GFsa Index for Adjustment of the Researchers’ Productivity/Ranking, considering the Two Most Relevant Variables Neglected: Total Number of Citations and “Scientific Age” – a Proof of Concept with the Assessment of 1,020 Highly-Cited Researchers in De

1. Introduction

Research articles are essential for describing new ideas, techniques, and procedures and consolidating concepts. It creates an opportunity to expose studies and publicly assimilate published knowledge [1]. The depth and extension of recognition, acceptance, and utilization of methods transmitted by these articles will result in the author's metrics. Currently, author metrics are available at Scopus (Elsevier), Web of Science, Google Scholar Citations, ImpactStory, ResearchGate, Academia.edu, and Plum Analytics [2]. Five main metrics are used to evaluate quality: h-index, i10-index, g-index, Eigenfactor, and Article Influence Score, but others also exist [3,4]. Therefore, one of them is the most used and accepted to verify the author’s scientific impact: the h-index or Hirsch index. It provides a robust single metric that combines quality and quantity.

1.1. H-Index: The Most Important Currently Index

Hirsch (2005) [5] proposed a number (H-index) as a simple and useful way to characterize the cumulative scholarly impact of a researcher's scientific output. It measures the productivity and impact of an author’s published study [2]. It is defined as the highest number of publications of a scientist that received h or more citations each, while the other publications have not more than h citations each [6]; e.g., a researcher with an h-index of 10 had published 10 papers, each of which has been cited by others at least 10 times. Therefore, comparing individuals within different disciplines may not be optimal, even though they can be closely related [7,8,9]. Then, it is considered discipline-size dependent. Thereby, the pattern of citations and publications differs across various medical and health sciences disciplines.

Due to the importance of this index, it was suggested that researchers with values over 18 could be promoted to full professors, and it can be used as part of the data required by some tenure/promotion committees [10]. An H-index between 3 and 5 can be set as a standard for assistant professors; 8 to 12 for associate professors; and 15 to 20 is a good standard for appointment to full professors. In many disciplines, a general rule is followed for an acceptable H-index matching the number of years the author has worked in that discipline. Also, a good H-index can be considered 20; 40 is outstanding; and 60 is exceptional; therefore, high numbers are reached after many years of research life [5]. H-index has several advantages: (1) it is a reliable and robust indicator of scholarly achievement [11]; (2) it applies to researchers individually or in a group; (3) it is a mathematically simple index; (4) it combines two types of activity (in the original setting this is citation impact and publications); (5) any document can be included; (6) publications that are hardly ever cited do not influence the h-index - the h-index discourages publishing unimportant work; (7) single peaks (top publications) have hardly any influence on the h-index; (8) h-index is closely correlated to total publication output [5]; and (9) it can be easily obtained from databases such as Google Scholar, ISI Web of Knowledge, and Scopus. It is important to highlight some critical factors when using Google Scholar as source: (1) in many cases, it indexes the names of only the first and last authors; (2) it uses initials rather than first names, so searches may yield articles from a variety of authors who share first initials and last names, and (3) it does not totally capture articles in languages other than English (LOTE articles), leading to mistakes or underestimation of the H-index. Therefore, in spite of these questions, the comparison of h-indices obtained by using Google Scholar and Scopus were highly correlated [10].

As disadvantages, (1) the H-index puts, in its original setting [5], newcomers at a disadvantage since both publication output and observed citation rates will be relatively low (it is based on long-term observations) - researchers with shorter scientific carriers may have fewer articles and citations than with longer scientific life; (2) it allows scientists to rest on their results (H-index obtained), since the number of citations received may increase even if no new papers are published - influence of researcher “scientific age or academic age”; (3) it is only useful for comparing the better scientists in a field (it does not discriminate among average scientists); (4) this indicator can never decrease; (5) it is only weakly sensitive to the number of citations received; (6) the major and minor (or no) contributor in the research gained equal h-index; there is the influence of self-citation of an author by quoting earlier research publication [12]. Then, some relevant criticisms were raised for the H-index because it may provide incorrect information about a scientist's output [13], such as (1) overall citations, neglecting single contributions; (2) does not consider the context of the citations - in respected journals (with high impact factor [IF]) or otherwise; (3) does not account for the length of the author’s byline, and that it is directly related to an author’s number of publications [14]; (4) scientists with outstanding and highly cited articles but few in quantity, cannot achieve a high H-index. Then, it is difficult to propose a competitive or acceptable H-index for the recruitment/promotion of faculties or for funding and grants purposes.

