Guogen Shan

An efficient and exact approach for detecting trends with binary endpoints

Lloyd (Aust. Nz. J. Stat., 50, 329-345, 2008) developed an exact testing approach to control for nuisance parameters, which was shown to be advantageous in testing for differences between two population proportions. We utilized this approach to obtain unconditional tests for trends in 2 × K contingency tables. We compare the unconditional procedure with other unconditional and conditional approaches based on the well-known Cochran-Armitage test statistic. We give an example to illustrate the approach, and provide a comparison between the methods with regards to type I error and power. The proposed procedure is preferable because it is less conservative and has superior power properties.

Unconditional tests for comparing two ordered multinomials.

We consider two exact unconditional procedures to test the difference between two multinomials with ordered categorical data. Exact unconditional procedures are compared to other approaches based on the Wilcoxon mid-rank test and the proportional odds model. We use a real example from an arthritis pain study to illustrate the various test procedures and provide an extensive numerical study to compare procedures with regards to type I error rates and power under the unconditional framework. The exact unconditional procedure based on estimation followed by maximization is generally more powerful than other procedures, and is therefore recommended for use in practice.

Optimal adaptive two-stage designs for early phase II clinical trials

Simons optimal two-stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints. With this approach, the second-stage sample size is fixed when the trial passes the first stage with sufficient activity. Adaptive designs, such as those due to Banerjee and Tsiatis (2006) and Englert and Kieser (2013), are flexible in the sense that the second-stage sample size depends on the response from the first stage, and these designs are often seen to reduce the expected sample size under the null hypothesis as compared with Simons approach. An unappealing trait of the existing designs is that they are not associated with a second-stage sample size, which is a non-increasing function of the first-stage response rate. In this paper, an efficient intelligent process, the branch-and-bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected. The proposed optimal design is observed to have smaller expected sample sizes compared to Simons optimal design, and the maximum total sample size of the proposed adaptive design is very close to that from Simons method. The proposed optimal adaptive two-stage design is recommended for use in practice to improve the flexibility and efficiency of early phase therapeutic development.

Some tests for detecting trends based on the modified Baumgartner-Weiíß-Schindler statistics

We propose a modified nonparametric Baumgartner-Weiβ-Schindler test and investigate its use in testing for trends among K binomial populations. Exact conditional and unconditional approaches to p-value calculation are explored in conjunction with the statistic in addition to a similar test statistic proposed by Neuhäuser (2006), the unconditional approaches considered including the maximization approach (Basu, 1977), the confidence interval approach (Berger and Boos, 1994), and the E + M approach (Lloyd, 2008). The procedures are compared with regard to actual Type I error and power and examples are provided. The conditional approach and the E + M approach performed well, with the E + M approach having an actual level much closer to the nominal level. The E + M approach and the conditional approach are generally more powerful than the other p-value calculation approaches in the scenarios considered. The power difference between the conditional approach and the E + M approach is often small in the balance case. However, in the unbalanced case, the power comparison between those two approaches based on our proposed test statistic show that the E+ M approach has higher power than the conditional approach.

A note on exact conditional and unconditional tests for Hardy-Weinberg Equilibrium

The exact conditional approach is frequently used for testing Hardy-Weinberg equilibrium in population genetics. This approach respects the test size as compared to the traditionally used asymptotic approaches. It is a full-enumeration method and very computational. Many efficient algorithms have been successfully developed to implement this exact approach. An alternative to the conditional approach is the unconditional approach, which relaxes the restriction of the fixed number of allelic counts as in the conditional approach. The first unconditional test considered in this study is the one based on maximization, which has been shown to be more powerful than the conditional test to loci with two alleles for small sample sizes. By using the p value of the conditional approach as a test statistic in the following maximization step, the second unconditional test is uniformly more powerful than the conditional approach. We compared these exact tests based on three commonly used test statistics with regards to type I error rate and power. It is recommended to use the second unconditional approach in practice due to the power gain in the case with two alleles.

Exact confidence intervals for the relative risk and the odds ratio

For comparison of proportions, there are three commonly used measurements: the difference, the relative risk, and the odds ratio. Significant effort has been spent on exact confidence intervals for the difference. In this article, we focus on the relative risk and the odds ratio when data are collected from a matched-pairs design or a two-arm independent binomial experiment. Exact one-sided and two-sided confidence intervals are proposed for each configuration of two measurements and two types of data. The one-sided intervals are constructed using an inductive order, they are the smallest under the order, and are admissible under the set inclusion criterion. The two-sided intervals are the intersection of two one-sided intervals. R codes are developed to implement the intervals. Supplementary materials for this article are available online.

Randomized two-stage Phase II clinical trial designs based on Barnard's exact test.

In areas such as oncology, two-stage designs are often preferred as compared to one-stage designs due to the ability to stop the trial early when faced with evidence of lack of sufficient efficacy and the associated sample size savings. We present exact two-stage designs based on Barnards exact test for differences in proportions and compare the designs to those proposed by Kepner (2010) and Jung (2010). In addition, we present tables of decision rules under a variety of assumed realities for use in trial planning. The procedure is recommended for use due to the substantial sample size savings experienced.

Two-stage k-sample designs for the ordered alternative problem

In preclinical studies and clinical dose-ranging trials, the Jonckheere-Terpstra test is widely used in the assessment of dose-response relationships. Hewett and Spurrier (1979) presented a two-stage analog of the test in the context of large sample sizes. In this paper, we propose an exact test based on Simons minimax and optimal design criteria originally used in one-arm phase II designs based on binary endpoints. The convergence rate of the joint distribution of the first and second stage test statistics to the limiting distribution is studied, and design parameters are provided for a variety of assumed alternatives. The behavior of the test is also examined in the presence of ties, and the proposed designs are illustrated through application in the planning of a hypercholesterolemia clinical trial. The minimax and optimal two-stage procedures are shown to be preferable as compared with the one-stage procedure because of the associated reduction in expected sample size for given error constraints.

Exact two-stage designs for phase II activity trials with rank-based endpoints

Features common to phase II clinical trials include limited knowledge of the experimental treatment being evaluated, design components reflecting ethical considerations, and small to moderate sample sizes as a result of resource constraints. It is for these reasons that there exist many two-stage designs proposed in the literature for use in this context. The majority of these designs are for binary endpoints and based on exact probability calculations, or are for continuous endpoints and rooted in asymptotic approximations to the null distribution. We present exact two-stage Mann-Whitney designs in the context of two-arm randomized clinical trials. In addition to describing the designs, we present tables of decision rules under a variety of assumed realities for use in trial planning.

Sample size calculation based on efficient unconditional tests for clinical trials with historical controls

ABSTRACT In historical clinical trials, the sample size and the number of success in the control group are often considered as given. The traditional method for sample size calculation is based on an asymptotic approach developed by Makuch and Simon (1980). Exact unconditional approaches may be considered as alternative to control for the type I error rate where the asymptotic approach may fail to do so. We provide the sample size calculation using an efficient exact unconditional testing procedure based on estimation and maximization. The sample size using the exact unconditional approach based on estimation and maximization is generally smaller than those based on the other approaches.