Optimal weighting systems for direct age-adjustment of vital rates

Age-adjustment of rates is a basic tool for epidemiologists. The methodologies can be classified into direct and indirect types. The direct methods facilitate a valid comparison between populations or across calendar periods. However, they suffer from the problem of instability. By contrast, the indirect methods achieve maximal precision but may sacrifice a valid inter-populational comparison (violating the 'consistency criteria'). In this paper, we propose a new weighting system to summarize the rates. The weighting system is optimal in the sense that it produces age-adjusted rates which are most stable and ensure a valid comparison between populations. The new weighting system calls for an iterative algorithm. However, the procedure simplifies considerably under some conditions. We use real and simulated data to demonstrate the new method.