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Traditionally, sample size considerations for phase 2 trials are based on the desired properties of the design and response information from the trials. In this article, we propose to design phase 2 trials based on program-level optimization. We present a framework to evaluate the impact that several phase 2 design features have on the probability of phase 3 success and the expected net present value of the product. These factors include the phase 2 sample size, decision rules to select a dose for phase 3 trials, and the sample size for phase 3 trials. Using neuropathic pain as an example, we use simulations to illustrate the framework and show the benefit of including these factors in the overall decision process.

The rapidly increasing cost to develop new drugs calls for new tools that efficiently enable the demonstration of the safety and effectiveness of a new drug. When validating such a decision-enabling tool, a traditional approach is typically to apply the tool on a positive control, known to be effective, and ascertain that a statistically significant effect is obtained. We argue, however, that the validation study should be designed to show that the tool provides a variability that is small in relation to the treatment effect, which means that the tool has the capacity of providing decision-enabling results in small-sample studies in routine use. We give details on the relevant test to perform in the validation of a decision-enabling tool and use the development of a human pharmacological model, aimed at studying neuropathic pain in 2 × 2 crossover trials, as a motivating example. We also develop power and sample size calculations, and illustrate the implications on sample size needed for a validation study. Results show that to obtain pertinent evidence that the decision-enabling tool is useful, that is, to reject the relevant null hypothesis, a substantially increased sample size would often be needed in the validation study, as compared to traditional approaches.

Assessment of consistency of treatment effect across regions is often a key issue in a multiregional clinical trial (MRCT) because of differences in intrinsic and extrinsic factors. Careful consideration of consistency assessment of treatment effect across regions is necessary at the design stage. This article is part 1 of a cross-industry PhRMA team’s effort to provide perspective and recommendations on the issue of regional consistency, with primary focus on design considerations. We argue that given the premise of an MRCT that there is no or limited regional variation, choices of appropriate consistency criteria for assessing regional consistency need to reflect this a priori belief and should not add an additional burden of proving regional consistency in addition to meeting the primary study objectives. The total sample size of the MRCT should be mainly driven by the primary objectives and hypotheses. Appropriate sample size partitioning and distribution across regions may be considered to achieve a target “assurance probability” based upon predefined consistency criteria such as modified PMDA (Pharmaceutical and Medical Devices Agency) methods. Prespecification and documentation of the plan for regional assessment in the protocol are important for interpreting the results. We also encourage communication with health authorities, and acknowledge negotiation may be necessary to reach an agreement, especially when there are region or country-specific interests.

The Japanese regulatory guideline “Basic Principles in Global Clinical Trials,” issued in September 2007, serves to encourage the participation of Japan in international phase 3 clinical trials and, as such, is very much welcome, helping to avoid repeat, stand-alone trials in Japanese patients that are often underpowered. However, the guideline raises a concern regarding the consistency of outcomes in the subset of Japanese patients and the total trial population and offers two alternative criteria to determine the fraction of Japanese patients that should be recruited. The first criterion requires that sufficient Japanese patients are entered such that, if the treatment effects in the Japanese and overall populations are truly the same, there is an 80% chance that the effect in Japanese patients will be shown to be at least half of the effect in the total trial population. The second criterion requires that sufficient patients be entered per geographical region included in the trial such that, if there is a true effect in the overall population, the probability that each region (including Japan) will also show a positive effect is 80%. The purpose of this article is to explore the implications of these criteria in terms of overall power and the fraction of the Japanese patients that need to be recruited to satisfy them and to consider some potential alternative criteria that might offer advantages over those stated in the guideline.

Sampling inspection is implemented to ensure the quality of a biological product before its release to the market. However, the existing procedures in sampling inspection for lot release focus on the manufacturer’s risk. If both risks are accounted for, a much larger sample size would be required under certain circumstances. Sometimes the sample size might be too large to be implemented in practice. This article first illustrates the sampling process using the American National Standard, and then proposes a multiple-stage sampling procedure for lot release with control of both manufacturer’s and consumer’s risks at prespecified levels. Examples are presented to illustrate the use of the proposed procedure. Issues for lot release and the use of different sampling procedures are discussed.

It is important to calculate the proper sample size for a thorough QTc study to ensure adequate study power without enrolling unnecessary subjects. In current practice, at least two tasks need to be performed to rule out clinically relevant QT liability of the study drug: (a) demonstrate that the largest 90% two-sided upper confidence bound for the baseline-adjusted mean differences between the study drug and the placebo is less than 10 ms; and (b) establish assay sensitivity of the study. Traditionally, the sample size is determined by the primary task (a), and then subjects are equally assigned into each treatment arm. This practice might not be the most appropriate method. In this article, an optimal sample size allocation scheme is introduced and discussed.

