Assessing the similarity of dose response and target doses in two non-overlapping subgroups

We consider two problems that are attracting increasing attention in clinical dose finding studies. First, we assess the similarity of two non-linear regression models for two non-overlapping subgroups of patients over a restricted covariate space. To this end, we derive a confidence interval for the maximum difference between the two given models. If this confidence interval excludes the equivalence margins, similarity of dose response can be claimed. Second, we address the problem of demonstrating the similarity of two target doses for two non-overlapping subgroups, using again a confidence interval based approach. We illustrate the proposed methods with a real case study and investigate their operating characteristics (coverage probabilities, Type I error rates, power) via simulation.Comment: Keywords and Phrases: equivalence testing, multiregional trial, target dose estimation, subgroup analyse

Equivalence tests for binary efficacy-toxicity responses

Clinical trials often aim to compare a new drug with a reference treatment in terms of efficacy and/or toxicity depending on covariates such as, for example, the dose level of the drug. Equivalence of these treatments can be claimed if the difference in average outcome is below a certain threshold over the covariate range. In this paper we assume that the efficacy and toxicity of the treatments are measured as binary outcome variables and we address two problems. First, we develop a new test procedure for the assessment of equivalence of two treatments over the entire covariate range for a single binary endpoint. Our approach is based on a parametric bootstrap, which generates data under the constraint that the distance between the curves is equal to the pre-specified equivalence threshold. Second, we address equivalence for bivariate binary (correlated) outcomes by extending the previous approach for a univariate response. For this purpose we use a 2-dimensional Gumbel model for binary efficacy-toxicity responses. We investigate the operating characteristics of the proposed approaches by means of a simulation study and present a case study as an illustration

Performance Assessment for a Guided Wave-Based SHM System Applied to a Stiffened Composite Structure

To assess the ability of structural health monitoring (SHM) systems, a variety of prerequisites and contributing factors have to be taken into account. Within this publication, this variety is analyzed for actively introduced guided wave-based SHM systems. For these systems, it is not possible to analyze their performance without taking into account their structure and their applied system parameters. Therefore, interdependencies of performance assessment are displayed in an SHM pyramid based on the structure and its monitoring requirements. Factors influencing the quality, capability and reliability of the monitoring system are given and put into relation with state-of-the-art performance analysis in a non-destructive evaluation. While some aspects are similar and can be treated in similar ways, others, such as location, environmental condition and structural dependency, demand novel solutions. Using an open-access data set from the Open Guided Waves platform, a detailed method description and analysis of path-based performance assessment is presented. The adopted approach clearly begs the question about the decision framework, as the threshold affects the reliability of the system. In addition, the findings show the effect of the propagation path according to the damage position. Indeed, the distance of damage directly affects the system performance. Otherwise, the propagation direction does not alter the potentiality of the detection approach despite the anisotropy of composites. Nonetheless, the finite waveguide makes it necessary to look at the whole paths, as singular phenomena associated with the reflections may appear. Numerical investigation helps to clarify the centrality of wave mechanics and the necessity to take sensor position into account as an influencing factor. Starting from the findings achieved, all the issues are discussed, and potential future steps are outlined

Equivalence of regression curves

Die Dissertation "Equivalence of Regression Curves" untersucht die Fragestellung, wann zwei (oder mehr) Regressionskurven als äquivalent betrachtet werden können. Zum Beantworten dieser Frage bedarf es verschiedener statistischer Methoden, von denen eine Vielzahl in dieser Arbeit entwickelt werden. Zunächst wird die Fragestellung näher untersucht, d.h. präzisiert, was Äquivalenz von Kurven konkret bedeutet. Danach werden erst gleichmäßige Konfidenzbänder für die Differenz zweier Regressionskurven hergeleitet und dann die Äquivalenzhypothesen definiert. In dieser Arbeit werden hauptsächlich zwei Abstandsmaße betrachtet, der quadrierte L2-Abstand der Kurven und ihr maximaler absoluter Abstand. Nach Herleiten der asymptotischen Verteilungen werden je zwei verschiedene Tests entwickelt. Die erste beruht auf der errechneten Grenzverteilung, die zweite basiert auf einem parametrischen Bootstrap-Verfahren. Nach einigen Erweiterungen werden umfangreich Ergebnisse aus Simulationen dargestellt

Equivalence of regression curves sharing common parameters

In clinical trials the comparison of two different populations is a frequently addressed problem. Non-linear (parametric) regression models are commonly used to describe the relationship between covariates as the dose and a response variable in the two groups. In some situations it is reasonable to assume some model parameters to be the same, for instance the placebo effect or the maximum treatment effect. In this paper we develop a (parametric) bootstrap test to establish the similarity of two regression curves sharing some common parameters. We show by theoretical arguments and by means of a simulation study that the new test controls its level and achieves a reasonable power. Moreover, it is demonstrated that under the assumption of common parameters a considerable more powerful test can be constructed compared to the test which does not use this assumption. Finally, we illustrate potential applications of the new methodology by a clinical trial example

Testing for similarity of binary efficacy-toxicity responses

Clinical trials often aim to compare two groups of patients for efficacy and/or toxicity depending on covariates such as dose. Examples include the comparison of populations from different geographic regions or age classes or, alternatively, of different treatment groups. Similarity of these groups can be claimed if the difference in average outcome is below a certain margin over the entire covariate range. In this article, we consider the problem of testing for similarity in the case that efficacy and toxicity are measured as binary outcome variables. We develop a new test for the assessment of similarity of two groups for a single binary endpoint. Our approach is based on estimating the maximal deviation between the curves describing the responses of the two groups, followed by a parametric bootstrap test. Further, using a two-dimensional Gumbel-type model we develop methodology to establish similarity for (correlated) binary efficacy-toxicity outcomes. We investigate the operating characteristics of the proposed methodology by means of a simulation study and present a case study as an illustration