Unitarity in noncommutative QFTs

Das Unitaritätsproblem in NCQFT wird in dieser Arbeit ausführlich diskutiert, wobei gezeigt wird, dass das ursprüngliche negative Resultat für skalare Felder mit nichtkommutierenden Raumzeitkoordinaten eine Konsequenz davon ist, dass die Zeitordnung nicht mit dem Moyalprodukt kommutiert und man deshalb eine neue Art der Zeitordnung benötigt, die sogenannte Interaction-point time-ordering (IPTO), welche zu anderen Feynmanregeln führt und bei skalaren Feldern die Unitarität erhält. Diese neue Methode funktioniert für Eichfelder jedoch nicht, weil gezeigt wurde, dass eine Wardidentität für Comptonstreuung mit räumlich und zeitlicher Nichtkommutativität verletzt ist. Zuletzt wurden noch einige Lösungsvorschläge gemacht, jedoch noch nicht vollständig schlüssig ausgearbeitet.The unitarity problem of NCQFT is carefully investigated in this work where it is shown that the original negative result for scalar fields with noncommuting spacetime coordinates is a consequence of the time-ordering not commuting with the Moyalproduct. Therefore a new time-ordering is needed, the so-called interaction-point time-ordering (IPTO), which leads to different Feynman rules and renders scalar fields unitary. For gauge fields this new method doesn't work as it is shown that a Ward identity is violated for Compton scattering with spacetime noncommutativity. At the end some possible solutions are mentioned, but aren't conclusively worked out yet

Applicability and added value of novel methods to improve drug development in rare diseases

The ASTERIX project developed a number of novel methods suited to study small populations. The objective of this exercise was to evaluate the applicability and added value of novel methods to improve drug development in small populations, using real world drug development programmes as reported in European Public Assessment Reports. The applicability and added value of thirteen novel methods developed within ASTERIX were evaluated using data from 26 European Public Assessment Reports (EPARs) for orphan medicinal products, representative of rare medical conditions as predefined through six clusters. The novel methods included were 'innovative trial designs' (six methods), 'level of evidence' (one method), 'study endpoints and statistical analysis' (four methods), and 'meta-analysis' (two methods) and they were selected from the methods developed within ASTERIX based on their novelty; methods that discussed already available and applied strategies were not included for the purpose of this validation exercise. Pre-requisites for application in a study were systematized for each method, and for each main study in the selected EPARs it was assessed if all pre-requisites were met. This direct applicability using the actual study design was firstly assessed. Secondary, applicability and added value were explored allowing changes to study objectives and design, but without deviating from the context of the drug development plan. We evaluated whether differences in applicability and added value could be observed between the six predefined condition clusters. Direct applicability of novel methods appeared to be limited to specific selected cases. The applicability and added value of novel methods increased substantially when changes to the study setting within the context of drug development were allowed. In this setting, novel methods for extrapolation, sample size re-assessment, multi-armed trials, optimal sequential design for small sample sizes, Bayesian sample size re-estimation, dynamic borrowing through power priors and fall-back tests for co-primary endpoints showed most promise - applicable in more than 40% of evaluated EPARs in all clusters. Most of the novel methods were applicable to conditions in the cluster of chronic and progressive conditions, involving multiple systems/organs. Relatively fewer methods were applicable to acute conditions with single episodes. For the chronic clusters, Goal Attainment Scaling was found to be particularly applicable as opposed to other (non-chronic) clusters. Novel methods as developed in ASTERIX can improve drug development programs. Achieving optimal added value of these novel methods often requires consideration of the entire drug development program, rather than reconsideration of methods for a specific trial. The novel methods tested were mostly applicable in chronic conditions, and acute conditions with recurrent episodes. The online version of this article (10.1186/s13023-018-0925-0) contains supplementary material, which is available to authorized users

