Fractional h-index: a fairer method for assessing academic impact in medicine

The h-index, introduced by Hirsch (2005), has become a widely used metric for assessing the academic reputation and research impact of scientists. It combines productivity (the total number of a researcher’s publications) with impact (the influence of these publications on peers) into a single, straightforward indicator. The h-index is determined by the number “h” of publications that have been cited at least “h” times, with a higher h-index reflecting a greater impact through both volume and citations. In recent years, quantifying scientific impact has become essential in research evaluation as project approvals, hiring decisions, grant allocations and awards increasingly rely on objective metrics, with the h-index being one of the most widely applied measures.

Despite its popularity and advantages – such as providing an easily interpretable measure for ranking and comparison, applicability across all career stages due to its independence from minimum publication or career-length requirements and its lack of reliance on tuning thresholds or parameters – the h-index has notable drawbacks. For instance, the h-index does not consider career length, the impact of exceptionally cited papers, the recency of publications or variations in citation influence among researchers with the same score. To address these issues, alternative metrics, such as the m-quotient, g-index, h(2)-index, a-index, r-index, ar-index and h_w-index, have been proposed to offer a more equitable comparisons of a researcher’s impact that is frequently not captured by the h-index alone (Bornmann et al., 2008). A notable limitation of the h-index that has not been previously considered is its potential to underestimate or overestimate a researcher’s achievements in cases of co-authorship. Researchers with differing levels of contribution may end up with the same h-index, which does not fully capture individual roles. Consequently, relying solely on the h-index may not be optimal for evaluating candidates for academic positions, promotions or tenure (Akhtar, 2024). Nonetheless, the h-index is advocated as an objective measure of scientific credibility of a researcher and remains one of the most widely used metrics in academia for these purposes.

To achieve a more meritocratic evaluation of scientific impact, one possible approach is to consider author ranking, which often reflects the relative contributions of each author to the research. According to the guidelines of the International Committee of Medical Journal Editors (ICMJE, n.d.), authorship should be based on four key criteria: making substantial contributions to the study’s conception, design or data handling; actively drafting or critically revising the work; giving final approval of the version to be published and assuming accountability for the work’s integrity. While these criteria establish who qualifies for authorship, specific guidelines for author order are not explicitly codified. Nevertheless, authors are generally listed in descending order of their contributions and significance to the research. The first author is generally the primary investigator with the most significant role, followed by the second and third authors with decreasing levels of contribution. Middle authors typically have less prominent roles, while the last author is often a senior researcher or team leader, recognized as the overall coordinator of the study. The corresponding author, usually the first or last author, is responsible for handling correspondence and is often the main funding recipient for the study. Despite some slight variations (Nishizaki et al., 2020), this authorship ranking scheme is widely adopted in medicine and biomedical fields. Given these distinctions, it is clear that citations and h-index rewards should not be equally distributed among authors if we aim to more accurately assess individual scientific impact, at least in medicine. Different fields of research may have distinct conventions for authorship ranking in published articles (i.e. in mathematics or theoretical disciplines, authors are often listed alphabetically, reflecting equal contributions). Therefore, applying a uniform metric (h-index or fractional h-index) across diverse fields may not accurately capture individual contributions or research impact.

Here is proposed an alternative approach to h-index computation that considers author ranking within an article to provide a fairer metric of scientific impact. This method is inspired by a part of the research funding system in France, where publication quality and authorship ranking are evaluated through the SIGAPS (Système d’interrogation, de gestion et d’analyse des publications scientifiques) score, a bibliometric tool developed by the French Ministry of Health (Devos et al., 2003). The SIGAPS score is used primarily in France to assess the scientific output of researchers and institutions in biomedical fields, aiding in research funding allocation based on publication performance. The score is calculated according to the number and quality of publications (based on their impact factor from Journal Citation Reports) and the author’s rank on each paper. In this system, the first and last authors, who are typically the main contributors, receive higher scores (4 points), followed by the second author (3 points), the third and before-last authors (2 points) and all other contributors (1 point).

The proposed fractional citation count follows a rank-based evaluation of authorship contributions. The first and last authors, typically the primary contributors who lead or coordinate the research and often secure funding, receive 100% of the citation count. The second and third authors receive 75% and 50%, respectively, reflecting their substantial but secondary contributions. Middle authors are credited with 25% of the citation count as their roles are generally supportive rather than central. The before-last author is treated the same as other middle authors as this position does not consistently represent a unique role across disciplines. Collaborators who primarily participate in data collection for large clinical trials, thereby playing a marginal role in the study’s ideation and publication, are allocated 15% of the citation count. In cases of shared authorship ranks (i.e. co-first or co-last authors), the citation count for that position is divided equally among the authors sharing the rank. If the corresponding author is not listed among the primary authors (within the first three positions or as the last author), they are allocated 50% of the citation count toward the fractional h-index. For shared corresponding authorship, the citation count is divided accordingly, with each author retaining the higher value between their assigned rank-based citation count and their corresponding author status to prevent assigning this role to a middle author solely to increase their citation count (Table 1). This approach aims to offer a more nuanced and merit-based evaluation of scientific impact by accounting for authorship ranking, ultimately providing a fairer distribution of citation credit in calculating the h-index.

In an era where the “publish or perish” paradigm remains prevalent and competition for research funding and academic positions intensifies, precise and fair assessment of research merit becomes crucial (Rawat and Meena, 2014). Researchers competing for grants or academic roles should be evaluated using reliable metrics that consider the full context of their contributions, aspects often overlooked by the traditional h-index. For example, an author who consistently leads and makes substantial contributions to highly cited studies could have a similar or even lower h-index than an author who primarily plays a supporting role on similarly cited studies, failing to capture the true difference in their individual impact. This discrepancy can be addressed with the proposed fractional h-index, which rewards primary contributions more heavily. Under this system, an author with a leadership role in research would show a higher fractional h-index than the one who predominantly holds secondary roles (Figure 1). This metric (like the traditional h-index) cannot serve as a stand-alone measure for evaluating research merit; however, it aims to offer a fairer comparison between peers from diverse backgrounds or research environments, rewarding those who take on more prominent roles in their work. Additionally, it could encourage young researchers to be proactive, motivating them to pursue central or leadership roles in studies. While this proposal for a fractional h-index is perfectible and own itself some limitations (i.e. it may not effectively account for highly cited articles, the ranking may vary if adopted for field different from medicine), it should be viewed as a call to action to develop fairer metrics for evaluating researchers, ultimately promoting a more meritocratic academic landscape.