Furthermore, the H-index is also affected by the accuracy of the citation database used for its calculation, which different databases may present different H-indexes because each database covers different journals and years of indexation [15]. In addition, there was an incorrect correlation between the H-index and the researcher’s rank position; some authors [10] suggested that the H-index increases according to academic rank increases; the article reported that the persons with the highest H-indices were the Chairs of the department. This may occur because the H-index is also related to the time spent in a discipline (the longer the time, the more citations one’s papers will get). On the other hand, it is extremely incorrect to affirm, mainly because this index never used the variable time to ponder the researchers’ impact.

1.2. Time: One of the Most Important Variable

Time is one of the most important variables in human life and society. Time anchors our references: past, present, and future, categories used for life events (births, meetings, and work deadlines) and everything. Moreover, Zeno's paradoxes affirm that "time is not a reality, but a concept or a measure” [16], whereas Albert Einstein fundamentally changed the way of thinking about time. In his theory, time is real and relative; it is a dimension just as the three spatial ones, and they are all intertwined into a four-dimensional 'spacetime', forming the universe. Moreover, Kelly and Jennions [17] argued that it is distasteful to reduce a researcher's lifetime work to a mere numerical value, as Einstein rightly pointed out: “Not everything that counts is countable, and not everything that is countable counts” [18].

Thus, within the time concept of a measure, many existent indexes, including the H-index, neglected this important variable. Otherwise, some indices considered the variable TIME to formulate the researcher’s impact: the Age-weighted citation rate (AWCR, AWCRpA [AWCR per Author]), AW-index (age-weighted) [19]. The AWCR measures the number of citations to an entire body of work, adjusted for the age of each individual paper, where the number of citations to a given paper is divided by the age of that paper. The AWCRpA is similar to the plain AWCR but is normalized to the number of authors for each paper. The AW-index is adjusted for the age of each individual paper (the older the researcher is, the higher your h-index will be) and was defined as the square root of the AWCR to allow comparison with the h-index. The AR-index [19] is the square root of the sum of all age-weighted citation counts over all papers that contribute to the h-index.

1.3. Objective

Currently, there is not a single perfect bibliometric index that accurately describes a researcher's impact. Although the H-index is the most used, combining two or more metrics was suggested [20]. However, due to the lack of total citations and “scientific age” consideration, the aim of this study was to present a new index system (GFsa index) based on the two variables completely forgotten (total of citations and “scientific age”), considering both as the fairest way to rank the scientists in Dentistry. This proof of concept was developed, and the best-ranked researchers in Dentistry were included.

2. Materials and Methods

2.1. H-Index Explanation

The h-index measures the number of publications (productivity) as well as how often they were cited. It is determined based on the calculation (h-index = n of publications with a citation number greater than or equal to h). For example, if 10 publications are cited 10 times or more, the researcher will receive an h-index of 10. Therefore, this index, which is currently the most relevant, has two problems based on the lack of consideration of the variable time and forgetting the total of citations that a researcher can receive.

2.2.“.Scientific Age” or Researcher’s Lifetime: The Concept

This is the hardest parameter to define and acquire; maybe, for this reason, no other index has tried to use it. The definition is the time spent by a researcher since the beginning. Therefore, finding this first researcher’s moment is not simple; moreover, there is no registry to prove when the researcher “was born”. Then, the most practical and feasible data to help in this concept was the first time the author appeared in the literature, which was considered the “researcher’s birthday”.

It could be considered many landmarks in the author’s life, such as (1) when the researcher started their first investigation (first contact with science); or (2) when they started their master’s or Ph.D. Therefore, in order to standardize and permit feasible and simple access to the “researcher’s birthday”, it was considered the “YEAR” of the first publication publicly found, which means the year of the first article that the authors publicly appeared in, easily sought and found in Google Scholar.

It was calculated following the formula: (i) current year; less (ii) the year of the first publication found in the Google Scholar (in case of questions, PubMed/MedLine, PubMed Central, and Scopus databases were consulted). Then, “scientific age” (sa) = (Current year) – (Year of the first publication).

