Profit (p)-index: the degree to which authors profit from co-authors

Abstract

Current metrics for estimating a scientist's academic performance treat the author's publications as if these were solely attributable to the author. However, this approach ignores the substantive contributions of co-authors, leading to misjudgments about the individual's own scientific merits and consequently to misallocation of funding resources and academic positions. This problem is becoming the more urgent in the biomedical field where the number of collaborations is growing rapidly, making it increasingly harder to support the best scientists. Therefore, here we introduce a simple harmonic weighing algorithm for correcting citations and citation-based metrics such as the h-index for co-authorships. This weighing algorithm can account for both the nvumber of co-authors and the sequence of authors on a paper. We then derive a measure called the 'profit (p)-index', which estimates the contribution of co-authors to the work of a given author. By using samples of researchers from a renowned Dutch University hospital, Spinoza Prize laureates (the most prestigious Dutch science award), and Nobel Prize laureates in Physiology or Medicine, we show that the contribution of co-authors to the work of a particular author is generally substantial (i.e., about 80%) and that researchers' relative rankings change materially when adjusted for the contributions of co-authors. Interestingly, although the top University hospital researchers had the highest h-indices, this appeared to be due to their significantly higher p-indices. Importantly, the ranking completely reversed when using the profit adjusted h-indices, with the Nobel laureates having the highest, the Spinoza Prize laureates having an intermediate, and the top University hospital researchers having the lowest profit adjusted h-indices, respectively, suggesting that exceptional researchers are characterized by a relatively high degree of scientific independency/originality. The concepts and methods introduced here may thus provide a more fair impression of a scientist's autonomous academic performance.

Figure 1. The distribution of the profit (p)-index.

Among the University Medical Centre researchers (n = 161), the p-index was approximately normally distributed with a mean of 0.79 and a standard deviation of 0.05 (see also Table 1 ).

Figure 2. The relative contribution of co-authors.

Among the University Medical Centre researchers (n = 161), there was a non-significant trend for the association between the p-index and the h-index (ρ = +0.15, p = 0.067), while the p_h-index and the h-index were only weakly associated (ρ = +0.17, p = 0.031), suggesting that the relative contribution of co-authors to the work of an author is relatively stable over his/her scientific career.

Figure 3. Comparison between University Medical Centre researchers (top 15 with highest h -index), Spinoza laureates and Nobel laureates in the biomedical field with respect to different citation metrics.

The horizontal lines within the boxes represent the median values, the edges of the boxes indicate the interquartile range, and the outer horizontal lines indicate the minimum and maximum values. Data are given for: A. h-index; B. profit adjusted h-index (h_a-index); C. profit index (p-index); D. profit h-index (p_h-index). * Denotes p-values smaller than 0.05. P-values were calculated using the Mann-Whitney U test and indicate differences in median values. Please refer to Table 3 for the statistical outcomes of the other comparisons.