Kimanani E K, Lavigne J, Potvin D
Biometrics and Pharmacokinetics R&D, Phoenix International Life Sciences, 2350 Cohen Street, Saint-Laurent, Québec, H4R 2N6, Canada.
Stat Med. 2000 Oct 30;19(20):2775-95. doi: 10.1002/1097-0258(20001030)19:20<2775::aid-sim545>3.0.co;2-g.
The evaluation of individual bioequivalence (IBE) by bootstrap resampling using common statistical software, for example SAS, is extremely time consuming. In this article, an estimation procedure that can be implemented in a high level language with the same degree of accuracy as SAS is described. The necessary parameter estimating equations under both least square (LSE) and restricted maximum likelihood (REML) methods are given. The algorithms used to numerically compute these values are outlined and tested, in FORTRAN, on several simulated data sets and shown to reproduce SAS results with at least 10(-3) precision. More importantly, the REML bootstrap algorithm reduces the time taken in SAS by a factor of 20. Secondary results indicate that LSE and REML parameter estimates are similar for mild unbalancedness. PROC MIXED, with unstructured (UN) and compound symmetry heterogeneous (CSH) variance structures give the same results except when the subject-by-treatment interaction variance, sigma(2)(D), is 0 in which case CSH significantly overestimates sigma(2)(D) and underestimates the within-treatment variances. It is concluded that bootstrap evaluation of IBE is efficiently done using either the LSE or REML algorithm in FORTRAN.
使用常见统计软件（例如SAS）通过自助重抽样来评估个体生物等效性（IBE）极其耗时。本文描述了一种可以用高级语言实现的估计程序，其准确性与SAS相当。给出了最小二乘法（LSE）和限制最大似然法（REML）下的必要参数估计方程。概述并测试了用于数值计算这些值的算法，该算法用FORTRAN语言在几个模拟数据集上进行了测试，结果表明它能以至少10^(-3)的精度重现SAS的结果。更重要的是，REML自助算法将SAS所需的时间减少了20倍。次要结果表明，对于轻度不平衡情况，LSE和REML参数估计值相似。除了在个体-处理交互方差sigma(2)(D)为0的情况下，使用非结构化（UN）和复合对称异质性（CSH）方差结构的PROC MIXED给出相同的结果，在这种情况下，CSH会显著高估sigma(2)(D)并低估处理内方差。得出的结论是，使用FORTRAN语言中的LSE或REML算法可以有效地完成IBE的自助评估。