2.3. Databases Used and Researchers' Inclusion

The recently published AD Scientific Index was used as consultation (https://www.adscientificindex.com/?subject=Medical+and+Health+Sciences+%2F+Dentistry) (data obtained on March 18^th, 2024). All researchers included in this study were cited in the AD Scientific Index (2024) in the Dentistry field and had the respective Google Scholar page accessible and consulted (scholar.google.com) to obtain the desired information, which was performed by two authors (G.V.O.F. and J.C.H.F.). The data were assessed twice to avoid error or mistake.

There was a limitation/cutline for the inclusion of a minimum H-index value of 30 (March 29^th, 2024). The author was excluded whether: (i) did not have a Google Scholar page; (ii) duplicated author; or (iii) presented any suspicious activities about manipulation of articles. We collect all researchers' Google Scholar publications, including citation data. We filter out the first publication in order to obtain the year.

2.4. Total Citations

It has been observed that the H-index or i10 index count only some citations according to their parameters. This fact brings disadvantages as observed, e.g., a researcher with around 10,000 citations received an H-index of 33, and another research with 3,700 citations also received an H-index of 33. Analyzing and observing this question deeply, we judged that it was not fair. Then, we also introduce the use of total citations in order to correctly qualify the professional.

2.5. Data Collection for the Highly Cited Researchers in Dentistry

We construct a dataset of all researchers who were reported in Dentistry. The name, H-index, i10 index, and publications were retrieved. Then, we selected as previously established the highly cited researchers via Google Scholar. The retrieved researchers were sorted by the H-index. Each author included had the Google Scholar consulted.

2.6. GFsa © Formula

Whereas the H-index can be considered deficient in correctly evaluating the researcher, the GF index considers the researcher's real impact, evaluating the researcher's “scientific age” and taking into consideration the total citations received. It brings better weighting and comparison between all professionals, independent of age. It permits the elimination of the disadvantages of old researchers and new ones.

Within this context, considering the “scientific age” as the most important parameter, the formula used to obtain the GFsa © was: .

2.7. Statistical Analysis

The data obtained was statistically evaluated. The Pearson correlation coefficient was measured, quantifying the strength and direction of the linear relationship between two quantitative variables (Index and “Scientific age”). The confidence interval was 95%. The range of the coefficient r takes values between –1 and 1. A positive r indicates a positive correlation, which means when one variable increases, the other tends to increase as well; whereas a negative r indicates a negative correlation: when one variable increases, the other tends to decrease. An r value of 0 implies no linear relationship between the variables. The strength of the correlation followed: (1) strongly positive: r > 0.5; (2) moderately positive: 0.3 < r ≤ 0.5; (3) weakly positive: 0 < r ≤ 0.3; (4) weakly negative: –0.3 ≤ r < 0; (5) moderately negative: –0.5 ≤ r < –0.3; and (6) strongly negative: r < –0.5.

3. Results

After manually evaluating the AD Scientific Index, we recorded a total of 9,093 researchers in Dentistry, of whom 1,020 were included, respecting the H-index of at least 30. All of them had Google Scholar also manually analyzed. Then, we collected all 1,020 researchers' Google Scholar data (publications, citations, and indexes). Specifically, each researcher's total citations and “scientific age” were registered and calculated (all data will be available at http://gfindex.us.to).

The minimum H-index registered was 30 (as previously established), and the maximum was 134 (mean = 46.22 ± 16.94; standard error of mean = 0.5311). The mean “scientific age” registered was 34.18 ± 13.34 (standard error of mean = 0.4181), with a minimum of 7 and a maximum of 103. With this information and data collected, GFsa index was calculated, presenting a minimum value of 0.2186 and a maximum of 154.8 (mean = 10.33 ± 11.82; standard error of mean = 0.3706) (Supplementry Table S1). Then, the data was organized and sorted following the ranking obtained in the GFsa index (Table 1).

Then, the interpretation was clear when observing the Pearson correlation coefficient obtained for the variables analyzed (Figure 1). The H-index had a weakly positive association with the researcher’s “scientific age”; this fact means that H-index will increase according to the “scientific age” increases. Otherwise, a moderately negative correlation between GFsa and “scientific age” was demonstrated, in which a higher GFsa had a lower “Scientific age”. This assessment shows that the variable introduced was fairly used. Moreover, a positive correlation was observed between both indexes (H-index and GFsa).