Methods of inference for estimates of absolute risk derived from population-based case-control studies

The absolute risk is the probability of developing a given disease over a specified time interval given age and risk factors. Gail, et al. (1989, Journal of the National Cancer Institute 81, 1879-1888) obtained point estimates from population-based case control data by combining relative risk estimates from the case control data and composite incidence estimates from the cohort data. They also obtained variance estimates, but they only took into account the variability in estimating relative risks. In this paper, we present variance estimates that take into account all components of variability, namely the variance of relative risk estimates and of baseline incidence estimates, as well as the covariance between the two, the latter term being obtained by using implicit delta method arguments (Benichou and Gail, 1989, The American Statistician 43, 41-44). Simulations demonstrate the validity of such variance estimates as well as of corresponding confidence intervals. These methods are applied to a population-based case control study of breast cancer.