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Inference about age-standardized rates with sampling errors in the denominators

Cancer incidence and mortality are typically presented as age-standardized rates. Inference about these rates becomes complicated when denominators involve sampling errors. We propose a bias-corrected rate estimator as well as its corresponding variance estimator that take into account sampling errors in the denominators. Confidence intervals are derived based on the proposed estimators as well. Performance of the proposed methods is evaluated empirically based on simulation studies. More importantly, advantage of the proposed method is demonstrated and verified in a real-life study of cancer mortality disparity. A web-based, user-friendly computational tool is also being developed at the National Cancer Institute to accompany the new methods with the first application being calculating cancer mortality rates by US-born and foreign-born status. Finally, promise of proposed estimators to account for errors introduced by differential privacy procedures to the 2020 decennial census products is discussed.