Randomized controlled trials are usually analysed by the group to which the patient was randomized, i.e. by "intention-to-treat", regardless of the degree of compliance. However, the "explanatory" effect, i.e. the effect that would occur if we had 100% compliance, is often of interest. This "explanatory" effect is diluted by poor compliance, and hence meta-analyses should ideally avoid both the heterogeneity of effect due to variation in compliance rates among studies, and the undeserved weight given to trials with poor compliance. Newcombe's deattenuation method, which adjusts estimates for the degree of compliance, is extended and applied to a meta-analysis of the five reported randomized controlled trials of mammographic screening. Compliance with screening varied across studies: from 61 to 93% assigned to screening had one or more mammograms. The adjusted estimate of the reduction in breast cancer mortality at 9 years follow-up is 0.37 (95% confidence interval: 0.21, 0.49).