Tolerance Interval Method for Quality Assessment
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Contributing OfficeCenter for Drug Evaluation and Research
Abstract
For quality assessment with a pre-specified specification, the reference interval (RI) (sample mean +/- k*standard deviation, k is defined as the multiplier of RI) has been used for many years, which cannot assure certain confidence level for passing the specification. Whereas the tolerance interval (TI) method with P% confidence level and Q% coverage was developed to assure that Q% of the population is within the specification with P% confidence level, such as the two one-sided TI proposed by Tsong et al. (2015). The conventional multiplier, k, used for RI is 3, which was calculated by the intention of covering 99.7% of the population. However, if we directly apply the same intended coverage of RI with k=3 to the TI (i.e., Q%=99.7%), it may reduce the probability of passing the specification since TI is much wider compared to RI under the same intended coverage, especially for small sample sizes. As shown in Tsong et al. (2019), the asymptotic coverage of 99.7% of the RI is actually equal to the average coverage of a two one-sided TI given P%=95% and Q%=86.4% when the sample size is 10, and Q%=99.2% when the sample size is 200 (Table 1 of Tsong et al., 2019). In this project, we propose an approach to appropriately use the TI method to determine the multiplier of RI that assures certain probability to pass a pre-specified specification under various sample sizes for quality assessment. More specifically, for a pre-specified specification and sample size, to assure certain probability to pass the specification, we will calculate the corresponding Q of the two one-sided TI with P% confidence level, and then use the calculated Q to determine the corresponding multiplier of RI. We will use dose content uniformity (DCU), delivered dose uniformity (DDU), and dissolution test as examples to illustrate how the TI method should be appropriately used for quality assessment.