In the development of acute migraine treatments, traditional phase 2 dose-finding trial designs are particularly challenging when a wide dose range needs to be investigated. In this article, an adaptive two-stage dose-finding design is introduced. The proposed design combines traditional phase 2a and 2b to serve the dual purpose of proof of concept and dose finding through the use of an unblinded interim analysis that provides an opportunity for adaptation. The design has a fixed total sample size but includes provisions for discontinuation of less effective doses at the interim analysis to allow for the allocation of patients into a more promising range of doses. The interim adaptation is designed to increase the amount of information collected on more effective doses and increase study power as compared to a traditional nonadaptive dose-finding design. On the other hand, despite the interim look and adaptation of the design, conventional statistical analyses of the final data can still be used for the final analysis and provide proper inferences with adequately controlled type I error and an ignorable amount of bias.

In clinical development of a test treatment, clinical trials are usually conducted to collect data for evaluation of safety and efficacy of the test treatment under investigation. To provide accurate and reliable assessment, well-controlled clinical trials under valid study designs are necessarily conducted. The clinical trial process is lengthy and costly, consisting of protocol development, trial conduct, data collection, statistical analysis and interpretation, and reporting. In practice, some controversial issues are commonly encountered regardless of compliance with good clinical practice. These issues include, but are not limited to, statistical hypotheses for clinical evaluation, instability of classical sample size calculation, integrity of blinding, clinical strategy for endpoint selection, impact of protocol amendments, flexibility and feasibility of adaptive design methods, multiplicity in clinical trials, and independence of data monitoring committees. In this article, these issues are briefly outlined. The impact of these issues on the evaluation of the safety and efficacy of the test treatment under investigation is assessed and discussed with examples whenever applicable. Recommendations regarding possible resolutions of these issues are also provided whenever possible.

Bioequivalence for different formulations of inhaled drugs poses special problems that require clinical studies in patients. 1 argue that these should contain multiple doses per formulation and derive a simple formula for the calculation of sample size for such studies.

We evaluate the probability of observing consistent results and the relationships between the required sample size and the effect size for a confirmatory multiregional trial. Three methods are evaluated, including two methods (methods 1 and 2) already proposed by the Ministry of Health, Labor and Welfare in 2007 and a new method proposed to confirm the ratio of one region to the other regions of the true treatment effect in a multiregional trial. We discuss method 1 and a new method with a survival endpoint and method 2 with a normal endpoint using numeric equations and simulations. We show that the probability of observing consistent results is not related to the effect size and the conditional probability is slightly superior to the unconditional one in both method 1 and the new method. We conclude that the probability of observing consistent results with the new method decreases according to the increase of the number of regions in method 1 previously proposed. Nonetheless, the slight difference betwee...

We propose a sample size calculation approach for the estimation of sensitivity and specificity of diagnostic tests with multiple observations per subjects. Many diagnostic tests such as diagnostic imaging or periodontal tests are characterized by the presence of multiple observations for each subject. The number of observations frequently varies among subjects in diagnostic imaging experiments or periodontal studies. Nonparametric statistical methods for the analysis of clustered binary data have been recently developed by various authors. In this paper, we derive a sample size formula for sensitivity and specificity of diagnostic tests using the sign test while accounting for multiple observations per subjects. Application of the sample size formula for the design of a diagnostic test is discussed. Since the sample size formula is based on large sample theory, simulation studies are conducted to evaluate the finite sample performance of the proposed method. We compare the performance of the proposed sample size formula with that of the parametric sample size formula that assigns equal weight to each observation. Simulation studies show that the proposed sample size formula generally yields empirical powers closer to the nominal level than the parametric method. Simulation studies also show that the number of subjects required increases as the variability in the number of observations per subject increases and the intracluster correlation increases.

When designing a clinical trial, a number of design features including the sample size have to be decided upon. The sample size calculation usually requires some discussion of relevant effect sizes and information about nuisance parameters such as standard deviations or overall event rates, with nuisance parameters being estimated from previous studies. Using a novel endpoint or moving into a new indication, no or only very limited information might be available and the sample size calculation is therefore subject to considerable uncertainty. Internal pilot study designs that allow sample size reestimation midcourse of the ongoing study have been proposed to make trials more robust to misspecifications of nuisance parameters in the planning phase. In this article we present the design of a recently completed randomized active controlled trial in dermatology as a case study. Furthermore, we demonstrate how type I error rate control can be achieved when testing for noninferiority and explore operating characteristics such as power and sample size distributions through simulations motivated by the case study. Finally, relevant regulatory guidelines on sample size reestimation are referred to.

