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Adaptive planning of clinical trials allows modifying the entire trial design at any time point mid-course. In this paper, we consider the case when a trial-external update of the planning assumptions during the ongoing trial makes an unforeseen design adaptation necessary. We take up the idea to construct adaptive designs with defined features by solving an optimization problem and apply it to the situation of unplanned design reassessment. By using the conditional error principle, we present an approach on how to optimally modify the trial design at an unplanned interim analysis while at the same time strictly protecting the type I error rate. This linking of optimal design planning and the conditional error principle allows sound reactions to unforeseen events that make a design reassessment necessary.

In clinical development, there is a trade-off between investment and level of confidence in the potential of the drug before going into phase III. Reduced investment requires the use of short-term endpoints. On new compounds, only limited information about the relationship between treatment effects of short- and long-term endpoints is usually available. Therefore, decision-making solely based on short-term endpoints does not seem desirable. Our goal is to plan an efficient development program, which uses short- and long-term endpoints data for decision-making. We found that with limited prior information and restrictions on maximum sample size, decision-making after phase II cannot be substantially improved. We follow the concept of a "phase 2+" design where after a go-to-phase-III-decision, further follow-up data from phase II are employed to make interim decisions on phase III. The program will be stopped early when additional phase II and/or available phase III data lead to a low probability of success (PoS). We utilize information from a multi-categorical short-term endpoint (response status) and a long-term endpoint (overall survival (OS)) to determine the PoS in phase III with OS as the primary endpoint. Optimal combinations of decision boundaries and time points are demonstrated in a simulation study. Our results show that the proposed second look using additional follow-up data from phase II/III improves PoS estimates compared to the first look, especially when prior data about the control arm is available. The proposed planning strategy allows a customized compromise between the quality of decision-making and program duration.

The feasibility of a new clinical trial may be increased by incorporating historical data of previous trials. In the particular case where only data from a single historical trial are available, there exists no clear recommendation in the literature regarding the most favorable approach. A main problem of the incorporation of historical data is the possible inflation of the type I error rate. A way to control this type of error is the so-called power prior approach. This Bayesian method does not "borrow" the full historical information but uses a parameter 0 ≤ δ ≤ 1 to determine the amount of borrowed data. Based on the methodology of the power prior, we propose a frequentist framework that allows incorporation of historical data from both arms of two-armed trials with binary outcome, while simultaneously controlling the type I error rate. It is shown that for any specific trial scenario a value δ > 0 can be determined such that the type I error rate falls below the prespecified significance level. The magnitude of this value of δ depends on the characteristics of the data observed in the historical trial. Conditionally on these characteristics, an increase in power as compared to a trial without borrowing may result. Similarly, we propose methods how the required sample size can be reduced. The results are discussed and compared to those obtained in a Bayesian framework. Application is illustrated by a clinical trial example.

Owing to increased costs and competition pressure, drug development becomes more and more challenging. Therefore, there is a strong need for improving efficiency of clinical research by developing and applying methods for quantitative decision making. In this context, the integrated planning for phase II/III programs plays an important role as numerous quantities can be varied that are crucial for cost, benefit, and program success. Recently, a utility-based framework has been proposed for an optimal planning of phase II/III programs that puts the choice of decision boundaries and phase II sample sizes on a quantitative basis. However, this method is restricted to studies with a single time-to-event endpoint. We generalize this procedure to the setting of clinical trials with multiple endpoints and (asymptotically) normally distributed test statistics. Optimal phase II sample sizes and go/no-go decision rules are provided for both the "all-or-none" and "at-least-one" win criteria. Application of the proposed method is illustrated by drug development programs in the fields of Alzheimer disease and oncology.

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re-estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re-estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre-specified level. Furthermore, some refinements of the re-estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes.

Baseline adjusted analyses are commonly encountered in practice, and regulatory guidelines endorse this practice. Sample size calculations for this kind of analyses require knowledge of the magnitude of nuisance parameters that are usually not given when the results of clinical trials are reported in the literature. It is therefore quite natural to start with a preliminary calculated sample size based on the sparse information available in the planning phase and to re-estimate the value of the nuisance parameters (and with it the sample size) when a portion of the planned number of patients have completed the study. We investigate the characteristics of this internal pilot study design when an analysis of covariance with normally distributed outcome and one random covariate is applied. For this purpose we first assess the accuracy of four approximate sample size formulae within the fixed sample size design. Then the performance of the recalculation procedure with respect to its actual Type I error rate and power characteristics is examined. The results of simulation studies show that this approach has favorable properties with respect to the Type I error rate and power. Together with its simplicity, these features should make it attractive for practical application. (C) Copyright 2009 John Wiley & Sons, Ltd.

For the proof of efficacy of a new drug in a placebo-controlled clinical trial it is not sufficient merely to demonstrate a statistically significant treatment difference. In recent years, regulatory authorities have strongly recommended assessing additionally whether the observed effect size is also of clinical relevance. This opinion is reflected in various guidelines which are of the utmost importance for the successful approval of a new drug. Clinical relevance can be investigated by responder analyses or by considering the point estimates on the original scale together with the associated confidence intervals. In this paper, we focus on the latter approach and discuss the suitability of different criteria which are commonly applied in medical research. Copyright © 2005 John Wiley & Sons, Ltd.

