Eight interval estimators of a common rate ratio under stratified Poisson sampling

Under the assumption that the rate ratio (RR) is constant across strata, we consider eight interval estimators of RR under stratified Poisson sampling: the weighted least-squares (WLS) interval estimator with the logarithmic transformation, the interval estimator using the principle analogous to that of Fieller's Theorem, the interval estimators using Wald's statistic with and without the logarithmic transformation, the interval estimators using the Mantel-Haenszel statistic with and without the logarithmic transformation, the score test-based interval estimator, and the asymptotic likelihood ratio test-based interval estimator. We apply Monte Carlo simulation to evaluate and compare the performance of these estimators with respect to the coverage probability and the average length in a variety of situations. We find that the coverage probability of the commonly used WLS interval estimator tends to be smaller than the desired confidence level, especially when we have a large number of strata with a small expected total number of cases (ETNC) per stratum and the underlying RR is far away from 1 (i.e. RR18 or RR8). We further find that the two estimators with the logarithmic transformation, as well as the two test-based estimators can consistently perform well in a variety of situations. When RR1 with a given reasonable size of ETNC per stratum, we note that the interval estimators without the logarithmic transformation can be preferable to the corresponding ones with the logarithmic transformation in the situations considered here. However, when evaluating the non-coverage probability in the two tails, we find that the former tends to shift the left, while the latter is generally not subject to this concern. We also note that interval estimator using the Mantel-Haenszel (MH) statistic with the logarithmic transformation is likely less efficient than the two test-based interval estimators using the score and the likelihood ratio tests. Finally, we use the data taken from a study of the postmenopausal hormone use on the risk of breast cancer in women as an example to illustrate the use of these interval estimators considered here.