Abstract Aim Based on data from randomised controlled trials (RCT) on primary cervical screening, it has been reported that the problem of more frequent false-positive tests in Human Papillomavirus (HPV) DNA screening compared to cytology could be overcome. However, these reports predominantly operated with a narrow definition of a (false-)positive test. The aim of this paper was to illustrate how the narrow definition affected the measured adverse effects of HPV DNA screening compared with cytology screening. Methods In the European RCT data, we measured the impact of the narrow definition of a positive screening test on the published relative positive predictive values (PPV), an indicator of the relative frequency of false-positive screening tests. Results Using the trialists’ definitions of positive screening tests, HPV screening combined with cytology triage had relative PPVs of 0.87 (95% confidence interval (CI): 0.60–1.26) for ⩾CIN3 based on Swedish RCT data, and 0.78 (0.52–1.16) for ⩾CIN2 in the Italian Phase 1 RCT (25–34 years). These PPVs changed to 0.44 (0.30–0.64) and 0.51 (0.33–0.79), respectively, when all positive HPV or cytology screening tests were accounted for. In the Finnish RCT data, HPV screening using the cut-off point of ⩾10 pg/ml had a relative PPV of 0.27 (0.15–0.50) for ⩾CIN3, which changed to 1.84 (0.99–3.41). Conclusion The relative PPV was incorrectly estimated in six out of seven studies. In three of those six studies, the relative PPV changed significantly after inclusion of the previously erroneously excluded false-positive HPV or cytology tests.