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In this work a new metric of surrogacy, the so-called individual causal association (ICA), is introduced using information-theoretic concepts and a causal inference model for a binary surrogate and true endpoint. The ICA has a simple and appealing interpretation in terms of uncertainty reduction and, in some scenarios, it seems to provide a more coherent assessment of the validity of a surrogate than existing measures. The identifiability issues are tackled using a two-step procedure. In the first step, the region of the parametric space of the distribution of the potential outcomes, compatible with the data at hand, is geometrically characterized. Further, in a second step, a Monte Carlo approach is proposed to study the behavior of the ICA on the previous region. The method is illustrated using data from the Collaborative Initial Glaucoma Treatment Study. A newly developed and user-friendly R package Surrogate is provided to carry out the evaluation exercise., (© 2016, The International Biometric Society.)

Background: Composite endpoints (CEP), such as progression-free survival, are commonly used in cancer research. Notwithstanding their popularity, however, CEP analyses suffer from a number of drawbacks, especially when death is combined with a nonterminal event (ie, progression or recurrence), exemplifying the semicompeting risks setting. We investigated the semicompeting risks framework as a complementary analysis strategy that avoids certain drawbacks of CEPs., Methods: The illness-death model under the semicompeting risks framework was compared with standard analysis approaches: CEP analyses and (separate) univariate analyses for each component endpoint. Data from a previously published phase III randomized clinical trial in metastatic colon cancer including 1419 participants in the N9741 trial (conducted between 1997 and 2003) were used to determine the impact of the loss of information associated with combining multiple endpoints, as well as of ignoring the potentially informative role of death. A simulation study was conducted to further explore these issues., Results: Failure to account for critical features of semicompeting risks data can lead to potentially severely misleading conclusions. Advantages of semicompeting risks analyses include a clear delineation of treatment effects on both events, the ability to draw conclusions about a patient's joint risk of the two events, and an assessment of the dependence between the two event types., Conclusions: Embedding and analyzing component outcomes in the semicompeting risks framework, either as a supplement or alternative to CEP analyses, represents an important, underutilized, and feasible opportunity for cancer research., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

Multiplicity is common in clinical studies and the current standard is to use the familywise error rate to ensure that the errors are kept at a prespecified level. In this paper, we will show that, in certain situations, familywise error rate control does not account for all errors made. To counteract this problem, we propose the use of the expected number of false claims (EFC). We will show that a (weighted) Bonferroni approach can be used to control the EFC, discuss how a study that uses the EFC can be powered for co-primary, exchangeable, and hierarchical endpoints, and show how the weight for the weighted Bonferroni test can be determined in this manner. ©2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd., (©2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.)

Conventionally, adaptive phase II/III clinical trials are carried out with a strict two-stage design. Recently, a varying-stage adaptive phase II/III clinical trial design has been developed. In this design, following the first stage, an intermediate stage can be adaptively added to obtain more data, so that a more informative decision can be made. Therefore, the number of further investigational stages is determined based upon data accumulated to the interim analysis. This design considers two plausible study endpoints, with one of them initially designated as the primary endpoint. Based on interim results, another endpoint can be switched as the primary endpoint. However, in many therapeutic areas, the primary study endpoint is well established. Therefore, we modify this design to consider one study endpoint only so that it may be more readily applicable in real clinical trial designs. Our simulations show that, the same as the original design, this modified design controls the Type I error rate, and the design parameters such as the threshold probability for the two-stage setting and the alpha allocation ratio in the two-stage setting versus the three-stage setting have a great impact on the design characteristics. However, this modified design requires a larger sample size for the initial stage, and the probability of futility becomes much higher when the threshold probability for the two-stage setting gets smaller. Copyright © 2016 John Wiley & Sons, Ltd., (Copyright © 2016 John Wiley & Sons, Ltd.)

Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness-death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure., (© 2016 American Heart Association, Inc.)

Nowadays, two main frameworks for the evaluation of surrogate endpoints, based on causal-inference and meta-analysis, dominate the scene. Earlier work showed that the metrics of surrogacy introduced in both paradigms are related, although in a complex way that is difficult to study analytically. In the present work, this relationship is further examined using simulations and the analysis of a case study. The results indicate that the extent to which both paradigms lead to similar conclusions regarding the validity of the surrogate, depends on a complex interplay between multiple factors like the ratio of the between and within trial variability and the unidentifiable correlations between the potential outcomes. All the analyses were carried out using the newly developed R package Surrogate, which is freely available via CRAN., (Copyright © 2015 John Wiley & Sons, Ltd.)

