Validity and bias of indicators of international collaboration: A theoretical analysis with an empirical study of Ukraine-Russia-United States and China-United States.

• Introduce the ORC, a new symmetric indicator of collaboration superior to the OER. • Give probabilistic interpretations of the AOER and the ORC. • AOER lacks content validity as an indicator. • Analysis of Ukraine collaborations with United States and Russia prior to invasion. • Analysis of United States/China relationship shows superiority of RIC over AOER. We examine three indicators that give a relative measure of collaborations between countries and introduce a fourth indicator. Of the three established indicators, the Asymmetric Observed to Expected Ratio (AOER-indicator) and the symmetric Observed to Expected Ratio (OER-indicator) have received criticism for some specific theoretical situations. The AOER fails as both a meaningful statistic and an indicator. The OER is a meaningful statistic but fails as an indicator. The Relative Intensity of Collaboration (RIC-indicator) is relatively recent measure that is a meaningful standard statistic and passes Rousseau's criterion for an indicator. The new indicator is the Odds Ratio of Collaboration (ORC-indicator). It is a symmetric and meaningful standard statistic that passes Rousseau's criterion for an indicator. We give interpretations for all four indicators to give a systematic comparison that recommends the RIC and ORC. We then compare them in analyzing some specific dynamic developments over a 20-year period: The Ukraine-Russia-United States relationship and the China-United States relationship. We believe the analysis illustrates the value of the RIC, the inadequacies of the AOER, and is interesting analysis of its own accord. [ABSTRACT FROM AUTHOR]