed as per their relationship with the respective effect sizes. Moreover, the presence of interrelated moderators was checked to avoid potential multicollinearity issues prior the conduction of the multivariate regression analysis. Due to the limited availability of data about the SEF diameter, and the SEF-FO, and SEF-FS distances in the given dataset, they were not used in this analysis. To detect the presence of publication bias, a Doi plot and a funnel plot were created. The asymmetry of each plot was estimated by calculating the LFK index [9] and Egger’s tests’ p value, respectively. Additionally, to detect the presence of the small-study effect, the phenomenon that smaller studies may show different, often larger effects than large ones [33], a funnel plot of the prevalence against the sample size was constructed and regression-based Egger’s test was estimated. The arithmetic difference between percentages was expressed in percentage point units [39]. Unless otherwise stipulated, the statistical significance was established at p = 0.05 (two-tailed).

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