BACKGROUND: In the Swedish two-county trial women aged 40-74 years from two counties in Sweden were randomised to invitation to mammographic screening for breast cancer. METHODS: This paper uses random effects logistic regression models to analyse recent data from the trial. The analysis accounts for the structure of the trial, where small geographical units are randomised within larger geographical strata (blocks of two or three small units that are socio-economically similar). RESULTS: Fixed effects and a variety of random effects models show a strong degree of agreement and yield a significant 29% or 30% reduction in breast-cancer mortality. DISCUSSION: Fixed effects and random effects models agree for this example, because heterogeneity both between strata and within strata between clusters is small and because the effect of treatment does not vary much in different strata.