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The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflect the size of the population under consideration. Incorporation of the population size is possible in a decision-theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two-arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, N∗ in the case of geometric discounting, becomes large, the optimal trial size is O(N1/2) or O(N∗1/2). The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes.

If the response to treatment depends on genetic biomarkers, it is important to identify predictive biomarkers that define (sub-)populations where the treatment has a positive benefit risk balance. One approach to determine relevant subpopulations are subgroup analyses where the treatment effect is estimated in biomarker positive and biomarker negative groups. Subgroup analyses are challenging because several types of risks are associated with inference on subgroups. On the one hand, by disregarding a relevant subpopulation a treatment option may be missed due to a dilution of the treatment effect in the full population. Furthermore, even if the diluted treatment effect can be demonstrated in an overall population, it is not ethical to treat patients that do not benefit from the treatment when they can be identified in advance. On the other hand, selecting a spurious subpopulation increases the risk to restrict an efficacious treatment to a too narrow fraction of a potential benefiting population. We propose to quantify these risks with utility functions and investigate nonadaptive study designs that allow for inference on subgroups using multiple testing procedures as well as adaptive designs, where subgroups may be selected in an interim analysis. The characteristics of such adaptive and nonadaptive designs are compared for a range of scenarios.

The confirmatory analysis of pre-specified multiple hypotheses has become common in pivotal clinical trials. In the recent past multiple test procedures have been developed that reflect the relative importance of different study objectives, such as fixed sequence, fallback, and gatekeeping procedures. In addition, graphical approaches have been proposed that facilitate the visualization and communication of Bonferroni-based closed test procedures for common multiple test problems, such as comparing several treatments with a control, assessing the benefit of a new drug for more than one endpoint, combined non-inferiority and superiority testing, or testing a treatment at different dose levels in an overall and a subpopulation. In this paper, we focus on extended graphical approaches by dissociating the underlying weighting strategy from the employed test procedure. This allows one to first derive suitable weighting strategies that reflect the given study objectives and subsequently apply appropriate test procedures, such as weighted Bonferroni tests, weighted parametric tests accounting for the correlation between the test statistics, or weighted Simes tests. We illustrate the extended graphical approaches with several examples. In addition, we describe briefly the gMCP package in R, which implements some of the methods described in this paper.

For clinical trials with interim analyses conditional rejection probabilities play an important role when stochastic curtailment or design adaptations are performed. The conditional rejection probability gives the conditional probability to finally reject the null hypothesis given the interim data. It is computed either under the null or the alternative hypothesis. We investigate the properties of the conditional rejection probability for the one sided, one sample t-test and show that it can be non monotone in the interim mean of the data and non monotone in the non-centrality parameter for the alternative. We give several proposals how to implement design adaptations (that are based on the conditional rejection probability) for the t-test and give a numerical example. Additionally, the conditional rejection probability given the interim t-statistic is investigated. It does not depend on the unknown σ and can be used in stochastic curtailment procedures. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In recent months one of the most controversially discussed topics among regulatory agencies, the pharmaceutical industry, journal editors, and academia has been the sharing of patient-level clinical trial data. Several projects have been started such as the European Medicines Agency´s (EMA) “proactive publication of clinical trial data”, the BMJ open data campaign, or the AllTrials initiative. The executive director of the EMA, Dr. Guido Rasi, has recently announced that clinical trial data on patient level will be published from 2014 onwards (although it has since been delayed). The EMA draft policy on proactive access to clinical trial data was published at the end of June 2013 and open for public consultation until the end of September 2013. These initiatives will change the landscape of drug development and publication of medical research. They provide unprecedented opportunities for research and research synthesis, but pose new challenges for regulatory authorities, sponsors, scientific journals, and the public. Besides these general aspects, data sharing also entails intricate biostatistical questions such as problems of multiplicity. An important issue in this respect is the interpretation of multiple statistical analyses, both prospective and retrospective. Expertise in biostatistics is needed to assess the interpretation of such multiple analyses, for example, in the context of regulatory decision-making by optimizing procedural guidance and sophisticated analysis methods.

In the literature various multiple test procedures to compare k treatments with a control have been investigated. They can be applied to establish either treatment efficacy or treatment safety. In this paper we propose procedures which control the multiple level α with respect to efficacy and safety simultaneously. On the one hand we consider a method with stagewise rejective adjustments of local levels applied to appropriately defined subfamilies of null hypotheses. When order restrictions are assumed to hold among the parameters of interest we can alternatively split the multiple level between the families of efficacy and safety null hypotheses. If either all treatments are declared to be safe or all are declared to be effective then the other family can be tested at the full multiple level α, respectively. The methods are compared in a simulation study.

Proschan and Hunsberger (1995) suggest the use of a conditional error function to construct a two stage test that meets the α level and allows a very flexible reassessment of the sample size after the interim analysis. In this note we show that several adaptive designs can be formulated in terms of such an error function. The conditional power function defined similarly provides a simple method for sample size reassessment in adaptive two stage designs.