Two-stage Testing of Safety: A Statistical View

Sample sizes given in regulatory guidelines are not based on statistical reasoning. However, from an ethical, scientific, and regulatory point of view, a mutagenicity experiment must have a reasonable chance of supporting the decision as to whether a result is negative or positive. Consequently, the sample size should be based on type I and type II errors, the underlying variability, and the specific size of a treatment effect. A two-stage adaptive interim analysis is presented, which permits an adaptive choice of sample size after an interim analysis of the data from the first stage. Because the sample size of the first stage is considered to be a minimum requirement, this stage can also be regarded as a pilot study.

Asymmetric inner wedge group sequential tests with applications to verifying whether effective drug concentrations are similar in adults and children

Extrapolating from information available on one patient group to support conclusions about another is common in clinical research. For example, the findings of clinical trials, often conducted in highly selective patient cohorts, are routinely extrapolated to wider populations by policy makers. Meanwhile, the results of adult trials may be used to support conclusions about the effects of a medicine in children. For example, if the effective concentration of a drug can be assumed to be similar in adults and children, an appropriate paediatric dosing rule may be found by 'bridging', that is, by matching the adult effective concentration. However, this strategy may result in children receiving an ineffective or hazardous dose if, in fact, effective concentrations differ between adults and children. When there is uncertainty about the equality of effective concentrations, some pharmacokinetic-pharmacodynamic data may be needed in children to verify that differences are small. In this paper, we derive optimal group sequential tests that can be used to verify this assumption efficiently. Asymmetric inner wedge tests are constructed that permit early stopping to accept or reject an assumption of similar effective drug concentrations in adults and children. Asymmetry arises because the consequences of under- and over-dosing may differ. We show how confidence intervals can be obtained on termination of these tests and illustrate the small sample operating characteristics of designs using simulation. Copyright © 2016 John Wiley & Sons, Ltd.

A Comparison of Testing Parameters and the Implementation of a Group Sequential Design for Equivalence Studies Using Paired-sample Analysis

We address the problem of establishing two-sided equivalence using paired-sample analysis of two treatments or two laboratory tests with a binary endpoint. Through real data examples and monte carlo simulations, we compare three commonly used testing parameters, namely, the difference of response probabilities, the ratio of response probabilities, and the ratio of discordant probabilities based on score test statistics for constructing equivalence hypothesis tests of paired binary data. We provide suggestions on the choice of these three testing parameters and proper equivalence margins in hypothesis formulation of equivalence testing. In addition, we describe the implementation of a group sequential design in the context of equivalence testing with early stopping to reject, as well as to declare equivalence.

Reducing sample sizes in genome scans: Group sequential study designs with futility stops

Group sequential study designs can greatly facilitate analyses of genetic linkage in complex traits. We recently proposed designs allowing stopping investigations early if the result is significant (König et al. [2001] Am. J. Hum. Genet. 69:590-600), thereby decreasing average sample sizes under the alternative hypothesis. However, average sample sizes were slightly increased under the null hypothesis. We now present designs where the analysis of markers is additionally stopped in case of futility, i.e., if the probability for significant results is sufficiently low. These sequential designs are applied to linkage analyses of single loci. We calculated sample sizes, time points, and critical boundaries for all analyses for 2- and 3-stage designs at an overall significance level of 0.0001. To confirm the validity of asymptotic approximations, Monte Carlo simulations were performed. The utility is demonstrated analyzing genome scan data provided for the Genetic Analysis Workshop 12. Application of the novel sequential designs yields tremendous decreases in average sample sizes, regardless of the size of the underlying genetic effect at investigated loci. Depending on the applied design, almost half of the sample size is spared on average. These enormous savings are expected to have a special impact on costs and time of large-scale studies such as genome scans.

The use of sequential designs in genome scans for asthma susceptibility loci with affected sib pairs

We use optimized group sequential study designs to analyze data from two genome scans (German and CSGA) for asthma susceptibility loci with affected sib pairs from Genetic Analysis Workshop (GAW) 12. Results are compared with those from a fixed sample design and the sequential probability ratio test (SPRT). The SPRT does not reach significance at any position. Using the fixed sample design, evidence for linkage is found on chromosomes 6 and 9 in the German and on chromosome 1 in the CSGA scan. The group sequential designs identify the same regions on chromosomes 1 and 6 with a reduced sample size.

Optimized group sequential study designs for tests of genetic linkage and association in complex diseases

The study of genetic linkage or association in complex traits requires large sample sizes, as the expected effect sizes are small and extremely low significance levels need to be adopted. One possible way to reduce the numbers of phenotypings and genotypings is the use of a sequential study design. Here, average sample sizes are decreased by conducting interim analyses with the possibility to stop the investigation early if the result is significant. We applied optimized group sequential study designs to the analysis of genetic linkage (one-sided mean test) and association (two-sided transmission/disequilibrium test). For designs with two and three stages at overall significance levels of.05 and.0001 and a power of.8, we calculated necessary sample sizes, time points, and critical boundaries for interim and final analyses. Monte Carlo simulation analyses were performed to confirm the validity of the asymptotic approximation. Furthermore, we calculated average sample sizes required under the null and alternative hypotheses in the different study designs. It was shown that the application of a group sequential design led to a maximal increase in sample size of 8% under the null hypothesis, compared with the fixed-sample design. This was contrasted by savings of up to 20% in average sample sizes under the alternative hypothesis, depending on the applied design. These savings affect the amounts of genotyping and phenotyping required for a study and therefore lead to a significant decrease in cost and time.

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.