Surrogate endpoint validation has been well established by the meta-analytical correlation-based approach as outlined in the seminal work of Buyse et al. (Biostatistics, 2000). Surrogacy can be assumed if strong associations on individual and study levels can be demonstrated. Alternatively, if an effect on a true endpoint is to be predicted from a surrogate endpoint in a new study, the surrogate threshold effect (STE, Burzykowski and Buyse, Pharmaceutical Statistics, 2006) can be used. In practice, as individual patient data (IPD) are hard to obtain, some authors use only aggregate data and perform simplified regression analyses. We are interested in to what extent such simplified analyses are biased compared with the ones from a full model with IPD. To this end, we conduct a simulation study with IPD and compute STEs from full and simplified analyses for varying data situations in terms of number of studies, correlations, variances and so on. In the scenarios considered, we show that, for normally distributed patient data, STEs derived from ordinary (weighted) linear regression generally underestimate STEs derived from the original model, whereas meta-regression often results in overestimation. Therefore, if individual data cannot be obtained, STEs from meta-regression may be used as conservative alternatives, but ordinary (weighted) linear regression should not be used for surrogate endpoint validation., (Copyright © 2015 John Wiley & Sons, Ltd.)

'Multistage testing with adaptive designs' was the title of an article by Peter Bauer that appeared 1989 in the German journal Biometrie und Informatik in Medizin und Biologie. The journal does not exist anymore but the methodology found widespread interest in the scientific community over the past 25 years. The use of such multistage adaptive designs raised many controversial discussions from the beginning on, especially after the publication by Bauer and Köhne 1994 in Biometrics: Broad enthusiasm about potential applications of such designs faced critical positions regarding their statistical efficiency. Despite, or possibly because of, this controversy, the methodology and its areas of applications grew steadily over the years, with significant contributions from statisticians working in academia, industry and agencies around the world. In the meantime, such type of adaptive designs have become the subject of two major regulatory guidance documents in the US and Europe and the field is still evolving. Developments are particularly noteworthy in the most important applications of adaptive designs, including sample size reassessment, treatment selection procedures, and population enrichment designs. In this article, we summarize the developments over the past 25 years from different perspectives. We provide a historical overview of the early days, review the key methodological concepts and summarize regulatory and industry perspectives on such designs. Then, we illustrate the application of adaptive designs with three case studies, including unblinded sample size reassessment, adaptive treatment selection, and adaptive endpoint selection. We also discuss the availability of software for evaluating and performing such designs. We conclude with a critical review of how expectations from the beginning were fulfilled, and - if not - discuss potential reasons why this did not happen., (© 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

A new three-arm parallel design was recently proposed to investigate the biosimilarity between a biological product and a reference product by using the relative distance. The purpose of this article is to extend their results to binary endpoints for three popular metrics: the risk difference, the log relative risk, and the log odds ratio. The relative distances based on the three metrics are defined, and corresponding test procedures are developed. The type I error rates and powers are investigated theoretically and empirically.

In this paper, we propose a design that uses a short-term endpoint for accelerated approval at interim analysis and a long-term endpoint for full approval at final analysis with sample size adaptation based on the long-term endpoint. Two sample size adaptation rules are compared: an adaptation rule to maintain the conditional power at a prespecified level and a step function type adaptation rule to better address the bias issue. Three testing procedures are proposed: alpha splitting between the two endpoints; alpha exhaustive between the endpoints; and alpha exhaustive with improved critical value based on correlation. Family-wise error rate is proved to be strongly controlled for the two endpoints, sample size adaptation, and two analysis time points with the proposed designs. We show that using alpha exhaustive designs greatly improve the power when both endpoints are effective, and the power difference between the two adaptation rules is minimal. The proposed design can be extended to more general settings., (Copyright © 2015 John Wiley & Sons, Ltd.)

When performing a pivotal clinical trial, it may be of interest to assess the probability of success (PoS) of that trial. Initially evaluated when the trial is designed, PoS can be updated as the trial progresses and new information about the drug effect becomes available. Such information can be external to the trial, such as results from trials conducted in parallel, or internal, such as continuing after an interim analysis. We develop a framework to update PoS based on such internal and external information for a time-to-event endpoint and illustrate it using a realistic development program for a new molecule.