The adaptive group sequential design of Lehmacher and Wassmer allows fully flexible redetermination of sample size after each of a predetermined number of interim looks. Study 02CLLIII, a large, randomized, multicenter trial in chronic lymphocytic leukemia, was based on this approach, with five planned analyses. The study terminated for efficacy at the third interim analysis. While it was clear how statistical significance was to be determined, calculations of proper P values as well as point and interval estimates turned out to be much less straightforward. We extend existing analysis approaches to the stratified binary and time-to-event data from this trial, investigate the properties of the estimators for the primary endpoint, and highlight remaining issues with full statistical inference after such a design. In conclusion, the flexibility offered by the adaptive features renders statistical inference more difficult and less precise. We believe that there are situations where it may be worth paying this price.

Multiregional clinical trials (MRCTs) present great opportunities but also challenges to the trial community. To address the challenges and fully realize the opportunities, a PhRMA MRCT Cross-Functional Key Issue Team (KIT) was formed in 2008. One of the work streams within the KIT particularly focuses on the assessment of consistency of treatment effects across regions. As the main objective of this work stream, this research explores a number of definitions for consistency assessments. We address the issues primarily for superiority trials with continuous endpoints, then extend briefly to noninferiority trials, random effect models, binary endpoints, and survival endpoints. Computations and simulations are used to study the properties of the proposed definitions, particularly the power for showing consistency. To illustrate applications of the methods, we use a trial example with a continuous endpoint. We discuss considerations for trial design as well as for data analysis. The consistency assessment relies heavily on the definition of regions and the number of regions. We recommend working with health authorities to define region in a manner that is sensible from a practical interpretation standpoint and also makes region consistency assessment a feasible undertaking.

Modern drug development requires an efficient clinical development program to have a reasonable chance of successfully leading to the submission of the therapy, given that the therapy is effective, or to early stopping if this is not the case. Clinical trials and programs should be designed to effectively support this final goal. Currently, the statistical planning in drug development is based on parts of a clinical program in isolation, conditioned on one fixed setting, focusing on sample size calculation or simple design questions. There is, however, an increasing demand for a clinical program optimization and acceleration as well as an unconditional evaluation of relative program efficiency, robustness, and validity. The complexity of the development process, however, often does not allow for simple solutions, frequently requiring computer simulations to support these assessments. We propose a general framework for comparing competing options for clinical programs, trial designs, and analysis methods as a basis for decision making and to facilitate the internal and external dialogue with key stakeholders. The final decision making ultimately needs to factor in quantitative aspects as well as additional qualitative dimensions such as logistic feasibility, regulatory acceptance, and so on. A terminology is introduce that clearly describes the different aspects of such a framework, the range of underlying assumptions, the competing options, and the metrics that are used to assess and compare these options. Three specific case studies are presented that illustrate these concepts at three different levels: program planning, trial design, and analysis methods.

With the passage of the Food and Drug Administration Amendments Act of 2007 (FDAAA), greater emphasis has been given to evaluating Risk Evaluation and Mitigation Strategies (REMS) and the tools used to mitigate risks. The FDAAA requires tool evaluation as part of even a minimal REMS, to be repeated at 1.5, 3, and 7 years after program implementation. Sponsors and FDA have become more concerned that the studies used to evaluate REMS interventions be sufficient in size and scope and fairly pose questions to people who prescribe, dispense, and use the drug and biological products evaluated. This article discusses several important issues in the design of survey evaluations such as: (1) identifying the survey sample and administrating the survey, (2) determining and justifying the sample size, (3) focusing survey questions on topics of need and of interest, and (4) how to design questionnaires to minimize bias and provide useful and actionable information.

A predictive marker is a marker that predicts the differential efficacy of a particular therapy based on marker status. Standard statistical methods compare treatments, not validate prediction. We propose a failure-time mixture model that achieves both objectives. We also explain how to evaluate efficacy in biomarker subpopulations. We use the maximum likelihood method to estimate the mixture model. We explain the computational aspects of the model and discuss the underlying statistical inference. We discuss sample size determination. We illustrate the methodology with a computer-generated data set The proposed mixture model is simple and capable of assisting investigators seeking to design marker-based clinical trials in their analyses.

