Inference about ratios of age-standardized rates with sampling errors in the population denominators for estimating...

A rate ratio (RR) is an important metric for comparing cancer risks among different subpopulations. Inference for RR becomes complicated when populations used for calculating age-standardized cancer rates involve sampling errors, a situation that arises increasingly often when sample surveys must be used to obtain the population data. We compare a few strategies of estimating the standardized RR and propose bias-corrected ratio estimators as well as the corresponding variance estimators and confidence intervals that simultaneously consider the sampling error in estimating populations and the traditional Poisson error in the occurrence of cancer case or death. Performance of the proposed methods is evaluated empirically based on simulation studies. An application to immigration disparities in cancer mortality among Hispanic Americans is discussed. Our simulation studies show that a bias-corrected RR estimator performs the best in reducing the bias without increasing the coefficient of variation; the proposed variance estimators for the RR estimators and associated confidence intervals are fairly accurate. Finding of our application study are both interesting and consistent with the common sense as well as the results of our simulation studies.