In this large-scale research based on bibliometric, biographical and administrative data, we examine how gender disparities in international research collaboration differ by collaboration intensity, academic position, age, and academic discipline. The following are the major findings: (1) While female scientists exhibit a higher rate of general, national, and institutional collaboration, male scientists exhibit a higher rate of international collaboration. (2) An aggregated picture of gender disparities hides a more nuanced cross-disciplinary picture of them. (3) An analysis of international research collaboration at three separate intensity levels (low, medium, and high) reveals that male scientists dominate in international collaboration at each level. However, at each level, there are specific disciplines in which females collaborate internationally more than males. Furthermore (4), gender disparities in international research collaboration are clearly linked with age: they are the lowest and statistically insignificant for young scientists and the highest and statistically significant for the oldest scientists. Finally, we estimate the odds ratios of being involved in international research collaboration using an analytical linear logistic model. The examined sample includes 25,463 internationally visible Polish university professors from 85 universities, grouped into 24 disciplines, and 158,743 Scopus-indexed articles.