Clinical trials with multiple objectives in small populations

In klinischen Studien zur Entwicklung von Therapien für seltenen Erkrankungen stellt die niedrige Fallzahl an Patienten, welche in einem überschaubaren Zeitraum rekrutiert werden können, ein zentrales Problem für statistische Schlussfolgerungen dar. Diese Dissertation beschäftigt sich mit dem Testen von Hypothesen im Rahmen von konfirmatorischen Studien mit kleinen Fallzahlen. Eine Reduktion der benötigten Fallzahl kann durch Zwischenanalysen mit der Möglichkeit auf Grund von erwiesener Effektivität oder Aussichtslosigkeit zu stoppen, durch die Verwendung effizienterer multipler Testprozeduren oder durch Verfahren zur Kombination mehrerer Endpunkte erreicht werden. Da die Wahrscheinlichkeit mindestens eines positiven Testresultats mit der Anzahl der durchgeführten Tests zunimmt (auch wenn kein Behandlungseffekt vorherrscht), verlangen konfirmatorische Analysen eine Anpassung für Zwischenanalysen und multiples Testen, um die Häufigkeit eines multiplen Fehlers 1. Art zu kontrollieren. In Kapitel 2 wird der derzeitige Stand der Methoden zu adaptiven Studiendesigns, multiplen Testprozeduren und kombinierter Endpunkte illustriert, auf welchem die späteren Kapitel 3, 5 und 4 mit den Publikationen dieser kumulativen Dissertation aufbauen. Der Artikel in Kapitel 3 beschäftigt sich mit mehrarmigen gruppensequentiellen Studien zum Vergleich mehrerer Behandlungsarme zu einem Kontrollarm bezüglich eines Endpunktes mit einer Zwischenanalyse, welche die Möglichkeit des Stoppens bietet. Zwei Stoppregeln entsprechend unterschiedlicher Studienziele werden betrachtet, ihre Verwerfungsgrenzen optimiert und ihre Performance verglichen. Bei Studiendesigns mit simultanem Stoppen wird die gesamte Studie beendet, sobald für einen der Behandlungsarme die Nullhypothese keines Behandlungseffektes verworfen werden kann. Bei Studiendesigns mit separatem Stoppen stoppt nur die Patientenrekrutierung zu Behandlungsarmen, für welche ein signifikanter Behandlungseffekt bereits nachgewiesen werden konnte, alle anderen werden weitergeführt. Die Häufigkeit eines Fehlers 1. Art wird durch eine sogenannte "closed testing procedure" angewandt auf gruppensequentielle Tests der Schnitt- und Elementarhypothesen kontrolliert. Es wird gezeigt, dass bei simultanem Stoppen weniger konservative Verwerfungsgrenzen für die lokalen Tests der Elementarhypothesen angewandt werden können. Der zweite Artikel in Kapitel 5 beschäftigt sich mit dem Problem der Analyse von heterogenen, patientenzentrierten Daten eines "goal attainment scaling" (GAS) Endpunktes. Als Bewertungsmethode evaluiert GAS Behandlungen auf der Basis individueller, patientenspezifischer Ziele, deren Erreichen auf einer präspezifizierten gemeinsamen ordinalen Skala abgebildet wird. Die Eigenschaften unterschiedlicher Möglichkeiten des Hypothesentestens werden basierend auf einem allgemeinen statistischen Modell für GAS Daten untersucht. Simulationen werden durch Anwendung eines latenten Variablenansatzes zur Generierung der GAS Daten durchgeführt. Der Einfluss bestimmter Modellparameter wird untersucht und Empfehlungen für das Design klinischer Studien mit einem GAS Endpunkt werden abgeleitet. Kapitel 4 enthält einen Review über bestehende Methoden multiple Endpunkte im Falle geringer Fallzahlen zu kombinieren oder zu testen, um einerseits die Power für Tests einer globalen Nullhypothese zu erhöhen und andererseits konfirmatorische Schlüsse für mehrere Endpunkte zu ermöglichen. Der Fokus liegt hierbei auf der Durchführbarkeit von Methoden, welche nicht alleinig