Lui Kung-Jong
Department of Mathematics and Statistics, College of Sciences, San Diego State University, San Diego, CA 92182-7720, USA.
Stat Med. 2005 Apr 30;24(8):1275-85. doi: 10.1002/sim.1989.
The discussions on interval estimation of the proportion ratio (PR) of responses or the relative risk (RR) of a disease for multiple matching have been generally focused on the odds ratio (OR) based on the assumption that the latter can approximate the former well. When the underlying proportion of outcomes is not rare, however, the results for the OR would be inadequate for use if the PR or RR was the parameter of our interest. In this paper, we develop five asymptotic interval estimators of the common PR (or RR) for multiple matching. To evaluate and compare the finite sample performance of these estimators, we apply Monte Carlo simulation to calculate the coverage probability and the average length of the resulting confidence intervals in a variety of situations. We note that when we have a constant number of matching, the interval estimator using the logarithmic transformation of the Mantel-Haenszel estimator, the interval estimator derived from the quadratic inequality given in this paper, and the interval estimator using the logarithmic transformation of the ratio estimator can consistently perform well. When the number of matching varies between matched sets, we find that the interval estimator using the logarithmic transformation of the ratio estimator is probably the best among the five interval estimators considered here in the case of a small number (=20) of matched sets. To illustrate the use of these interval estimators, we employ the data studying the supplemental ascorbate in the supportive treatment of terminal cancer patients.
关于多个匹配情况下反应比例（PR）或疾病相对风险（RR）的区间估计的讨论，通常基于优势比（OR）能很好地近似前两者的假设，而聚焦于优势比。然而，当潜在结局比例并非罕见时，如果我们感兴趣的参数是PR或RR，那么基于优势比的结果就不太适用。在本文中，我们针对多个匹配情况开发了五个常见PR（或RR）的渐近区间估计量。为了评估和比较这些估计量的有限样本性能，我们应用蒙特卡罗模拟来计算在各种情况下所得置信区间的覆盖概率和平均长度。我们注意到，当匹配数固定时，使用Mantel-Haenszel估计量对数变换的区间估计量、本文基于二次不等式推导的区间估计量以及使用比率估计量对数变换的区间估计量，始终表现良好。当匹配数在匹配集之间变化时，我们发现，在匹配集数量较少（=20）的情况下，使用比率估计量对数变换的区间估计量可能是这里所考虑的五个区间估计量中最好的。为了说明这些区间估计量的用法，我们采用了研究补充抗坏血酸在晚期癌症患者支持治疗中的数据。
