Novel Statistical Approaches to Assessing the Risk of QT Prolongation and Sample Size Calculations in 'thorough QT/QTc studies'

Abstract

ANAND, SURAJ P. Novel Statistical Approaches to Assessing the Risk of QT Prolongation and Sample Size Calculations in ‘thorough QT/QTc studies’. (Under the direction of Professor S. K. Ghosh). The ICH E14 guidelines mandate performing a ‘thorough QT/QTc study’ on any non-antiarrythmic drug, to assess its potential effect on cardiac repolarization, as detected by QT prolongation, before it can be approved and marketed. The standard way of analyzing a thorough QT (TQT) study to assess a drug for its potential for QT prolongation is to construct a 90% two-sided (or a 95% one-sided) confidence interval (CI), for the difference in baseline-corrected mean QTc (heart-rate corrected version of QT) between drug and placebo at each time point, and to conclude non-inferiority if the upper limit for each CI is less than 10 ms. The ICH E14 guidelines define a negative thorough QT study as one in which the upper 95% CI for the maximum time-matched mean effect of the drug as compared to placebo is less than 10 ms. A Monte Carlo simulation-based Bayesian approach is proposed to resolve this problem by constructing a posterior credible interval for the maximum difference parameter. While an interval estimation-based approach may be a way to address the QT prolongation problem, it does not necessarily confirm to the actual intent of the ICH E14 guidelines, which is to establish that the mean effect of the drug is less than 5 ms. Also proposed is a novel Bayesian approach that attempts to directly calculate the probability that the mean effect is no larger than 5 ms, thereby, providing a direct measure of evidence of whether the drug prolongs mean QTc beyond the tolerable threshold of 5 ms. Performance of the proposed approaches has been assessed using simulated data, and illustrations of the methods have been provided through real data sets obtained from TQT studies conducted at GlaxoSmithKline (GSK). Both these proposed methods as well as the other methods for analyzing QTc data are based on multivariate normal models, with common covariance structure for both drug and placebo. Such modeling assumptions may be violated and when the sample sizes are small the statistical inference can be sensitive to such stringent assumptions. A flexible class of parametric models is proposed to address the above-mentioned limitations of the currently used models. A Bayesian methodology is used for data analysis, and model comparisons are performed using the deviance information criterion (DIC). Superior performance of the proposed models over the currently used models is illustrated through a real data set obtained from a GSK-conducted TQT study. Both the proposed methods for analyzing QT data can be extended to this flexible class of models. Another major aspect of TQT studies is the sample size determination. Costs involved in conducting such studies are substantial and hence sample size calculations play a very important role in ensuring a small but adequate TQT study. A variety of methods have been proposed to perform sample size calculations under the frequentist paradigm. Such methods have a limited scope and usually apply in the context of linear mixed models, with some assumed covariance structure for the observations. A sample size determination method, using the proposed novel Bayesian method involving estimation of the probability of concluding a thorough QT study negative, is provided, which would ensure that the total error rate in the context of declaring a TQT study negative is restricted to a desired low level. This method does not rely on any restrictive covariance assumptions.