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In quality control of drug products, tolerance intervals are commonly used methods to assure a certain proportion of the products covered within a pre-specified acceptance interval. Depending on the nature of the quality attributes, the corresponding acceptance interval could be one-sided or two-sided. Thus, the tolerance intervals can also be one-sided or two-sided. To better utilize tolerance intervals for quality assurance, we reviewed the computation method and studied their statistical properties in terms of batch acceptance probability in this article. We also illustrate the application of one-sided and two-sided tolerance, as well as two one-sided tests through the examples of dose content uniformity test, delivered dose uniformity test, and dissolution test.

In order to validate the results of a thorough QT/QTc clinical trial, ICH E14 recommended that a concurrent positive control treatment be included in the trial. Zhang (2008) recommended that the study results are validated if the positive control establishes assay sensitivity, i.e., has an effect on the mean QT/QTc interval of 5 ms or more. Zhang (2008) and Tsong et al. (2008) discussed the intersection-union test approach and an alternative global average test approach for testing assay sensitivity during the validation process. In this article, we further discuss the multiple comparison issues of the repeatedly measured QT difference between positive control treatment and placebo in the validation test. We describe and discuss several approaches for type I error rate adjustment that are applicable to the situation.

The primary objective of a thorough QT clinical trial is to demonstrate the lack of QT prolongation induced by the test treatment. The ICH E14 guidance defined drug-induced prolongation of QT interval as evidenced by an upper bound of the 95% one-sided confidence interval around the mean effect on QTc of 10 ms. Furthermore, it defined a negative thorough QT/QTc study as one in which the upper bound of the 95% one-sided confidence interval for the largest time-matched mean effect of the drug on the QTc interval excludes 10 ms. Conventionally, this objective is tested with the intersection-union test by testing the mean difference between the test treatment and placebo of QTc changes from baseline at each of the matched time points. The multiple-comparison nature of the test leads to higher false positive rate when comparisons are made repeatedly at multiple time points. Many approaches have been proposed in the last 5 years in order to improve the efficiency of the test. In this article, we survey and discuss some of the approaches.

The ICH (2005) defined drug-induced prolongation of QT interval, i.e., the duration of depolarization and repolarization of ventricles, as evidenced by an upper bound of the 95% confidence interval around the mean effect on QTc (QT corrected for heart rate) of 10 ms. Furthermore, it defined that a negative thorough QT/QTc study is one in which the upper bound of the 95% one-sided confidence interval for the largest time-matched mean effect of the drug on the QTc interval excludes 10 ms. This objective leads to the application of intersection-union tests by testing the mean difference between test treatment and placebo of QTc change from baseline at each of the matched time points at which the observations are collected. The nature of the higher false positive rate due to more observational time points leads to the concern of study efficiency. Based on the concept of clinical pharmacology, a concentration-response modeling approach is often adopted to assess the prolongation size of QTc interval induced by a drug without carefully examining the validity of the assumptions involved. In most of the applications, the model is assumed either to be linear, log-linear, or logistic. The supporter of the modeling often emphasizes the advantage of power improvement and reduction in estimation error. However, it has been often pointed out by statisticians and pharmacologists that modeling under an invalid uniformity assumption across study population often leads to severe bias in testing and estimation. In this article, we examine data sets of New Drug Applications to illustrate the bias and lack of validity of the linearity assumptions.

In order to validate the results of a thorough QT/QTc (the duration of depolarization and repolarization of ventricles or the duration corrected for heart rate) clinical trial, ICH E14 recommended to include a concurrent positive control treatment in the trial. It further recommended that validation is achieved if the positive control has an effect on the mean QT/QTc interval of about 5 ms. Zhang (2008) discussed the intersection-union test approach for testing the validation hypotheses and an alternative global average test approach. In this article, we further discuss the difference and relationship of the two sets of hypotheses and the difference in the efficiencies of the two approaches. We conclude that validation can be achieved if either one test rejects the null hypotheses without inflating the family-wise Type I error rate. However, using both approaches may improve the efficiency in validation assessment.

Analytical method transfer is an important part of analytical method development and maintenance. The current common practice of analytical method transfer is based on the equivalence of the means between the original laboratory and the receiving laboratory. However, for some assays the most scientifically sound approach would be to show the equivalency of individual sample readings between the two laboratories. In this study, statistical approaches such as limit of agreement, total deviation index, and tolerance interval approach to address individual equivalence between laboratories are discussed. Using a tolerance interval approach that is equivalent to the two one-sided hypothesis testing is proposed. These approaches are compared with each other and also with the mean equivalence approach on their statistical properties. Examples are presented to illustrate each analysis approach and the comparisons.

Postmarketing stability studies of vaccines that tend to be close to their clinical specification at the end of the expiration dating period may require enhanced annual monitoring. In addition, an early assessment of product stability prior to completion of each individual study is desired. However, predictive measures of individual lots may produce early indication of failure. In many cases, these prove to be false alarms. For such products, continued product quality after marketing should, therefore, depend less on evaluating individual observations or individual lot projections, and more on assuring that the underlying stability profile of the product as a whole has not changed. We propose a monitoring procedure and an index of the average quality of vaccine lots currently on the market. We explore the statistical properties of the index for several experimental designs for sampling of marketed lots, and we describe an optimality property of the index.