Risk time splitting for improved estimation of screening programs effect on later mortality
There is a great need for evaluating screening programs, but analysing data from population screening is often complicated by a delayed screening effect. In cancer screening, only new, not yet clinically diagnosed cases, might benefit from screening through earlier treatment. Hence, mortality data following screening should be analysed based on refined mortality, separating cases based on diagnosis before and after first screening invitation. Historically, refined mortality has been implemented by selecting comparison groups from the available data to disentangle the causal effect. While giving valid estimates, the ignorance of large parts of the available data has limited study precision. In BMJ 2014, Weedon-Fekj{\ae}r et al. used a new estimation approach applying all the available Norwegian mammography screening data. The estimation uses historic pre-screening data on time from clinical diagnosis to death estimating the proportion of post-screening mortality which is expected to be based on cases incident before first screening invitation, in the absence of a screening effect. Utilizing this expected proportion of post-screening incident cases, Poisson regression offsets are added to align the expected number of cases. The screening effect is then estimated adjusting for relevant covariables. While the method increases study precision, it has not been easily available and widely adopted. We here explain the method in detail, add maximum likelihood estimation, and lay the foundation for widespread use. Applying the method on Norwegian and Danish data, bootstrap confidence intervals are considerably narrower than intervals seen using other refined mortality methods, especially for the gradually introduced Norwegian program.