修正大樣本法於精密度檢測、遺傳率檢定、生體相等性檢定樣本數決定之研究

Abstract

Statistical criteria for evaluation of precision or variation often involve functions of the second moments of the normal distribution. Under the two-stage nested random-effects model, heritability is defined as the ratio of genetic variance to the total variance. Under replicated crossover designs, the criteria for individual bioequivalence (IBE) proposed by the guidance of the US Food and Drug Administration (FDA) contain the squared mean difference, variance of treatment-by-subject interaction, and the difference in within-subject variances between the generic and innovative products. On the other hand, the criterion for evaluation of the within precision for in-vitro diagnostic devices (IVD) is the sum of the variance components due to day, run, and replicates. The criterion for the in-vitro population bioequivalence (PBE) proposed by the draft guidance of the US FDA consists of the squared mean difference, the sum of the differences in variance components due to batch, sample, and life-stage. These criteria can be reformulated as linear combinations of variance components under the logarithmic transformation. The one-sided confidence limits for the linearized criteria derived by the modified large sample (MLS) method have been proposed as the test statistics for the inference in different applications. However, due to complexity of the power function, the literature for the sample size determination for the inference based on the second moments is scarce. We proved that the distribution of the one-sided confidence bound of the linearized criterion is asymptotically normal. Hence the asymptotic power can be derived for sample size determination with different applications to within-device precision, heritability, IBE and in-vitro PBE. Simulation studies were conducted to investigate the impact of magnitudes of means differences and variance components on sample sizes. In addition, empirical powers obtained from simulation studies are compared with the asymptotic powers to examine whether the sample sizes determined by our proposed methods can provide sufficient power. The proposed methods are illustrated with real data for practical applications. Discussion, final remarks and future research are also presented.