Loss of lifetime due to radiation exposure-averaging problems

A new method is presented for assessing a years of life lost (YLL) due to stochastic effects caused by the exposure to ionizing radiation. The widely accepted method from the literature uses a ratio of means of two quantities, defining in fact the loss of life as a derived quantity. We start from the real stochastic nature of the quantity (YLL), which enables us to obtain its mean values in a consistent way, using the standard averaging procedures, based on the corresponding joint probability density functions needed in this problem. Our method is mathematically different and produces lower values of average YLL. In this paper we also found certain similarities with the concept of loss of life expectancy among exposure induced deaths (LLE-EID), which is accepted in the recently published UNSCEAR report, where the same quantity is defined as years of life lost per radiation induced case (YLC). Using the same data base, the YLL and the LLE-EID are calculated and compared for the simplest exposure case-the discrete exposure at age a. It is found that LLE-EID overestimates the YLL, and that the magnitude of this overestimation reaches more than 15%, which depends on the effect under consideration.