Bebu Ionut, Mathew Thomas
Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University, Washington, DC 20057, USA.
Stat Med. 2008 Jun 30;27(14):2684-96. doi: 10.1002/sim.3080.
For a bivariate log-normal distribution, a confidence interval is developed for the ratio of the means. The generalized confidence interval approach is used for this purpose, and the procedure is applicable regardless of the sample size. It is also noted that the same approach can be used to obtain a confidence interval for the ratio of the variances. A modified signed log-likelihood ratio procedure is also described for computing confidence intervals. The coverage probabilities of the proposed confidence intervals are estimated by Monte Carlo, and the generalized confidence intervals are found to exhibit satisfactory performance even for small sample sizes. Numerical results also show that the corresponding test procedures provide larger power compared with the modified signed log-likelihood ratio test. Two examples are given: one dealing with the comparison of the means and variances of health-care costs and the other dealing with testing mean equivalence in quantitative assays.
对于双变量对数正态分布，为均值比构建了一个置信区间。为此使用了广义置信区间方法，并且该程序无论样本大小如何均适用。还指出可以使用相同的方法来获得方差比的置信区间。还描述了一种用于计算置信区间的修正符号对数似然比程序。通过蒙特卡罗方法估计所提出置信区间的覆盖概率，并且发现广义置信区间即使对于小样本量也表现出令人满意的性能。数值结果还表明，与修正符号对数似然比检验相比，相应的检验程序具有更大的功效。给出了两个例子：一个涉及医疗保健成本均值和方差的比较，另一个涉及定量分析中均值等效性的检验。
