A New Test for Cross-Over Clinical Trials with Order Effects

In cross-over designs for the comparison of two treatments, A and B, each patient receives both treatments in a randomized order. We will consider such design when the response of each patient is binary and propose a new test for treatment effect incorporating the information available from like pairs of response.     

Two Stage Sampling for Simultaneously Testing Main and Side Effects in Clinical Trials

In clinical trials for the comparison of two treatments it seems reasonable to stop the study if either one treatment has worked out to be markedly superior in the main effect, or one to be severely inferior with respect to an adverse side effect. Two stage sampling plans are considered for simultaneously testing a main and side effect, assumed to follow a bivariate normal distribution with known variances, but unknown correlation. The test procedure keeps the global significance level under the null hypothesis of no differences in main and side effects. The critical values are chosen under the side condition, that the probability for ending at the first or second stage with a rejection of the elementary null hypothesis for the main effect is controlled, when a particular constellation of differences in mean holds; analogously the probability of ending with a rejection of the null hypotheses for the side effect, given certain treatment differences, is controlled too. Plans “optimal” with respect to sample size are given.     

On the Estimation of True Treatment Response when Patients Enter Staggeredly in a Clinical Trial

Due to staggered entries of patients during a clinical trial, the available exposure to observe the patients under a treatment is less and non-uniform while the patients with whom the trial is started initially are exposed to uniform exposures to the treatment. Because of this, the true response of the treatment gets masked. Here we have attempted to estimate the true response of the treatment in presence of staggered entries. Further, by Martingale approach the probability of acceptance/rejection has been worked out for both staggered and no staggered entry cases. The results are then compared with the help of a numerical example which shows that under staggered entries the treatment is rejected with higher probability.     

A Problem of Equivalence in Clinical Trials

Several methods exist for testing the bioequivalence in bioavailability trials. In this article we propose a method for testing the equivalence of two drugs in clinical trials when the response variable is assumed to have a normal distribution. The null and alternative hypotheses are formulated in a nonconventional manner. Computing aspects for the power and sample size are discussed.     

Modelling Survival Data to Examine Length of Treatment Effectiveness in a Clinical Trial

In some clinical trials where the experimental treatment is found to be effective in increasing survival, an important question is how long should the patient remain under treatment. Although the trial may not be designed to specifically answer this question, comparisons of the hazard curves among the treatment groups can yield some useful information. The survival data may be modelled using a flexible set of hazard functions and specific models are then chosen for further examination. This paper illustrates the approach using data from the Beta-Blocker Heart Attack Trial. Parametric and semi-parametric models are fitted and likelihood methods are used to assess length of treatment effectiveness.     

Intelligent design and mathematical statistics: a troubled alliance

The explanatory filter is a proposed method to detect design in nature with the aim of refuting Darwinian evolution. The explanatory filter borrows its logical structure from the theory of statistical hypothesis testing but we argue that, when viewed within this context, the filter runs into serious trouble in any interesting biological application. Although the explanatory filter has been extensively criticized from many angles, we present the first rigorous criticism based on the theory of mathematical statistics.

Designs for Discrimination Between Bivariate Binary Response Models

We propose a test statistic for discrimination between alternative bivariate binary response models and the optimal design procedure which is an extension of T-optimality. Under certain conditions we prove that the maximum value of the power can be-obtained when the degrees of freedom of the test statistic is one. The conclusion is the same as that in discrimination between alternative univariate separate models. However the test statistics are different.     

Dynamic Comparison of Kaplan–Meier Proportions: Monitoring a Randomized Clinical Trial with a Long-Term Binary Endpoint

Summary .   The approach to early termination for efficacy in a trial where events occur over time but the primary question of interest relates to a long-term binary endpoint is not straightforward. This article considers comparison of treatment groups with Kaplan–Meier (KM) proportions evaluated at increasing times from randomization, at increasing calendar testing times. This strategy is employed to improve the ability to detect important treatment effects and provide critical treatments to patients in a timely manner. This dynamic Kaplan–Meier (DKM) approach is shown to be robust; that is, it produces high power and early termination time across a wide range of circumstances. In contrast, a fixed time KM comparison and the log-rank test are both shown to be more variable in performance. Practical considerations of implementing the DKM method are discussed.     

Comparative methods based on species mean values

Comparative methods that use simple linear regression based on species mean values introduce three difficulties with respect to the standard regression model. First, species values may not be independent because they form part of a hierarchically structured phylogeny. Second, variation about the regression line includes two sources of error: 'biological error' due to deviations of the true species mean values from the regression line and sampling error associated with the estimation of these mean values [B. Riska, Am. Natural. 138 (1991) 283]. Third, sampling error in the independent variable results in an attenuated estimate of the regression slope. We consider estimation and hypothesis testing using two statistical models which explicitly justify the use of the species mean values, without the need to account for phylogenetic relationships. The first (random-effects) is based on an evolutionary model whereby species evolve to fill a bivariate normal niche space, and the second (fixed-effects) is concerned with describing a relationship among the particular species included in a study, where the only source of error is in the estimation of species mean values. We use a modification of the maximum-likelihood method to obtain an unbiased estimate of the regression slope. For three real datasets we find a close correspondence between this slope and that obtained by simply regressing the species mean values on each other. In the random effects model, the P-value also approximates that based on the regression of species mean values. In the fixed effects model, the P-value is typically much lower. Simulated examples illustrate that the maximum-likelihood approach is useful when the accuracy in estimating the species mean values is low, but the traditional method based on a regression of the species mean values may often be justified provided that the evolutionary model can be justified.