Inference about the ratio of age-standardized rates between two overlapping populations

We develop a robust bias-corrected method of inference about the ratio of age-standardized rates (RASR) for comparing the age-standardized rate (ASR) between a subpopulation and the whole population. Unlike previous methods, the proposed approach does not rely on the proportional age-distribution (PAD) assumption, which is often unrealistic in many situations. Like an existing approach, the method corrects for bias resulting from sampling errors when using sample-based population estimates, instead of census-based populations, as the denominators for estimating ASRs. This broadens the applicability of the proposed method in studying cancer risk factors beyond the basic demographic characteristics. The robust bias-corrected estimator of the RASR and the associated variance estimator and confidence intervals are derived. We show empirically that the proposed RASR estimator performs significantly better than the existing estimator, which relies on the PAD assumption, especially when the latter assumption fails. Specifically, the proposed RASR estimator significantly reduces the bias without increasing the variance. On the other hand, when the PAD assumption holds, our RASR estimator performs similarly to the existing estimator. The proposed method has also shown highly desirable performance when at-risk population estimates used for calculating ASRs are subject to sampling errors. We also show empirically that the proposed variance estimator performs satisfactorily. A real-data application is discussed.