auf asymptotischen Resultaten beruhen, in Studien mit kleiner Fallzahl. Die Anwendbarkeit der unterschiedlichen Methoden wird mit Beispielen klinischer Studien illustriert.Statistical inference in clinical trials for the development of therapies of rare diseases suffers from the limitation of low numbers of patients who can be recruited in a reasonable time frame. This thesis is concerned with hypothesis testing in the framework of confirmatory studies with small sample sizes. A reduction of the required sample size for clinical trial designs can be achieved by including interim analyses with the possibility to stop the trial early due to efficacy or futility or by using more powerful multiple testing and combined endpoint methodology. As the probability of at least one positive result increases with the number of tests performed (even in case there is no treatment effect), confirmatory analyses demand an adjustment for interim analyses and multiple testing to control the multiple type I error rate. In Chapter 2, on which Chapters 3, 4 and 5 containing the publications of this cumulative thesis are based, the current state of methodology concerning adaptive clinical trial designs, multiple testing procedures and the combination of multiple endpoints is illustrated. The article in Chapter 3 deals with two-stage multi-arm group sequential trials comparing several treatments to a common control with one interim analysis with the possibility to stop. Two stopping rules corresponding to different trial objectives are considered, the corresponding rejection boundaries optimized and the operating characteristics compared. For trial designs with simultaneous stopping, the whole trial is stopped as soon as for any of the arms the null hypothesis of no treatment effect can be rejected. For trial designs with separate stopping, only the recruitment to arms for which a significant treatment effect could be demonstrated is stopped, all others are continued. The multiple type I error rate is controlled by the closed testing procedure applied to group sequential tests of intersection and elementary hypotheses. It is shown that for the simultaneous stopping rule, less conservative rejection boundaries for the local tests of elementary hypotheses can be applied. Chapter 4 is a review on the current methodology for combining and testing multiple endpoints in small clinical trials to either increase power for testing a global hypothesis or enable confirmatory conclusions on several endpoints. The focus is on feasibility of methods which do not solely rely on asymptotic considerations in trials with small sample sizes. The article in Chapter 5 deals with the problem of analysing heterogeneous patient-centred outcomes using goal attainment scaling (GAS) as an endpoint. As an assessment instrument GAS evaluates interventions on the basis of individual, patient-specific goals whose attainment is mapped in a pre-specified way to levels on an ordinal scale common to all goals. The properties of different hypothesis testing approaches are investigated based on a general statistical model for GAS data. Simulations are performed applying a latent variable approach to generate GAS data. The impact of certain model parameters is assessed and recommendations for the design of clinical trials with a GAS endpoint are given. The applicability of the different methods is illustrated with clinical trial examples.submitted by Susanne UrachAbweichender Titel laut Übersetzung der Verfasserin/des VerfassersMedizinische Universität Wien, Dissertation, 2018OeBB(VLID)253792

