Adaptive group sequential confidence intervals for the ratio of normal means

In controlled group sequential trials, we consider the ratio of normal means as the effect measure of interest and derive group sequential nested confidence intervals on this parameter. In an interim analysis, the sample sizes of the following stages can be determined in a completely adaptive way using the unblinded data from all previously performed stages. Despite the data-dependent adaptation, the nested confidence intervals always keep the predefined confidence coefficient. Using nested confidence intervals, we make test decisions either in noninferiority or in superiority trials. However, in an interim analysis, we can change the planning from showing noninferiority to showing superiority or vice versa without affecting the predefined confidence coefficient of the nested intervals. A real data example is worked out in detail and the change in the planning from showing superiority to showing noninferiority is shown during the ongoing trial

Combined Test Procedures in the Meta-Analysis of Controlled Clinical Trials

Concerning the actual significance level, we investigate the commonly used combined test procedures of meta-analysis, which contain the choice of the model, in which the analysis is carried out, and the commonly used tests for treatment effect in the fixed and random effects model, and some new combined test procedures, which use an alternative test statistic in the random effects model or the t-distribution as test distribution of the commonly used test statistics. A simulation study indicates that the new combined test procedures are better with respect to a prescribed significance level

Adaptive Group Sequential Trials with the Standardized Mean Difference as Effect Size

In a thorough and extensive simulation study, we investigate the practical properties of repeated confidence intervals and point estimates for the standardized difference of normal means in adaptive group sequential trials. The theoretical foundations have been described in Hartung and Knapp (2009, 2010). In the simulation study, we consider an adaptive three-stage Pocock (1977)-type design for planning and showing noninferiority and an adaptive five-stage O'Brien-Fleming (1979)-type design for planning and showing superiority

Adaptive confidence intervals of desired length and power for normal means

In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates, in form of confidence intervals on the parameters of interest. The length of a confidence interval characterizes the accuracy of the whole findings. Consequently, confidence intervals should be constructed to hold a desired length. Basic ideas go back to Stein (1945) and Seelbinder (1953) who proposed a two-stage procedure for hypothesis testing about a normal mean. Tukey (1953) additionally considered the probability or power a confidence interval should possess to hold its length within a desired boundary. In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein's concept. Concrete rules for sample size updating are provided. Following an adaptive two-stage design of O'Brien and Fleming (1979) type, a real data example is worked out in detail

Adaptive controlled noninferiority group sequential trials

For studies comparing three independent arms: test group $T$, reference group $R$, and control group $C$, we consider the hierarchical testing of the a priori ordered hypotheses, that, in short, \begin{eqnarray*} \mbox{(I)}: &~& T > C, \\ \mbox{(II)}: &~& T > R - \Delta, \ \ \Delta > 0, \end{eqnarray*} in general adaptive group sequential designs. For normally distributed response variables with unknown variances, nested confidence intervals on the study parameters are derived at each stage of the trial, holding a predefined confidence level. During the course of the trial, the sample sizes can be calculated in a completely adaptive way based on the unblinded data of previous stages. Concrete formulae for sample size updating are provided in this paper. Moreover, in each interim analysis, it is possible to switch in the planning from showing noninferiority of $T$ in (II) to showing superiority of $T$, that is, $T > R$. A real data example is worked out in detail following an adaptive three-stage design of Pocock (1977) type. In the example, (I) is shown in the first stage and (II) in the second stage, so that the study stopped earlier at the second stage

Standardized mean differences in adaptive group sequential trials

For studies comparing two independent groups, experimental E and control C, with normally distributed response variables, the outcome measure standardized differences of means is considered that is scale and translation invariant. This effect measure enables a convenient specification of a noninferiority margin in a concrete application. The present paper provides in particular a group sequential confidence interval approach to noninferiority trials and to switching between noninferiority and superiority for the effect size measure standardized mean difference. During the course of the trial, the sample size can be calculated in a completely adaptive way, based on the unblinded data of previously performed stages. Concrete rules for sample size updating are provided in this paper. Moreover, in each interim analysis, it is possible to change the planning from showing noninferiority to showing superiority or vice versa. A real data example is worked out in detail and the change in the planning from showing noninferiority to showing superiority is considered during the ongoing trial

Messen faserförmiger Partikel

Die Umsetzung der Richtlinie zur Bestimmung der Anzahl von anorganischen faserförmigen Partikeln auf staubbelegten Filtern wurde in einem Ringversuch von VDI und DIN überprüft. Die Auswertung der Filter wurde zunächst in zwei Referenzlabors und danach in den teilnehmenden Prüflabors vorgenommen. Die Beurteilung der korrekten Umsetzung der Richtlinie durch ein Prüflabor sollte durch den Vergleich der Zählergebnisse aus diesem Prüflabor mit den Ergebnissen aus den beiden Referenzlabors erfolgen. Hier wird nun eine Auswertungsmethode für den Vergleich eines Prüfabors mit den beiden Referenzlabors vorgestellt, die auf einer Wurzeltransformation der Zählergebnisse basiert und mögliche Verzerrungen zwischen den Zählergebnissen der Referenzlabors sowie Korrelationen berücksichtigt. Die Umsetzung der Richtlinie wird schließlich mit Hilfe einer meta-analytischen Zusammenfassung von Teststatistiken überprüft

A confidence interval approach for difference and ratio of normal means in self-designing clinical trials

In self-designing clinical trials, confidence intervals are derived for the difference and the ratio of normal means, where the results of the independent study stages are combined using the weighted inverse normal method. The confidence intervals always hold the predefined nominal confidence level. During the course of the Self-designing trial, the sample sizes as well as the number of study stages can be determined simultaneously in a completely adaptive way. Self-designing may be considered as the limit case of adaptive group sequential designing of O'Brien and Fleming type when the full significance level is shifted to the last stage. We consider the effect measures difference and ratio of normal means, where the latter has not yet been considered in group sequential trials so far. Concrete rules are derived for updating sample sizes and assigning weights to the stages of the trial. The clinical trial may be originally designed either to show non-inferiority or superiority. But, in each interim analysis, it is possible to change the planning from showing non-inferiority to showing superiority or vice versa. The performance of the Self-designing and the resulting confidence intervals are demonstrated in real-data examples for both considered effect measures showing both kinds of switching during an ongoing trial