Age‐conditional probabilities of developing cancer

We propose an estimator of the probability of developing a disease in a given age range, conditional on never having developed the disease prior to the beginning of the age range. Our estimator improves the one described by Wun, Merrill and Feuer ( Lifetime Data Analysis 1998; 4, 169-186) that is currently used by the U.S. National Cancer Institute for the SEER Cancer Statistics Review. Both estimators use cross-sectional disease rates and provide an interpretation of these rates in terms of the age-conditional probability of developing disease in a hypothetical cohort. The difficulty of this problem is that rates are not available per person-years alive and disease free, but only per person-years alive. Wun et al. used ad hoc methods to handle this problem which did not properly account for competing risks, did not provide a measure of variability, and only allowed age ranges using prespecified 5-year age intervals. Here we solve the problem under a unified competing risks framework, which allows the calculation of the age-conditional probabilities for any age range. We generalize gamma confidence intervals to apply to our new statistic. Although our new method provides estimates which are numerically similar to that of Wun et al., this paper provides a comprehensive theoretical basis for estimation and inference about the age-conditional probability of developing a disease.