Background: In four randomised trials, human papillomavirus (HPV)-based screening for cervical cancer was compared with cytology-based cervical screening, and precursors of cancer were the endpoint in every trial. However, direct estimates are missing of the relative efficacy of HPV-based versus cytology-based screening for prevention of invasive cancer in women who undergo regular screening, of modifiers (eg, age) of this relative efficacy, and of the duration of protection. We did a follow-up study of the four randomised trials to investigate these outcomes. Methods: 176 464 women aged 20-64 years were randomly assigned to HPV-based (experimental arm) or cytology-based (control arm) screening in Sweden (Swedescreen), the Netherlands (POBASCAM), England (ARTISTIC), and Italy (NTCC). We followed up these women for a median of 6·5 years (1 214 415 person-years) and identified 107 invasive cervical carcinomas by linkage with screening, pathology, and cancer registries, by masked review of histological specimens, or from reports. Cumulative and study-adjusted rate ratios (experimental vs control) were calculated for incidence of invasive cervical carcinoma. Findings: The rate ratio for invasive cervical carcinoma among all women from recruitment to end of follow-up was 0·60 (95% CI 0·40-0·89), with no heterogeneity between studies (p=0·52). Detection of invasive cervical carcinoma was similar between screening methods during the first 2·5 years of follow-up (0·79, 0·46-1·36) but was significantly lower in the experimental arm thereafter (0·45, 0·25-0·81). In women with a negative screening test at entry, the rate ratio was 0·30 (0·15-0·60). The cumulative incidence of invasive cervical carcinoma in women with negative entry tests was 4·6 per 105 (1·1-12·1) and 8·7 per 105 (3·3- 18·6) at 3·5 and 5·5 years, respectively, in the experimental arm, and 15·4 per 105 (7·9-27·0) and 36·0 per 105 (23·2-53·5), respectively, in the control arm. Rate ratios did not differ by cancer stage, but were lower for adenocarcinoma (0·31, 0·14-0·69) than for squamous-cell carcinoma (0·78, 0·49-1·25). The rate ratio was lowest in women aged 30-34 years (0·36, 0·14-0·94). Interpretation: HPV-based screening provides 60-70% greater protection against invasive cervical carcinomas compared with cytology. Data of large-scale randomised trials support initiation of HPV-based screening from age 30 years and extension of screening intervals to at least 5 years. Funding: European Union, Belgian Foundation Against Cancer, KCE-Centre d'Expertise, IARC, The Netherlands Organisation for Health Research and Development, the Italian Ministry of Health.