In a typical two-stage design for a phase II cancer clinical trial for efficacy screening of cytotoxic agents, a fixed number of patients are initially enrolled and treated. The trial may be terminated for lack of efficacy if the observed number of tumour responses after the first stage is too small, thus avoiding treatment of patient with inefficacious regimen. Otherwise, an additional fixed number of patients are enrolled and treated to accumulate additional information on efficacy as well as safety. The minimax and the so-called 'optimal' designs by Simon have been widely used, and other designs have largely been ignored in the past for such two-stage cancer clinical trials. Recently Jung et al. proposed a graphical method to search for compromise designs with features more favourable than either the minimax or the optimal design. In this paper, we develop a family of two-stage designs that are admissible according to a Bayesian decision-theoretic criterion based on an ethically justifiable loss function. We show that the admissible designs include as special cases the Simon's minimax and the optimal designs as well as the compromise designs introduced by Jung et al. We also present a Java program to search for admissible designs that are compromises between the minimax and the optimal designs.

Due to ethical and practical issues, clinical trials are conducted in multiple stages, but the reported p-values often fail to reflect the design aspect of the trials. We investigate some approaches to p-value calculation in analyzing multi-stage Phase II clinical trials that have a binary variable, such as response, as the primary endpoint. The sample space consists of the paired outcomes of the stopping stage and the number of responses, which jointly define a complete and sufficient statistic for the true binomial proportion. Calculating a p-value requires an ordering of the paired outcomes so that outcomes more extreme than the observed can be identified. We consider the orderings based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. We will compare, using some examples, the p-values based on these alternative orderings and the one ignoring the multistage design aspect of phase II trials.

The likelihood function of a seasonal model, Y t ¼ qY t)d + e t as implemented in computer algorithms under the assumption of stationary initial conditions is a function of q which is zero at the point q ¼ 1. It is a smooth function for q in the above seasonal model with a well-defined maximum regardless of the data-generating mechanism. Gonzalez-Farias (PhD Thesis, North Carolina State University, 1992) proposed tests for unit roots based on maximizing the stationary likelihood function in nonseasonal time series. We extend it to seasonal time series. The limiting distribution of seasonal unit root test statistics based on the unconditional maximum likelihood estimators are shown. Models having a single mean, seasonal means, and a single-trend variable across the seasons are considered.

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Cluster analysis involves grouping objects, subjects or variables, with similar characteristics into groups. Similarity or dissimilarity of objects is measured by a particular index of association. The focus here is on clustering of variables instead of subjects. Types of methods that cluster variables based on correlation structure of variables or factorial structure of variables are considered, where factorial structure refers to a structure obtained from principal component analysis or factor analysis. The approaches described for cluster analysis use various indices of association such as factor loadings, correlation matrix, and cosine matrix. Examples of these are shown and the advantages and disadvantages of each approach are discussed.