Given the general difficulty of working out an exact answer or a good approximation algebraically, it would be useful to have an alternative approach that is simple to use to estimate the sample size of study planning. With the speed of modern computers it is now feasible to replace approximations with algorithm methods. The method that we introduce in this article is an extremely powerful tool that is used internally by a computer program to calculate the sample sizes of various tests.

The typical pivotal experimental therapeutic study design in multiple sclerosis (MS) is a randomized, double-blind, placebo-controlled clinical trial with clinical primary outcomes. In earlier phase studies, primary endpoints are often not clinical and typically include changes in magnetic resonance imaging (MRI) parameters, such as the cumulative number of new gadolinium-enhanced lesions over six months of treatment. In this article, we compare two trial designs—a group sequential method and an adaptive method—with respect to differences in power level and required sample size to those of a classical one-stage study design without interim analysis. The results of a simulation study based on pooled MRI data from a large number of clinical MS trials show that using a group-sequential design provides a significant reduction in required sample size compared with the classical one-stage design. If the observed treatment effect on study is smaller than the assumed one, the power of the adaptive method is larger than in the classical approach.

Pharmaceutical development is a risky, complex, costly, and time-consuming endeavor. More than half of development duration is spent in clinical trials. Despite the large number of potential candidates available and the lengthy process of clinical development, the success rate is disappointing. Hence, there is an urgent need for new strategies and methodology for efficient and cost-effective designs to screen potential candidates based on the idea of the proof of the concept for efficacy in a rapid and reliable manner to minimize the total sample size and hence to shorten the duration of the trials. In this article, a two-stage screening design based on continuous efficacy endpoints is proposed. The proposed two-stage screening designs minimize the expected sample size if the new candidate has low efficacy activity subject to the constraint upon the type I and type II error rates. In addition, two-stage screening designs that minimize the maximum sample size (minimax) are presented. Tables of two-stage and minimax designs for various combinations of design parameters are also provided. Applications to the phase 1 and 2 stages of clinical development are illustrated.

Sample size software is readily available for many univariate statistical procedures that involve one dependent variable per subject However, power analysis is less available for designs with repeated measures, particularly for repeated binary outcome variables. Repeated measurement studies usually involve missing data and serial correlations within each subject. As a consequence, generalized estimating equation (GEE) models, which do not require complete data for all subjects and which do not depend on the restrictive “symmetry assumption,” are being increasingly recommended for the evaluation of treatment effects in controlled clinical trials. GEE has been widely used to examine whether the rates of changes are significantly different between groups due to its robustness to misspecification of the true correlation structure and randomly missing data. We illustrate how the sample size can be estimated in detail through examples and also present the effect of dropouts in the sample size estimate for the repeated binary outcomes. In the presence of dropouts, it is suggested to estimate the sample size using the closed form formula provided in this article instead of adjusting the sample size estimate by dividing the sample size estimate obtained under no missing data by the proportions of completers.

The desire to make valuable medicines available to patients globally at approximately the same time has led many pharmaceutical sponsors to consider conducting multiregional trials. In this article, we propose an approach to rationalize partitioning the total sample size among the constituent regions in a confirmatory multiregional trial. Our approach is to find the minimal sample size for the smallest region so that there is a high probability of observing a consistent trend in the estimated treatment effect across regions if the treatment effect is positive and uniform across regions. We investigate this probability in two ways, namely, unconditional and conditional on the overall treatment effect being statistically significant. In the case of three regions, the proportion of patients from the smallest region could be as low as 15% to have an 80% probability that the observed treatment effects are consistent across the three regions, conditional on concluding a statistically significant overall treatment effect.

Fisher’s (protected) least significant difference (LSD) procedure has been suggested in the design and analysis of multiarm clinical trials with survival endpoints. In this article, the power of this procedure is evaluated and compared with that of Bonferroni and Hochberg procedures by Monte Carlo simulations under three scenarios of alternative hypothesis encountered in three arm clinical trials with survival endpoint. The approach of sample size calculation based on the power of a global test in the first step of Fisher’s LSD procedure is also evaluated and contrasted with that based on Bonferroni adjustment. It is shown that Bonferroni and Hochberg procedures are more powerful than Fisher’s LSD procedure when two specific pair-wise comparisons are of interest, while Fisher’s LSD procedure is the most powerful if all three pairwise comparisons are performed. It is recommended that the formula of Makuch and Simon be used in the sample size calculations for all three types of alternative hypothesis considered in this article. However, the Hochberg procedure should be used in the analysis if only two specific pairwise comparisons are of interest and the Fisher’s LSD procedure should be used in the analysis when objective of the trial includes all of three pairwise comparisons.

