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Frank Bretz

Publications and source records attributed to Frank Bretz.

11 recordsLinked to original sources
PubMed2006

Power and sample size computations in simultaneous tests for non-inferiority based on relative margins.

In this paper, we address the problem of calculating power and sample sizes associated with simultaneous tests for non-inferiority. We consider the case of comparing several experimental treatments with an active control. The approach is based on the ratio view, where the common non-inferiority margin is chosen to be some percentage of the mean of the control treatment. Two power definitions in multiple hypothesis testing, namely, complete power and minimal power, are used in the computations. The sample sizes associated with the ratio-based inference are also compared with that of a comparable inference based on the difference of means for various scenarios. It is found that the sample size required for ratio-based inferences is smaller than that of difference-based inferences when the relative non-inferiority margin is less than one and when large response values indicate better treatment effects. The results are illustrated with examples.

Data Interpretation, Statistical↗
PubMed2006

Confirmatory seamless phase II/III clinical trials with hypotheses selection at interim: applications and practical considerations.

Adaptive seamless phase II/III designs combine a phase II and a phase III study into one single confirmatory clinical trial. Several examples of such designs are presented, where the primary endpoint is binary, time-to-event or continuous. The interim adaptations considered include the selection of treatments and the selection of hypotheses related to a pre-specified subgroup of patients. Practical aspects concerning the planning and implementation of adaptive seamless confirmatory studies are also discussed.

Clinical Trials, Phase II as Topic↗
PubMed2006

Confirmatory seamless phase II/III clinical trials with hypotheses selection at interim: general concepts.

Traditional drug development consists of a sequence of independent trials organized in different phases. Full development typically involves (i) a learning phase II trial and (ii) one or two confirmatory phase III trial(s). For example, in the phase II trials several doses of the new compound might be compared to a control and/or placebo with the goal of deciding whether to stop or continue development and, in the latter case, selecting one or two "best" doses to carry forward into the confirmatory phase. The phase III trials are then conducted as stand-alone confirmatory studies, not incorporating in their statistical analyses data collected in the previous phases. Seamless phase II/III designs are aimed at interweaving the two phases of full development by combining them into one single, uninterrupted study conducted in two stages. In the dose-finding example above, one (or more) dose(s) are selected after the first stage based on the available data at interim, and are then observed further in the second stage. The final analysis of the selected dose(s) includes patients from both stages and is performed such that the overall type I error rate is controlled at a prespecified level regardless of the dose selection rule used at interim. The adequacy of the dose selection at interim is obviously a critical step for the success of a seamless phase II/III trial. In this paper we focus on the description of flexible test procedures allowing for adaptively selecting hypotheses at interim and thus allowing the combination of learning and confirming in a single seamless trial. We review the statistical background, introduce different test procedures and compare them in a power study. In a subsequent paper (Schmidli et al., 2006) we give several applications from our daily practice and discuss related implementation issues in conducting adaptive seamless designs.

Biometry↗
PubMed2006

Design and analysis of dose-finding studies combining multiple comparisons and modeling procedures.

The search for an adequate dose involves some of the most complex series of decisions to be made in developing a clinically viable product. Typically decisions based on such dose-finding studies reside in two domains: (i) "proof" of evidence that the treatment is effective and (ii) the need to choose dose(s) for further development. We consider a unified strategy for designing and analyzing dose-finding studies, including the testing of proof-of-concept and the selection of one or more doses to take into further development. The methodology combines the advantages of multiple comparisons and modeling approaches, consisting of a multi-stage procedure. Proof-of-concept is tested in the first stage, using multiple comparison methods to identify statistically significant contrasts corresponding to a set of candidate models. If proof-of-concept is established in the first stage, the best model is then used for dose selection in subsequent stages. This article describes and illustrates practical considerations related to the implementation of this methodology. We discuss how to determine sample sizes and perform power calculations based on the proof-of-concept step. A relevant topic in this context is how to obtain good prior values for the model parameters: different methods to translate prior clinical knowledge into parameter values are presented and discussed. In addition, different possibilities of performing sensitivity analyses to assess the consequences of misspecifying the true parameter values are introduced. All methods are illustrated by a real dose-response phase II study for an anti-anxiety compound.

Algorithms↗
PubMed2005

Adaptive designs based on the truncated product method.

BACKGROUND: Adaptive designs are becoming increasingly important in clinical research. One approach subdivides the study into several (two or more) stages and combines the p-values of the different stages using Fisher's combination test. METHODS: Alternatively to Fisher's test, the recently proposed truncated product method (TPM) can be applied to combine the p-values. The TPM uses the product of only those p-values that do not exceed some fixed cut-off value. Here, these two competing analyses are compared. RESULTS: When an early termination due to insufficient effects is not appropriate, such as in dose-response analyses, the probability to stop the trial early with the rejection of the null hypothesis is increased when the TPM is applied. Therefore, the expected total sample size is decreased. This decrease in the sample size is not connected with a loss in power. The TPM turns out to be less advantageous, when an early termination of the study due to insufficient effects is possible. This is due to a decrease of the probability to stop the trial early. CONCLUSION: It is recommended to apply the TPM rather than Fisher's combination test whenever an early termination due to insufficient effects is not suitable within the adaptive design.

