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.     

Maximin D-optimal designs for longitudinal mixed effects models

In this article, the optimal selection and allocation of time points in repeated measures experiments is considered. D-optimal cohort designs are computed numerically for the first- and second-degree polynomial models with random intercept, random slope, and first-order autoregressive serial correlations. Because the optimal designs are locally optimal, it is proposed to use a maximin criterion. It is shown that, for a large class of symmetric designs, the smallest relative efficiency over the model parameter space is substantial.     

The efficiency of designs for fine-mapping of quantitative trait loci using combined linkage disequilibrium and linkage

In a simulation study, different designs were compared for efficiency of fine-mapping of QTL. The variance component method for fine-mapping of QTL was used to estimate QTL position and variance components. The design of many families with small size gave a higher mapping resolution than a design with few families of large size. However, the difference is small in half sib designs. The proportion of replicates with the QTL positioned within 3 cM of the true position is 0.71 in the best design, and 0.68 in the worst design applied to 128 animals with a phenotypic record and a QTL explaining 25% of the phenotypic variance. The design of two half sib families each of size 64 was further investigated for a hypothetical population with effective size of 1000 simulated for 6000 generations with a marker density of 0.25 cM and with marker mutation rate 4 × 10^-4 per generation. In mapping using bi-allelic markers, 42~55% of replicated simulations could position QTL within 0.75 cM of the true position whereas this was higher for multi allelic markers (48~76%). The accuracy was lowest (48%) when mutation age was 100 generations and increased to 68% and 76% for mutation ages of 200 and 500 generations, respectively, after which it was about 70% for mutation ages of 1000 generations and older. When effective size was linearly decreasing in the last 50 generations, the accuracy was decreased (56 to 70%). We show that half sib designs that have often been used for linkage mapping can have sufficient information for fine-mapping of QTL. It is suggested that the same design with the same animals for linkage mapping should be used for fine-mapping so gene mapping can be cost effective in livestock populations.     

Curve-free and model-based continual reassessment method designs

Gasparini and Eisele (2000, Biometrics 56, 609 615) present a development of the continual reassessment method of O'Quigley, Pepe, and Fisher (1990, Biometrics 46, 33-48). They call their development a curve-free method for Phase I clinical trials. However, unless we are dealing with informative prior information, then the curve-free method coincides with the usual model-based continual reassessment method. Both methods are subject to arbitrary specification parameters, and we provide some discussion on this. Whatever choices are made for one method, there exists equivalent choices for the other method, where " equivalent" means that the operating characteristics (sequential dose allocation and final recommendation) are the same. The insightful development of Gasparini and Eisele provides clarification on some of the basic ideas behind the continual reassessment method, particularly when viewed from a Bayesian perspective. But their development does not lead to a new class of designs and the comparative results in their article, indicating some preference for curve-free designs over model-based designs, are simply reflecting a more fortunate choice of arbitrary specification parameters. Other choices could equally well have inversed their conclusion. A correct conclusion should be one of operational equivalence. The story is different for the case of informative priors, a situation that is inherently much more difficult. We discuss this. We also mention the important idea of two-stage designs (Moller, 1995, Statistics in Medicine 14, 911-922; O'Quigley and Shen, 1996, Biometrics 52, 163-174), arguing, via a simple comparison with the results of Gasparini and Eisele (2000), that there is room for notable gains here. Two-stage designs also have an advantage of avoiding the issue of prior specification altogether.     

An easy-to-handle semi-automated method for media development using a colorimetric viability assay and fractional factorial designs

A rapid and effective semi-automated screening method has been developed for the development of growth media for mammalian cell culture. The method has proven to be a powerful tool for preliminary evaluation and comparison of new media formulations, but has some inherent disadvantages, which are important to recognise in order to interpret the results.     

A graphical method for determining inhibition constants

A new simple graphical method is described for the determination of inhibition type and inhibition constants of an enzyme reaction without any replot. The method consists of plotting experimental data as (V–v)/v versus the inhibitor concentration at two or more concentrations of substrate, where V and v represent the maximal velocity and the velocity in the absence and presence of inhibitor with given concentrations of the substrate, respectively. Competitive inhibition gives straight lines that converge on the abscissa at a point where [I]?=??K_i. Uncompetitive inhibition gives parallel lines with the slope of 1/K’_i. For mixed type inhibition, the intersection in the plot is given by [I]?=??K_i and (V–v)/v?=??K_i/K’_i in the third quadrant, and in the special case where K_i?=?K’_i (noncompetitive inhibition) the intersections occur at the point where [I]?=??K_i and (V–v)/v?=??1. The present method, the “quotient velocity plot,” provides a simple way of determining the inhibition constants of all types of inhibitors.     

Sequential designs for ordinal phase I clinical trials

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start‐up design, a follow‐on design and a sequential dose‐finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.     

Systematic designs for experiments with mixtures

In this paper systematic designs for experiments with mixtures are developed. The plan of analysis of the experiment is discussed for a quadratic model of SCHEFF É (1958) for q-component mixture with orthogonal polynomials of third degree describing the time trends.     

A modified graphical method for determination of equilibrium constants

A modification is described of the method of Dixon (1965) for determining equilibrium constants (K) of combinations of the type A+Bright harpoon over left harpoonAB. The method obviates drawing of a tangent to the curve at the origin.     

Adaptive two-stage designs for single-arm phase IIA cancer clinical trials

The main purpose of a phase IIA trial of a new anticancer therapy is to determine whether the therapy has sufficient promise against a specific type of tumor to warrant its further development. The therapy will be rejected for further investigation if the true response rate is less than some uninteresting level and the test of hypothesis is powered at a specific target response rate. Two-stage designs are commonly used for this situation. However, in many situations investigators often express concern about uncertainty in targeting the alternative hypothesis to study power at the planning stage. In this article, motivated by a real example, we propose a strategy for adaptive two-stage designs that will use the information at the first stage of the study to either reject the therapy or continue testing with either an optimistic or a skeptic target response rate, while the type I error rate is controlled. We also introduce new optimal criteria to reduce the expected total sample size.