Exact calculation of power and sample size in bioequivalence studies using two one‐sided tests

The number of subjects in a pharmacokinetic two‐period two‐treatment crossover bioequivalence study is typically small, most often less than 60. The most common approach to testing for bioequivalence is the two one‐sided tests procedure. No explicit mathematical formula for the power function in the context of the two one‐sided tests procedure exists in the statistical literature, although the exact power based on Owen's special case of bivariate noncentral t‐distribution has been tabulated and graphed. Several approximations have previously been published for the probability of rejection in the two one‐sided tests procedure for crossover bioequivalence studies. These approximations and associated sample size formulas are reviewed in this article and compared for various parameter combinations with exact power formulas derived here, which are computed analytically as univariate integrals and which have been validated by Monte Carlo simulations. The exact formulas for power and sample size are shown to improve markedly in realistic parameter settings over the previous approximations. Copyright © 2014 John Wiley & Sons, Ltd.     

Model free audit methodology for bias evaluation of tumour progression in oncology

Many oncology studies incorporate a blinded independent central review (BICR) to make an assessment of the integrity of the primary endpoint, progression free survival. Recently, it has been suggested that, in order to assess the potential for bias amongst investigators, a BICR amongst only a sample of patients could be performed; if evidence of bias is detected, according to a predefined threshold, the BICR is then assessed in all patients, otherwise, it is concluded that the sample was sufficient to rule out meaningful levels of bias. In this paper, we present an approach that adapts a method originally created for defining futility bounds in group sequential designs. The hazard ratio ratio, the ratio of the hazard ratio (HR) for the treatment effect estimated from the BICR to the corresponding HR for the investigator assessments, is used as the metric to define bias. The approach is simple to implement and ensures a high probability that a substantial true bias will be detected. In the absence of bias, there is a high probability of accepting the accuracy of local evaluations based on the sample, in which case an expensive BICR of all patients is avoided. The properties of the approach are demonstrated by retrospective application to a completed Phase III trial in colorectal cancer. The same approach could easily be adapted for other disease settings, and for test statistics other than the hazard ratio. Copyright © 2015 John Wiley & Sons, Ltd.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

A Bivariate Distribution Family with Specified Correlation Coefficient and Given Marginals

For given continuous distribution functions F(x) and G(y) and a Pearson correlation coefficient ρ, an algorithm is provided to construct a sequence of continuous bivariate distributions with marginals equal to F(x) and G(y) and the corresponding correlation coefficient converges to ρ. The algorithm can be easily implemented using S-Plus or R. Applications are given to generate bivariate random variables with marginals including Gamma, Beta, Weibull, and uniform distributions.     

年龄标本库的建立及其在现代医学领域的应用

创建“人体器官切片库”是以人体的不同年龄制备的胎儿组、幼年组、成年组、老年组的组织器官切片系列,共为四套,研究各自器官、组织的结构特点;准确、动态反映年龄标本库的人体年龄信息,为医学基础的教学、科研和临床应用提供形态学依据,具有一定的推广应用价值。     

山楂叶螨在苹果树上空间分布型及取样方法的研究

经定点调查测定,山楂叶螨在苹果树上的空间分布型为聚集分布,四个方位上的螨量,以南方、东方为最多,同方位上下两层的螨量差异不大。据此,提出山楂叶螨的田间调查方法为:取苹果树5株,从东下或南下方位,每株随机取样5点,每点查10只叶片。     

A modified Kolmogorov-Smirnov test for a rectangular distribution with unknown parameters: Computation of the distribution of the test statistic

A recursive scheme for the calculation of the distribution of the test statistic of a modified Kolmogorov-Smirnov-test for a rectangular distribution with unknown parameters is given.     

Distance sampling methodology

We consider the method of distance sampling described by Buckland, Anderson, Burnham and Laake in 1993. We explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design- and model-based frameworks. In particular, we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework. These results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling.     

Three-stage designs for monitoring clinical trials

Optimal three-stage designs with equal sample sizes at each stage are presented and compared to fixed sample designs, fully sequential designs, designs restricted to use the fixed sample critical value at the final stage, and to modifications of other group sequential designs previously proposed in the literature. Typically, the greatest savings realized with interim analyses are obtained by the first interim look. More than 50% of the savings possible with a fully sequential design can be realized with a simple two-stage design. Three-stage designs can realize as much as 75% of the possible savings. Without much loss in efficiency, the designs can be modified so that the critical value at the final stage equals the usual fixed sample value while maintaining the overall level of significance, alleviating some potential confusion should a final stage be necessary. Some common group sequential designs, modified to allow early acceptance of the null hypothesis, are shown to be nearly optimal in some settings while performing poorly in others. An example is given to illustrate the use of several three-stage plans in the design of clinical trials.     

Non-parametric estimation of the conditional mode

The problem of estimating the mode of a conditional probability density function is considered. It is shown that under some regularity conditions the estimate of the conditional mode obtained by maximizing a kernel estimate of the conditional probability density function is strongly consistent and asymptotically normally distributed.