Charles Locke

On a Class of Tests of Exponentiality

The class of statistics T, = (Σα i=1, X α i /n)/ x , where α > 0 and ≠ 1, have been considered in the literature for testing exponentiality versus omnibus alternatives. These tests have a twosided rejection region. It is shown here that tests based on these statistics are not consistent for certain alternatives. However, it is shown that one-sided tests based on these statistics are consistent for IFRA (DFRA) distributions. A Monte Carlo power study suggests that lower tail tests based on T ½ and T 2 are very competitive for DFRA and IFRA alternatives, respectively. The null distributions of T ½ and T 2 are approximated by members of the Johnson families of distributions.

A Simulation Study of Power in Thorough QT/QTc Studies and a Normal Approximation for Planning Purposes

We report the results of a simulation study on power in a thorough QT/QTc study with a four-period crossover design in which the treatments are placebo, positive control, higher dose of investigational drug, and therapeutic dose of investigational drug. In the study, QTc interval values were obtained for several specified times during treatment. An assessment of noninferiority of the higher dose to placebo was performed by the intersection-union test within the framework of a linear mixed-effects analysis. With a noninferiority bound of 8 ms and a peak drug effect of 4 ms, it is found that 96 or more subjects would be required to have 80% power, but with a noninferiority bound of 10 ms, 48 subjects give more than an estimated 80% power if the number of times of measurement is 10 or fewer. For the purposes of planning such a study, a power approximation based on the multivariate normal distribution of the estimator of the difference in means of high dose of investigational drug and placebo is presented. The approximated power and the power estimate from the simulation study were quite close.

On tests of uniformity

Let X1,…,Xn be independent observations from a distribution on the interval (a,b). Fur each of three types of nonuniformity, we consider tests of uniformity (a and b known) designed to detect alternatives of that type. The types of nonuniformity are (i) U-shaped, (ii) unimodal symmetric or nearly symmetric, and (iii) nonsymmetric distributions that have decreasing density or that are unimodal with mode close to a. A Monte Carlo power study is given. The application to testing the distributional hypothesis of exponentiality against specific types of nonexponentiality is discussed. An easy extension of tests of uniformity to the case of unknown endpoints is pointed out; and an investigation of power properties, including a Monte Carlo study, is given.

A test for the composite hypothesis that a population has a gamma distribution

A test of the composite hypothesis that a population has a gamma distribution is presented. The test is conducted by using a rank test of bivariate independence, such as the one .based on Kendallfs sample tau coefficient. The performance of the test is examined by means of a Monte Carlo study.

Use of a more general model for bioavailability studies

Use of a multivariate model for bioavailability crossover studies is discussed. The model affords a convenient way to obtain from untransformed data exact confidence intervals and general hypothesis tests for ratios that are pertinent for comparing formulations. Previously, confidence intervals for the case of a two period study of two formulations have been presented. This paper treats the case of three or more formulations in a study in which each subject receives each formulation. The model requires weaker assumptions than the assumptions of other models that have been commonly used. In addition to inferences on ratios, it is pointed out how to obtain from the model tests of the hypotheses of equal formulation effects, equal period effects, and equal sequence effects. The use of these concepts for studies in which a formulation is received more than once by subjects isalso discussed.

Sample Size and Power Estimation in Thorough QT/QTc Studies with Parallel Group Design

We developed analytical results for computing the power in a thorough QT/QTc study with a four-group parallel design in which the treatments are placebo, positive control, supratherapeutic dose of investigational drug, and therapeutic dose of investigational drug. An assessment of non-inferiority of the supratherapeutic dose to placebo is performed by the intersection–union test within the framework of a linear mixed effects analysis with baseline covariate. The power estimates obtained using analytical results and from the simulation study were presented and they are quite close and hence the analytical results could be used for computing power and sample size in the planning stage of a thorough QT/QTc study.

On the dependence of X1 + X2 and X1/X2

A well-known characterization of the family of gamma distributions is that if X1 and X2 are Independent positive random variables, then X1 + X2 and X1/X2 are independent if and only if X1 and X2 have gamma distributions with the same scale parameter. We describe the dependence of X1 + X2 and X1/X2 for certain classes of distributions, which include the common models used for positive random variables of the continuous type. A method for testing the hypothesis that a random sample comes from a gamma distribution is proposed.

Exposure-Response Modeling Approach for Assessing QT Effect in Thorough QT/QTc Studies

We assess the QT effect using an exposure-response model in a “thorough QT/QTc study” with a four-period crossover design in which the treatments are placebo, positive control, higher dose of investigational drug, and therapeutic dose of investigational drug. In the study, QTc interval values and the drug concentrations are obtained for several specified times during treatment. This approach to the assessment of non-inferiority of the higher dose to placebo is an alternative strategy suggested in ICH-E14 guideline (Section 2.2.5) to the intersection–union test.

Crossover versus parallel designs: dose-escalation design comparisons for first-in-human studies.

We study the statistical efficiency for rising-dose designs in the context of first-in-human studies. Specifically, we identify a class of crossover designs that are appealing in terms of both subject safety and statistical efficiency and, for a three-period, two-panel design in such a class, we compare its A-efficiency relative to the corresponding parallel designs and optimal/efficient crossover designs, respectively, under various plausible models. In the meantime, we also evaluate the impact of inclusion of baseline measurements as a covariate in the statistical analysis, for both crossover and parallel studies.

The joint modeling of drug and positive control effects to estimate sample size and power in crossover "thorough" QT/QTc studies.

We present analytical results for computing the power and sample size in a thorough QT/QTc study with a four-period crossover design in which the treatments are placebo, positive control, supratherapeutic dose of investigational drug, and therapeutic dose of investigational drug. An assessment of noninferiority of the supratherapeutic dose to placebo is performed by the intersection–union test and assay sensitivity is tested (union–intersection test) at prespecified time points using positive control within the framework of a linear mixed-effects analysis. The power and sample size estimates are obtained using the joint distribution of statistics to test noninferiority of the supratherapeutic dose to placebo and to test assay sensitivity using positive control.