Journal of Biopharmaceutical Statistics / Methods for the analysis of multiple endpoints in small populations: A review

While current guidelines generally recommend single endpoints for primary analyses of confirmatory clinical trials, it is recognized that certain settings require inference on multiple endpoints for comprehensive conclusions on treatment effects. Furthermore, combining treatment effect estimates from several outcome measures can increase the statistical power of tests. Such an efficient use of resources is of special relevance for trials in small populations. This paper reviews approaches based on a combination of test statistics or measurements across endpoints as well as multiple testing procedures that allow for confirmatory conclusions on individual endpoints. We especially focus on feasibility in trials with small sample sizes and do not solely rely on asymptotic considerations. A systematic literature search in the Scopus database, supplemented by a manual search, was performed to identify research papers on analysis methods for multiple endpoints with relevance to small populations. The identified methods were grouped into approaches that combine endpoints into a single measure to increase the power of statistical tests and methods to investigate differential treatment effects in several individual endpoints by multiple testing.(VLID)509614

Applicability and added value of novel methods to improve drug development in rare diseases

BACKGROUND: The ASTERIX project developed a number of novel methods suited to study small populations. The objective of this exercise was to evaluate the applicability and added value of novel methods to improve drug development in small populations, using real world drug development programmes as reported in European Public Assessment Reports. METHODS: The applicability and added value of thirteen novel methods developed within ASTERIX were evaluated using data from 26 European Public Assessment Reports (EPARs) for orphan medicinal products, representative of rare medical conditions as predefined through six clusters. The novel methods included were 'innovative trial designs' (six methods), 'level of evidence' (one method), 'study endpoints and statistical analysis' (four methods), and 'meta-analysis' (two methods) and they were selected from the methods developed within ASTERIX based on their novelty; methods that discussed already available and applied strategies were not included for the purpose of this validation exercise. Pre-requisites for application in a study were systematized for each method, and for each main study in the selected EPARs it was assessed if all pre-requisites were met. This direct applicability using the actual study design was firstly assessed. Secondary, applicability and added value were explored allowing changes to study objectives and design, but without deviating from the context of the drug development plan. We evaluated whether differences in applicability and added value could be observed between the six predefined condition clusters. RESULTS AND DISCUSSION: Direct applicability of novel methods appeared to be limited to specific selected cases. The applicability and added value of novel methods increased substantially when changes to the study setting within the context of drug development were allowed. In this setting, novel methods for extrapolation, sample size re-assessment, multi-armed trials, optimal sequential design for small sample sizes, Bayesian sample size re-estimation, dynamic borrowing through power priors and fall-back tests for co-primary endpoints showed most promise - applicable in more than 40% of evaluated EPARs in all clusters. Most of the novel methods were applicable to conditions in the cluster of chronic and progressive conditions, involving multiple systems/organs. Relatively fewer methods were applicable to acute conditions with single episodes. For the chronic clusters, Goal Attainment Scaling was found to be particularly applicable as opposed to other (non-chronic) clusters. CONCLUSION: Novel methods as developed in ASTERIX can improve drug development programs. Achieving optimal added value of these novel methods often requires consideration of the entire drug development program, rather than reconsideration of methods for a specific trial. The novel methods tested were mostly applicable in chronic conditions, and acute conditions with recurrent episodes

Applicability and added value of novel methods to improve drug development in rare diseases

BACKGROUND: The ASTERIX project developed a number of novel methods suited to study small populations. The objective of this exercise was to evaluate the applicability and added value of novel methods to improve drug development in small populations, using real world drug development programmes as reported in European Public Assessment Reports. METHODS: The applicability and added value of thirteen novel methods developed within ASTERIX were evaluated using data from 26 European Public Assessment Reports (EPARs) for orphan medicinal products, representative of rare medical conditions as predefined through six clusters. The novel methods included were 'innovative trial designs' (six methods), 'level of evidence' (one method), 'study endpoints and statistical analysis' (four methods), and 'meta-analysis' (two methods) and they were selected from the methods developed within ASTERIX based on their novelty; methods that discussed already available and applied strategies were not included for the purpose of this validation exercise. Pre-requisites for application in a study were systematized for each method, and for each main study in the selected EPARs it was assessed if all pre-requisites were met. This direct applicability using the actual study design was firstly assessed. Secondary, applicability and added value were explored allowing changes to study objectives and design, but without deviating from the context of the drug development plan. We evaluated whether differences in applicability and added value could be observed between the six predefined condition clusters. RESULTS AND DISCUSSION: Direct applicability of novel methods appeared to be limited to specific selected cases. The applicability and added value of novel methods increased substantially when changes to the study setting within the context of drug development were allowed. In this setting, novel methods for extrapolation, sample size re-assessment, multi-armed trials, optimal sequential design for small sample sizes, Bayesian sample size re-estimation, dynamic borrowing through power priors and fall-back tests for co-primary endpoints showed most promise - applicable in more than 40% of evaluated EPARs in all clusters. Most of the novel methods were applicable to conditions in the cluster of chronic and progressive conditions, involving multiple systems/organs. Relatively fewer methods were applicable to acute conditions with single episodes. For the chronic clusters, Goal Attainment Scaling was found to be particularly applicable as opposed to other (non-chronic) clusters. CONCLUSION: Novel methods as developed in ASTERIX can improve drug development programs. Achieving optimal added value of these novel methods often requires consideration of the entire drug development program, rather than reconsideration of methods for a specific trial. The novel methods tested were mostly applicable in chronic conditions, and acute conditions with recurrent episodes