Effects of exposure uncertainties in the TSCE model and application to the Colorado miners data

The simulations in this paper show that exposure measurement error affects the parameter estimates of the biologically motivated two-stage clonal expansion (TSCE) model. For both Berkson and classical error models, we show that likelihood-based techniques of correction work reliably. For classical errors, the distribution of true exposures needs to be known or estimated in addition to the distribution of recorded exposures conditional on true exposures. Usually the exposure uncertainty biases the model parameters toward the null and underestimates the precision. But when several parameters are allowed to be dependent on exposure, e.g. initiation and promotion, then their relative importance is also influenced, and more complicated effects of exposure uncertainty can occur. The application part of this paper shows for two different types of Berkson errors that a recent analysis of the data for the Colorado plateau miners with the TSCE model is not changed substantially when correcting for such errors. Specifically, the conjectured promoting action of radon remains as the dominant radiation effect for explaining these data. The estimated promoting action of radon increases by a factor of up to 1.2 for the largest assumed exposure uncertainties.