Clinical and experimental studies show that differences exist in cardiac electrophysiology between women and men, especially in electrocardiographical patterns of ventricular repolarization. We examined the variability of QT intervals from two thorough QT/QTc clinical studies, one conducted in a male population and one conducted in a female population. The results show variability differences in QT measurements between males and females, with females having larger intersubject and intrasubject variability than males. This article presents those results as well as discusses the implications for sizing thorough QT/QTc studies when studies include a mixture of men and women.

This article discusses an evaluation method of reliability regarding the overall ratings of ordinal scales by multiple raters (k ≥ 3). It is shown that when the sample size (n) is large enough compared with the number of raters (n >> k), both the simple mean Fleiss-Cohen-type weighted kappa statistics averaged over all pairs of raters and the Davies-Fleiss-Schouten-type weighted kappa statistics for multiple raters are approximately equivalent to the intraclass correlation coefficient (ICC) obtained by assigning the integer (natural number) scores for ordinal scales. These kappa statistics and the corresponding ICCs are illustrated in the overall ratings independently given by the three raters from some diagnostic agents studies for magnetic resonance imaging. Both fixed and random effects for raters are discussed and some comparative methods between treatment groups (test and reference) are proposed with an interpretation of the reliability for the overall ratings in the ordinal scale.

In this article, the label comprehension and actual use studies that may be required for an over-the-counter new drug regulatory submission are introduced. Design for these studies and statistical issues are described. Because confidence interval is a tool that plays a central role in these studies, information needed and appropriate sample size estimation approaches are discussed. Carefully designed and analyzed studies would enhance their success rate and provide more useful information from the studies.

Interim analyses, commonly applied in clinical trials, are rarely used in the nonclinical field, although they are potentially useful for ethical and practical reasons. The purpose of our work was to evaluate the benefits of such analyses in the discovery area, with the aim of reducing sample size. Following a literature review, we focused on the Bauer and Kohne method (Biometrics 1994) because it allows early stopping in favor of H0 and H1 in either one-or two-sided situations. Moreover, as the methodology is based on Fisher combination of P values, it can be applied to any selected statistical test. Early stopping requires the selection of two interdependent parameters: α0 and α1 (thresholds for early stop in favor of H0 and H1, respectively) while controlling the type I error rate. The efficiency of the several-stage design compared to the single-analysis design was investigated using simulations based on realistic characteristics of the preclinical area: small sample sizes, low expected proportions of active compounds in screening process, and large effect sizes. The assessment criteria were (1) the sample size gain compared to the single-analysis design at fixed power and (2) the proportions of early stops in favor of H0 and/or H1. In addition, the simulations allowed the determination of optimal values for α0 and α1. Results obtained in one-and two-sided situations in the case of a two-group comparison using a two-stage design are presented and illustrated in an application. Our first results led, within a relatively simple framework, to the conclusion that although appealing, interim analyses have a smaller application potential in terms of sample size reduction in the nonclinical field than initially expected.

In recentyears, the Westernization of traditional Chinese medicine (TCM) has attracted much attention in pharmaceutical research and development. One of the key issues in Westernization of TCM is how to conduct a scientifically valid clinical trial to evaluate safety and effectiveness of the TCM under investigation. A typical approach is to conduct a clinical trial the Western way by ignoring the fact that there are fundamental differences between a TCM and a West-em medicine intended for the same indication. These fundamental differences include (1) medical theory/mechanism and practice (ie, the concept of global dynamic balance/harmony among organs of the body versus local site of action); (2) techniques for diagnosis (ie, subjective diagnosis of inspection, auscultation and olfaction, interrogation, pulse taking and palpation versus objectively clinical evaluation); and (3) treatment (ie, personalized flexible dose of multiple components versus fixed dose). In this article, some practical issues, including validation of a quantitative instrument, the use of matching placebo, and sample size calculation when conducting a TCM clinical trial are discussed. We also discuss strategy for statistical quality control (QC) for raw materials, in-process materials or final product in terms of testing for consistency, stability analysis for estimation of drug expiration dating period, and regulatory requirements for future TCM research and development.

