Estimation and prediction for cancer screening models using deconvolution and smoothing

The model that specifies that cancer incidence, I, is the convolution of th e preclinical incidence, g, and the density of time in the preclinical phas e, f, has frequently been utilized to model data from cancer screening tria ls and to estimate such quantities as sojourn time, lead time, and sensitiv ity. 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. Prev iously, g was either assumed to be equal to clinical incidence or assumed t o 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 th e absence of screening) is known. With I known, g then becomes a function o f f, which can be solved for using (numerical) deconvolution, thus eliminat ing the need to estimate g or make assumptions about it. Since numerical de convolution procedures may be highly unstable, however, we incorporate a sm oothing procedure that produces a realistic g function while still closely reproducing the original incidence function I upon convolution with f. We h ave also added the concept of competing mortality to the convolution model. This, along with the realistic preclinical incidence function described ab ove, results in more accurate estimates of sojourn time and lead time and a llows for estimation of quantities related to overdiagnosis, which we defin e here.