Optimal spending functions for asymmetric group sequential designs

We present optimized group sequential designs where testing of a single parameter theta is of interest. We require specification of a loss function and of a prior distribution for theta. For the examples presented, we pre-specify Type I and II error rates and minimize the expected sample size over the prior distribution for theta. Minimizing the square of sample size rather than the sample size is found to produce designs with slightly less aggressive interim stopping rules and smaller maximum sample sizes with essentially identical expected sample size. We compare optimal designs using Hwang-Shih-DeCani and Kim-DeMets spending functions to fully optimized designs not restricted by a spending function family. In the examples selected, we also examine when there might be substantial benefit gained by adding an interim analysis. Finally, we provide specific optimal asymmetric spending function designs that should be generally useful and simply applied when a design with minimal expected sample size is desired.     

Precision of the genotypic correlation estimated from variety trials conducted in incomplete block designs

 Precise assessment of an association among traits of a crop plant is helpful in developing crop-improvement strategies. Two types of association, genotypic correlation and phenotypic correlation, may be used. An estimate of correlation is required along with a measure of precision in terms of standard error. Methods for the evaluation of the standard errors of genotypic and phenotypic correlations are not available in the literature, and when trials are conducted in incomplete blocks an algebraic evaluation of such correlation is cumbersome. Three methods – simulation, jackknife and bootstrap – have been used to evaluate bias and standard errors of genotypic, phenotypic and environmental correlations. We have evaluated their performance with data on grain yield, days-to-heading, and plant height, in barley genotypes in triple lattices. Simulation and jackknife techniques were found to be closer, compared to bootstrap, and can be recommended for assessing the precision of correlation estimates. Received: 9 December 1996 / Accepted: 2 May 1997     

Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and of classical group sequential approaches

A general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing. This allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs. The concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans.     

A unifying family of group sequential test designs

Currently, the design of group sequential clinical trials requires choosing among several distinct design categories, design scales, and strategies for determining stopping rules. This approach can limit the design selection process so that clinical issues are not fully addressed. This paper describes a family of designs that unifies previous approaches and allows continuous movement among the previous categories. This unified approach facilitates the process of tailoring the design to address important clinical issues. The unified family of designs is constructed from a generalization of a four-boundary group sequential design in which the shape and location of each boundary can be independently specified. Methods for implementing the design using error-spending functions are described. Examples illustrating the use of the design family are also presented.