In clinical trials, data quality is one of the key factors in determining the success or failure of a drug development program. Data audit is an important step in assessing and ensuring the quality of clinical databases. However, despite the availability of many sophisticated statistical methodologies in analyzing clinical data, there are few data audit methods that are both efficient and statistically sound. A frequent method is auditing data for a fixed percentage of the subjects in a clinical study. Such a method either wastes too many resources or lacks statistical rigor in determining the quality status of a database. In this article, we give a short review of some recent developments and provide an example of database audit strategy. The methodology was developed for, and applied to, a real clinical study. Such a method is both statistically sound and efficient in saving resources needed for the conduct of the audit.

The aim of this paper is to discuss a behavioral Bayes approach to the question of the size of a clinical trial. The optimal size is obtained by maximizing the expected net benefit function, which is the expected benefit from subsequent use of the new treatment minus the cost of the trial. Aplausible model for thenumber of subsequent users of thenew treatment is introduced.

Despite best efforts, some crucial information used to design a confirmatory trial may not be available, or may be available but with a high degree of uncertainty, at the design stage. When this happens, it may be prudent to check the validity of those assumptions using interim data from the study and make midcourse adjustment if necessary. One such adjustment is to modify the sample size. In this article, we focus on sample size reestimation (SSR) for phase III and IV studies. The discussion is relevant to both continuous and binary endpoints even though the basis for SSR might differ for those two cases. We review commonly used approaches to adjust sample size and provide recommendations on how SSR should be implemented to achieve the objectives and maintain the integrity of the trial. The recommendations cover scientific, procedural, and logistic considerations.

A statistical problem of primary interest in a thorough QT/QTc study is that of deciding if a drug is noninferior to placebo in terms of QT/QTc prolongation. A standard way of approaching this problem is to construct a 90% two-sided (or a 95% one-sided) confidence interval, using the t distribution, at each time point in the study for the difference in mean QTc between drug and placebo and to conclude that the drug is noninferior to placebo if the upper end points of all of these confidence intervals is less than a prespecified constant, such as 10 ms. Under standard normality assumptions, this procedure corresponds to both an intersection-union test and the likelihood ratio test of size .05. It is not without its drawbacks, however. It is conservative in that the probability of a type I error may be smaller than the intended level .05. It is also biased, which means that the power function, for some values of parameters in the alternative space, takes values less than .05. The May 12, 2005, draft of the International Conference on Harmonisation E14 guidance states: “a negative ‘thorough QT/QTc study’ is one in which the upper bound of the 95% one-sided confidence interval for the largest time-matched mean effect of the drug on the QTc interval excludes 10 ms.” In this article, we show how an approximate confidence interval can be constructed for the largest difference in population mean QT/QTc between drug and placebo. The interval is approximate in the sense that, as sample sizes increase, the asymptotic probability of coverage is at least as large as intended. The results of simulations on a proposed one-sided 95% confidence interval are provided and discussed. Situations in which this interval works well, and does not work well, are delineated.

For some disorders such as irritable bowel syndrome, symptoms may wax and wane with variable periodicity. In clinical practice, treatment is usually targeted at symptom reduction during exacerbations. The management of such patients will likely involve intermittent courses of therapy tailored to the patient’s individual symptom pattern instead of chronic, uninterrupted treatment. Three study designs to assess the feasibility and efficacy of repeated drug treatment in patients with irritable bowel syndrome are discussed. The first design is a parallel group design in which patients, after the initial treatment period, may repeatedly receive the same treatment as in the first period (test drug or control). In the second design, patients who respond favorably to initial treatment with a test drug and whose symptoms recur when this treatment is stopped will be randomly assigned to receive the test drug or control in a second period. The third design has in addition a control group in the initial period. The three designs are compared regarding analysis and sample size.

We evaluate the performance of two commonly used methods to construct confidence intervals for noninferiority decisions when the primary end point is binary. The two methods are the classical asymptotic normal approximation procedure and the same procedure with the Hauck-Anderson type of continuity correction. Simulations were conducted to explore the rate of erroneously concluding noninferiority when the new treatment is worse than the active control by the amount defined by the noninferiority margin. The evaluation was conducted with sample sizes relevant to the confirmatory trials. Based on the findings from the simulations, we provide some practical guidance to individuals responsible for the analysis of such trial data.

