Disaggregating the mortality reductions due to cancer screening: model-based estimates from population-based data.

The mortality impact in cancer screening trials and population programs is usually expressed as a single hazard ratio or percentage reduction. This measure ignores the number/spacing of rounds of screening, and the location in follow-up time of the averted deaths vis-a-vis the first and last screens. If screening works as intended, hazard ratios are a strong function of the two Lexis time-dimensions. We show how the number and timing of the rounds of screening can be included in a model that specifies what each round of screening accomplishes. We show how this model can be used to disaggregate the observed reductions (i.e., make them time-and screening-history specific), and to project the impact of other regimens. We use data on breast cancer screening to illustrate this model, which we had already described in technical terms in a statistical journal. Using the numbers of invitations different cohorts received, we fitted the model to the age- and follow-up-year-specific numbers of breast cancer deaths in Funen, Denmark. From November 1993 onwards, women aged 50-69 in Funen were invited to mammography screening every two years, while those in comparison regions were not. Under the proportional hazards model, the overall fitted hazard ratio was 0.82 (average reduction 18%). Using a (non-proportional-hazards) model that included the timing information, the fitted reductions ranged from 0 to 30%, being largest in those Lexis cells that had received the greatest number of invitations and where sufficient time had elapsed for the impacts to manifest. The reductions produced by cancer screening have been underestimated by inattention to their timing. By including the determinants of the hazard ratios in a regression-type model, the proposed approach provides a way to disaggregate the mortality reductions and project the reductions produced by other regimes/durations.