Krishnamoorthy Kalimuthu, Mathew Thomas, Xu Zhao
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508-1010, USA;
Ann Occup Hyg. 2013 Nov;57(9):1200-12. doi: 10.1093/annhyg/met037. Epub 2013 Jul 15.
The problem of determining sample size for testing an upper percentile of a lognormal distribution based on samples with multiple detection limits is considered. Two tests, the signed likelihood ratio test and another test based on a pivotal statistic, are outlined. These tests are very satisfactory in controlling type I error rates and comparable in terms of powers. Procedures and R codes for calculating sample sizes for these tests to attain a specified power are given. It is noted that for guaranteeing a given power, increased sample size is necessary due to the presence of detection limits, and the required sample size goes up as the proportion of non-detects goes up. It is also noted that in the multiple detection limit scenario, sample-size determination does not require knowledge of the proportions of non-detects that are expected to be below the individual detection limits; rather, what is required is a knowledge of the overall percentage of non-detects that is to be expected in the entire sample. Sample-size calculation is illustrated using a practical situation.
考虑了基于具有多个检测限的样本确定对数正态分布上百分位数检验的样本量问题。概述了两种检验方法，即符号似然比检验和另一种基于枢轴统计量的检验。这些检验在控制第一类错误率方面非常令人满意，并且在功效方面具有可比性。给出了计算这些检验的样本量以达到指定功效的程序和R代码。需要注意的是，由于存在检测限，为保证给定的功效，需要增加样本量，并且所需样本量会随着未检出比例的增加而增加。还需要注意的是，在多个检测限的情况下，样本量的确定不需要了解预期低于各个检测限的未检出比例；相反，需要了解整个样本中预期的未检出总体百分比。通过一个实际情况说明了样本量的计算。