For binary endpoints, the required sample size depends not only on the known values of significance level, power and clinically relevant difference but also on the overall event rate. However, the overall event rate may vary considerably between studies and, as a consequence, the assumptions made in the planning phase on this nuisance parameter are to a great extent uncertain. The internal pilot study design is an appealing strategy to deal with this problem. Here, the overall event probability is estimated during the ongoing trial based on the pooled data of both treatment groups and, if necessary, the sample size is adjusted accordingly. From a regulatory viewpoint, besides preserving blindness it is required that eventual consequences for the Type I error rate should be explained. We present analytical computations of the actual Type I error rate for the internal pilot study design with binary endpoints and compare them with the actual level of the chi-square test for the fixed sample size design. A method is given that permits control of the specified significance level for the chi-square test under blinded sample size recalculation. Furthermore, the properties of the procedure with respect to power and expected sample size are assessed. Throughout the paper, both the situation of equal sample size per group and unequal allocation ratio are considered. The method is illustrated with application to a clinical trial in depression. Copyright © 2004 John Wiley & Sons Ltd.

In recent years, high failure rates in phase III trials were observed. One of the main reasons is overoptimistic assumptions for the planning of phase III resulting from limited phase II information and/or unawareness of realistic success probabilities. We present an approach for planning a phase II trial in a time-to-event setting that considers the whole phase II/III clinical development programme. We derive stopping boundaries after phase II that minimise the number of events under side conditions for the conditional probabilities of correct go/no-go decision after phase II as well as the conditional success probabilities for phase III. In addition, we give general recommendations for the choice of phase II sample size. Our simulations show that unconditional probabilities of go/no-go decision as well as the unconditional success probabilities for phase III are influenced by the number of events observed in phase II. However, choosing more than 150 events in phase II seems not necessary as the impact on these probabilities then becomes quite small. We recommend considering aspects like the number of compounds in phase II and the resources available when determining the sample size. The lower the number of compounds and the lower the resources are for phase III, the higher the investment for phase II should be. Copyright © 2015 John Wiley & Sons, Ltd.

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re-estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re-estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre-specified level. Furthermore, some refinements of the re-estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes.

The internal pilot study design allows for modifying the sample size during an ongoing study based on a blinded estimate of the variance thus maintaining the trial integrity. Various blinded sample size re-estimation procedures have been proposed in the literature. We compare the blinded sample size re-estimation procedures based on the one-sample variance of the pooled data with a blinded procedure using the randomization block information with respect to bias and variance of the variance estimators, and the distribution of the resulting sample sizes, power, and actual type I error rate. For reference, sample size re-estimation based on the unblinded variance is also included in the comparison. It is shown that using an unbiased variance estimator (such as the one using the randomization block information) for sample size re-estimation does not guarantee that the desired power is achieved. Moreover, in situations that are common in clinical trials, the variance estimator that employs the randomization block length shows a higher variability than the simple one-sample estimator and in turn the sample size resulting from the related re-estimation procedure. This higher variability can lead to a lower power as was demonstrated in the setting of noninferiority trials. In summary, the one-sample estimator obtained from the pooled data is extremely simple to apply, shows good performance, and is therefore recommended for application.

Clinical phase II trials in oncology are conducted to determine whether the activity of a new anticancer treatment is promising enough to merit further investigation. Two-stage designs are commonly used for this situation to allow for early termination. Designs proposed in the literature so far have the common drawback that the sample sizes for the two stages have to be specified in the protocol and have to be adhered to strictly during the course of the trial. As a consequence, designs that allow a higher extent of flexibility are desirable. In this article, we propose a new adaptive method that allows an arbitrary modification of the sample size of the second stage using the results of the interim analysis or external information while controlling the type I error rate. If the sample size is not changed during the trial, the proposed design shows very similar characteristics to the optimal two-stage design proposed by Chang et al. (Biometrics 1987; 43:865-874). However, the new design allows the use of mid-course information for the planning of the second stage, thus meeting practical requirements when performing clinical phase II trials in oncology.

Baseline adjusted analyses are commonly encountered in practice, and regulatory guidelines endorse this practice. Sample size calculations for this kind of analyses require knowledge of the magnitude of nuisance parameters that are usually not given when the results of clinical trials are reported in the literature. It is therefore quite natural to start with a preliminary calculated sample size based on the sparse information available in the planning phase and to re-estimate the value of the nuisance parameters (and with it the sample size) when a portion of the planned number of patients have completed the study. We investigate the characteristics of this internal pilot study design when an analysis of covariance with normally distributed outcome and one random covariate is applied. For this purpose we first assess the accuracy of four approximate sample size formulae within the fixed sample size design. Then the performance of the recalculation procedure with respect to its actual Type I error rate and power characteristics is examined. The results of simulation studies show that this approach has favorable properties with respect to the Type I error rate and power. Together with its simplicity, these features should make it attractive for practical application.