All original research publications from 2009 to 2013 were analyzed for the top 25 pediatric journalistic neurosurgeons in North America and Europe selected to build regional citation databases of all journal references. Regional differences were compared at each database. Egghe`s formulation and the verbal formulation of Bradford`s law were used to create specific citation density areas and identify basic journals. Egghe`s formulation has proven accurate for many different applications in bibliometric analysis . Egghe`s formulation can be used to create a graphical representation of the Bradford distribution. The following equations are used for this purpose: The citation database has been organized in descending order of the number of citations per journal (Table 3). The ordered distribution of the citation density can be seen in Fig. 1. The number of citations in the main journal, Journal of Neurosurgery, was used as Ym (1,553), and the total number of journals cited was used as T (2,231). Using these values in the Egghe formulation described above, we solved for the theoretical citation distribution for p = 3–8, where p is the number of zones.
Bradford`s law describes the number of basic journals in a particular field or topic and has recently been applied to neurosurgery. The aim of this study was to use the currently accepted formulations of Bradford`s Law to identify basic journals of paediatric neurosurgery. Additional analysis was performed to compare regional dependence with citation density in North American and European neurosurgeons. Bradford`s law of dispersion is a law of diminishing yield and dispersion. Bradford formulated the law in 1948, stating that for a particular field there are “very productive magazines, a greater number of more moderate producers, and an even greater number of ever-decreasing productivity” . For each issue or individual domain, the upper third (Zone 1 or Core) represents the journals most frequently cited in the literature on the subject and which are therefore of the greatest interest to researchers in the discipline. The middle third (zone 2) includes journals that had an average number of citations, and the bottom third (zone 3 or tail) includes the long tail of journals that are rarely cited and considered marginally important to the subject . Researchers have defined a topic in lexical, semantic, and subject diffusion terms , and some argue that problems may not play a role in defining the “topic,” provided it is applied consistently .
Using this method, we found that the distribution followed a pattern for certain p-values. Parameters c and k could be found for the first three areas that respond to the verbal formulation, while all areas beyond three did not reach the citation density expected for this Bradford multiplier. The closest agreement on the first three zones was for p = 4 (Fig. 3). With this formula, the core journals for pediatric neurosurgery have evolved to become the top nine journals with a Bradford multiplier of 4. The main journals of pediatric neurosurgery, organized by citations, are: the Journal of Neurosurgery, Neurosurgery, Epilepsia, Child`s Nervous System, Pediatric Neurosurgery, Neurology, Journal of Clinical Oncology, Cancer Research and New England Journal of Medicine. A Bradford legal analysis was also carried out for a group of 25 of Europe`s largest paediatric neurosurgeons. Citation density in this group was more closely correlated with Egghe`s formulation than with the North American dataset (Fig. 4). For continuity between group comparisons, bradford`s final model used was verbal formulation.
The verbal formulation of Bradford`s law for the European group showed five journals in the central area. The main journals in the European database, sorted by number of citations, are Child`s Nervous System, Journal of Neurosurgery, Neurosurgery, Pediatric Neurosurgery and Journal of Neurosurgery: Pediatrics. The regional comparison showed a preference for the Journal of Neurosurgery and Child`s Nervous System, respectively, but four of the top five reviews were common to both groups. By applying the verbal wording of Bradford`s law to the North American citation database, a citation density pattern was identified in the first three areas. Journals located in the first most frequently cited area are presented as basic journals. Bradford`s law uses three parameters to model c to ck to ck2. ckp – 1 sequence using the Egghe formulation. Parameter c defines the core number of journals. The parameter k defines the Bradford multiplier. These parameters depend on the choice of p, which represents the number of zones. They can be solved with the following equations: The citation distribution expected by Egghe`s formulation did not correspond to the observed citation distribution identified by our citation database (Fig. 2).
Egghe`s formulation would predict that all areas have roughly equal distribution of citation density, but our distribution did not meet this expectation. With four zoning differences between Bradford`s verbal formulation and Egghe`s formulation (Table 4), Egghe`s formulation was abandoned in favor of the verbal formulation of Bradford`s law.