Estimation and prediction for cancer screening models using deconvolution and smoothing

The model that specifies that cancer incidence, I, is the convolution of the preclinical incidence, g, and the density of time in the preclinical phase, f, has frequently been utilized to model data from cancer screening trials and to estimate such quantities as sojourn time, lead time, and sensitivity. When this model is fit to the above data, the parameters of f as well as the parameter(s) governing screening sensitivity must be estimated. Previously, g was either assumed to be equal to clinical incidence or assumed to be a constant or exponential function that also had to be estimated. Here we assume that the underlying incidence, I, in the study population (in the absence of screening) is known. With I known, g then becomes a function of f, which can be solved for using (numerical) deconvolution, thus eliminating the need to estimate g or make assumptions about it. Since numerical deconvolution procedures may be highly unstable, however, we incorporate a smoothing procedure that produces a realistic g function while still closely reproducing the original incidence function I upon convolution with f. We have also added the concept of competing mortality to the convolution model. This, along with the realistic preclinical incidence function described above, results in more accurate estimates of sojourn time and lead time and allows for estimation of quantities related to overdiagnosis, which we define here.