Identifying causal relationships between drugs and rare but serious/irreversible adverse events is an increasingly important issue in postmarketing studies. The observational cohort study is among the most rigorous and appropriate class of designs when it is unfeasible to conduct prospective, randomized clinical trials. A new class of hybrid designs is described in this article; this class uses external data such as established databases or pre-NDA (New Drug Application) data. These designs are intended to achieve the ideal of detecting associations between the drug and rare adverse events and have a moderate sample size requirement to reach safety decisions more quickly. A new sample size formula based on the Poisson distribution is developed for a design in which the incidence of adverse events for subjects treated with the compound is compared to an external control cohort not receiving the compound under study. The results provide direct evidence for a reduction in sample size with the incorporation of external controls.

Population pharmacokinetic studies with a single sampling design such as single-trough sampling have been frequently conducted in Japan, often with little statistical consideration to the sampling design as well as to the sample size. When pharmacokinetic parameters obtained by population pharmacokinetic analysis are used for comparing pharmacokinetic profiles between regions/populations, the difference may be overlooked for lack of power. To point out such problems in the current practice of population pharmacokinetic studies in Japan, we investigated the relationship between the sampling schedule and the necessary sample size to detect a difference of parameters between regions/populations with predefined power by simulation using a simple pharmacokinetic model. The result indicates that it is difficult to obtain enough power in studies with a single sampling design even when the number of subjects is 300 per group because the variances of the estimated parameters are too large. Also, the power is influenced by the sampling schedule as well as the kind of pharmacokinetic parameters for evaluation. In designing population pharmacokinetic studies, especially for those that are conducted to obtain confirmative information on pharmacokinetic parameters, it would be crucial to examine prospectively the suitable sampling design as well as the necessary sample size.

Flexible designs with adaptive interim analyses allow a data-driven modification of basic design features while controlling the prespecified type I error rate. For example, an adaptation of the initially planned sample size based on the observed treatment effect and/or variability is possible, as well as an alteration of the number and timing of planned interim analyses, selection of doses or early stopping of treatment groups in multi-armed trials, or a change of the test statistic prespecified for the analysis. Recently, a multiple test procedure has been proposed which enables a modification of the initially specified hypotheses structure for confirmatory analysis. In this case, the initially fixed order of hypotheses can be altered on the basis of the results of an interim analysis. In a Monte Carlo study, the power performance of the proposed procedure of adaptively changing the hierarchy of hypotheses is compared with alternative testing strategies that do not change the initially specified structure of the hypotheses. Our investigations indicate that imposing a hierarchy of hypotheses and relying on the option for an adaptation may be an inefficient strategy if ordering is not done due to clinical importance but according to expectations about the statistical significance of the results. Alternatively, multiple test procedures that do not require an a priori order may be applied.

Through a combination of bad luck and possibly selection bias, imbalances in prognostic baseline variables across treatment groups have plagued many randomized clinical trials. It is common, in practice, to test for imbalances and adjust for variables observed to be sufficiently unbalanced at baseline. Yet, the literature condemns these practices on the grounds that imbalances are necessarily random when observed in the context of a randomized trial (hence, testing is illogical), and suggests that all prognostic covariates, unbalanced or not, should be included in the model used for analysis. When there are a large number of covariates relative to the sample size, decisions need to be made regarding which covariates to actually include in a suitably parsimonious model. Proponents of the approach to model-building by testing for baseline imbalances might suggest reaching these decisions by considering the degree of imbalance of each covariate; those that criticize this approach might instead consider the ability of the covariate to predict the outcome of interest. Some hybrid approaches have been explored as well. We introduce a criterion that allows for the specification of an optimal hybrid approach.

Clinical trial databases are usually audited prior to database lock to assure that the data meet certain desired quality levels. The audit can be conducted based on either all data items in the database or samples of data items. If samples of data items are audited, issues of type I and type II errors arise and sample size determination becomes crucial in controlling these errors. In this paper, we discuss the statistical issues relating to data audit, focusing on how to control type I and type II errors. Formulas for sample size determination are proposed, procedures for conducting data audit are recommended, and different sampling schemes are discussed.

In a conventional randomized trial, the assignment of a patient to receive a treatment after obtaining the patient’s consent may completely depend on a chance mechanism. Thus, neither the patient nor the physician know exactly which treatment the patient will receive at the time of consent. This can compromise the relationship between the patient and the physician. To alleviate this concern, Zelen proposes use of a double consent randomized design, in which we ask each patient for consent after random assignment of patients to treatments. This paper discusses sample size calculation for the double consent randomized design. Because the variance of the test statistic used to derive the required sample size depends upon the null and alternative hypotheses, this paper derives three approximate sample size formulae. The first two formulae tend to provide a lower and an upper limit of the required sample size, and the third one, a simple average of these two formulae, attempts to provide a better approximation. This paper further employs Monte Carlo simulation to evaluate the performance of these approximate sample size formulae with respect to type I error and power. Finally, to help readers employ the results discussed here, tables that summarize the estimated required sample size in a variety of situations are provided.