Data Interpretation, Statistical↗
PubMed2004

MR imaging of lung parenchyma at 0.2 T: evaluation of imaging techniques, comparative study with chest radiography and interobserver analysis.

The purpose of this study was to evaluate low-field MR imaging of the lung parenchyma in comparison with postero-anterior (PA) and lateral chest radiographs (CR). One hundred one prospectively randomized patients who had received routine CR were additionally examined with magnetic resonance imaging (MRI) at 0.2 T. Utilized sequences were: constructive interference in steady state (CISS), true fast imaging in steady state precession (True-FISP) and T1-weighted spin-echo (T1SE). Consensus reading of two observers was performed for CR. Three other observers analyzed hardcopies of the MRI examinations for each sequence independently. The individual results for the comparisons between the sequences and CR were calculated using kappa coefficients with their corresponding confidence intervals. Additionally, an interobserver analysis was performed. The proportions of agreement for the three sequences compared with CR were high, with 0.93 for CISS, 0.89 for True-FISP and 0.91 for T1SE. The kappa coefficients and the corresponding confidence intervals were 0.81 [0.68; 0.95] for CISS, 0.72 [0.57; 0.88] for True-FISP and 0.78 [0.65; 0.92] for T1SE. Concerning CISS, differences between MRI and CR were mainly related to advantages resulting from cross-sectional imaging. The smallest 95% lower confidence bound of the three kappa measures for comparing the MR readers with each other was 0.97, indicating a high interobserver agreement. Low-field MRI of the lung parenchyma using the CISS sequence is well comparable with chest radiography and demonstrates slight advantages resulting from the cross-sectional imaging technique.

Adult↗
PubMed2004

Efficient two-sample designs for microarray experiments with biological replications.

In the last years, biostatistical research has begun to apply linear models and design theory to develop efficient experimental designs and analysis tools for gene expression microarray data. With two-colour microarrays, direct comparisons of RNA-targets are possible and lead to incomplete block designs. In this setting, efficient designs for simple and factorial microarray experiments have mainly been proposed for technical replicates. But for biological replicates, which are crucial to obtain inference that can be generalised to a biological population, this question has only been discussed recently and is not fully solved yet. In this paper, we propose efficient designs for independent two-sample experiments using two-colour microarrays enabling biologists to measure their biological random samples in an efficient manner to draw generalisable conclusions. We give advice for experimental situations with differing group sizes and show the impact of different designs on the variance and degrees of freedom of the test statistics. The designs proposed in this paper can be evaluated using SAS PROC MIXED or S+/R lme.

Data Interpretation, Statistical↗
PubMed2003

Identifying effective and/or safe doses by stepwise confidence intervals for ratios.

Typical randomized clinical dose-finding studies consist of the comparison of several doses of a drug versus a placebo. Interest lies in estimating relevant doses among those under investigation for efficacy and safety variables, such as the minimum effective dose or the maximum safe dose (or estimating both doses simultaneously). Step-down procedures have been proposed for comparing the standardized differences of the dose groups against placebo. In this paper we consider the ratio of population means and propose stepwise confidence intervals for these ratios. These confidence intervals do not require multiplicity adjustments and yield the same decisions as the associated test procedures. In addition, several power concepts are investigated within the present framework. The results allow sample size determination in the design phase of a study for the probability of estimating correctly the dose of interest. Auxiliary results of a numerical study show the range of application of these methods.

Allylamine↗
PubMed2003

Dose-response and thresholds in mutagenicity studies: a statistical testing approach.

The analysis of dose-response relationships is an important objective in toxicology, and one in which both modelling and testing approaches are used. One particular question is whether a threshold exists at low doses. The concept of a pragmatic threshold is used, i.e. low doses with biologically unimportant effects are assumed to be threshold doses. "Biologically unimportant" means, in statistical terms, a lower effect than the effect of the negative control, or at least a just-tolerable margin delta higher than the effect of the negative control. Therefore, threshold doses can be tested in terms of a one-sided hypothesis of equivalence. A new approach is proposed, assuming, at the least, that the low dose is a threshold dose, and the highest dose is superior to the negative control. By analogy to the k-fold rule commonly used in mutagenicity studies, tests on ratio-to-control are used. The a priori definition of the threshold margin is inherently needed. A further approach proposes the analysis of dose-response relationships by means of order-restricted inference (the so-called trend test). A modification of a multiple-contrast test is used, in which only those contrasts are included that are sensitive for no effects at low doses. A further modification treats the complicated, but real, problem of simultaneous existence of a threshold, a monotonic increase, and a downturn effect at high dose(s). A parametric procedure is considered, together with an extension for proportions. The important problem of a priori sample size definition is discussed. The approaches are demonstrated by means of examples based on real data.

Animal Testing Alternatives↗
PubMed2002

Detecting dose-response using contrasts: asymptotic power and sample size determination for binomial data.

Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.

Cabergoline↗