An interim analysis for sample size re-estimation is often carried out in a clinical trial when there is concern about the uncertainty of the estimate of variability used for the prestudy sample size estimation. The use of an unblinded third party to do the interim analysis instead of conventional blinded methods may be possible and may lead to the desired power for the study being more likely to be achieved. An example of a clinical trial where the unblinded, third-party approach was used is described. For the interim results obtained, the decision not to increase the sample size would also have been reached had the project team used either of two commonly adopted blinded sample size re-estimation methods. However, simulation results from some plausible alternative scenarios based on the example show that an unblinded, third-party interim analysis for sample size re-estimation can provide more accurate results than the two blinded methods.

It is common to assume a constant cluster size in the estimation of sample size for cluster randomized trials. Manatunga et al. (1) derived sample size estimation for continuous response variables in cases of varying cluster size. This paper discusses a parallel study for binary response variables. We compare the maximum cluster size method, the average cluster size method, and the proposed method.

Medical device companies report the performance of their products through actuarial survival curves. Analyses are based on “passive” databases. For pacemakers, a significant number of explanted devices may not be reported to manufacturers. Thus, expiant information is lost. High rates of underreporting of failures could result. Therefore, performance curves could indicate better survival rates than those that are actually occurring. Samples of closely-followed patients called active samples are used to adjust survival curves for underreported failures. Through simulations, this paper shows a need for a larger sample size for active components and what degree of underreporting failures would be necessary to assure better estimates using adjustments rather than estimates that ignore adjustments. The issues in this paper have a much broader context as pharmaceutical companies increasingly rely on medical devices to monitor patients ’ health or deliver drugs. This can also apply to survival cunes for adverse events in Phase 4 clinical trials.

In this paper we discuss a behavioral Bayes approach to the sample size question in clinical trials with binary responses for which the central limit theorem cannot be applied to provide an adequate approximation of the size of a trial. A fully Bayesian framework is considered. The optimal sample size is obtained by maximizing the expected net benefit, which is the benefit from subsequent use of the new treatment under consideration minus the cost of the trial. The regulatory requirements for granting a licence to the new treatment are discussed. It is shown, not surprisingly, that the optimal sample size depends strongly on the expected benefit from a conclusively favorable outcome, and on the strength of the evidence required by the regulator. Conventional approaches to the question ignore the trade-off between costs and benefits.

This paper describes an approach to performing interim sample size reestimation based on the observed treatment difference in clinical trials. The approach combines the advantages of the group sequential and sample size reestimation methods and provides an efficient design for clinical trials. It provides flexibility but still maintains the integrity of the trial. To control the overall type I error level, a method is proposed to adjust the group sequential stopping boundaries adjusted for sample size reestimation and negative stops. The adjusted stopping boundaries are flexible to different rules of sample size reestimation and reuse the alpha values saved by negative stops. The adjustment is based on the exact type I error change and, therefore, the penalty for the type I error inflation due to such an interim reestimation is kept to a minimum. The efficiency of sample size reestimation without positive stops is compared with the group sequential method using unconditional power and expected sample size. All results are based on sufficient mathematical justifications.

At the design phase of a clinical trial the total number of participants needed to detect a clinically important treatment difference with sufficient precision frequently depends on nuisance parame...

To overcome the problem of uncertainty in the planning phase of clinical trials, study designs have been proposed that allow for mid-course reestimation of the sample size. Using a study in asthma patients, we illustrate how blind sample size adjustment can be performed in an equivalence trial. Thereby, we demonstrate how the type I error rate can be controlled. Further, we show that the well-known expectation-maximization algorithm-based procedure by Gould and Shih is inappropriate for the purpose of sample size reestimation.

The determination of the appropriate sample size is an important aspect of planning a clinical trial. In recent years, procedures for estimation of a nuisance parameter to adjust the sample size if necessary have been examined. Here, it is assumed that the clinical trial is conducted for the comparison of two treatments, where the observations are assumed to have normal distributions with a common unknown variance. For sample size determination, the variance is assumed known and the resulting sample size is sensitive to misspecification of the variance. An estimate of the variance, obtained while the clinical trial is ongoing, can often be used to assess the appropriateness of the assumed variance. The use of a blinded estimate of the variance to potentially adjust the sample size is examined.