In many randomized controlled trials, treatment groups are of equal size, but this is not necessarily the best choice. This paper provides a methodology to calculate optimal treatment allocations for longitudinal trials when we wish to compare multiple treatment groups with a placebo group, and the comparisons may have unequal importance. The focus is on trials with a survival endpoint measured in discrete time. We assume the underlying survival process is Weibull and show that values for the parameters in the Weibull distribution have an impact on the optimal treatment allocation scheme in an interesting way. Additionally, we incorporate different cost considerations at the subject and measurement levels and determine the optimal number of time periods. We also show that when many events occur at the beginning of the trial, fewer time periods are more efficient. As an application, we revisit a risperidone maintenance treatment trial in schizophrenia and use our proposed methodology to redesign it and compare merits of our optimal design., (Copyright © 2015 John Wiley & Sons, Ltd.)

Background: The assessment of treatment success in clinical trials when multiple (repeated) doses (courses) are involved is quite common, for example, in the case of infertility treatment with assisted reproductive technology (ART), and medical abortion using misoprostol alone or in combination with mifepristone. Under these or similar circumstances, most researchers assess success using binomial proportions after a certain number of consecutive doses, and some have used survival analysis. In this paper we discuss the main problems in using binomial proportions to summarize (the overall) efficacy after two or more consecutive doses of the relevant treatment, particularly for the case of misoprostol in medical abortion studies. We later discuss why the survival analysis is best suited under these circumstances, and illustrate this by using simulated data., Methods: The formulas required for the binomial proportion and survival analysis (without and with competing risks) approaches are summarized and analytically compared. Additionally, numerical results are computed and compared between the two approaches, for several theoretical scenarios., Results: The main conceptual limitations of the binomial proportion approach are identified and discussed, caused mainly by the presence of censoring and competing risks, and it is demonstrated how survival analysis can solve these problems. In general, the binomial proportion approach tends to underestimate the "real" success rate, and tends to overestimate the corresponding standard error., Conclusions: Depending on the rates of censored observations or competing events between repeated doses of the treatment, the bias of the binomial proportion approach as compared to the survival analysis approaches varies; however, the use of the binomial approach is unjustified as the survival analysis options are well known and available in multiple statistical packages. Our conclusions also apply to other situations where success is estimated after multiple (repeated) doses (courses) of the treatment.

Seamless phase II/III clinical trials in which an experimental treatment is selected at an interim analysis have been the focus of much recent research interest. Many of the methods proposed are based on the group sequential approach. This paper considers designs of this type in which the treatment selection can be based on short-term endpoint information for more patients than have primary endpoint data available. We show that in such a case, the familywise type I error rate may be inflated if previously proposed group sequential methods are used and the treatment selection rule is not specified in advance. A method is proposed to avoid this inflation by considering the treatment selection that maximises the conditional error given the data available at the interim analysis. A simulation study is reported that illustrates the type I error rate inflation and compares the power of the new approach with two other methods: a combination testing approach and a group sequential method that does not use the short-term endpoint data, both of which also strongly control the type I error rate. The new method is also illustrated through application to a study in Alzheimer's disease., (© 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Surrogate end point research has grown in recent years with the increasing development and usage of biomarkers in clinical research. Surrogacy analysis is derived through randomized clinical trial data and it is carried out at the individual level and at the trial level. A common surrogate analysis at the individual level is the application of the Prentice criteria. An approach for the evaluation of the Prentice criteria is discussed, with a focus on its most difficult component, the determination of whether the treatment effect is captured by the surrogate. An interpretation of this criterion is illustrated using data from a randomized clinical trial in prostate cancer., (© The Author 2015. Published by Oxford University Press on behalf of the European Society for Medical Oncology. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

It is plausible to assume that the treatment effect in a longitudinal study will vary over time. It can become either stronger or weaker as time goes on. Here, we extend previous work on optimal designs for discrete-time survival analysis to trials with the treatment effect varying over time. In discrete-time survival analysis, subjects are measured in discrete time intervals, while they may experience the event at any point in time. We focus on studies where the width of time intervals is fixed beforehand, meaning that subjects are measured more often when the study duration increases. The optimal design is defined as the optimal combination of the number of subjects, the number of measurements for each subject, and the optimal proportion of subjects assigned to the experimental condition. We study optimal designs for different optimality criteria and linear cost functions. We illustrate the methodology of finding optimal designs using a clinical trial that studies the effect of an outpatient mental health program on reducing substance abuse among patients with severe mental illness. We observe that optimal designs depend to some extent on the rate at which group differences vary across time intervals and the direction of these changes over time. We conclude that an optimal design based on the assumption of a constant treatment effect is not likely to be efficient if the treatment effect varies across time., (Copyright © 2015 John Wiley & Sons, Ltd.)

This paper deals with the analysis of data from a HET-CAM(VT) experiment. From a statistical perspective, such data yield many challenges. First of all, the data are typically time-to-event like data, which are at the same time interval censored and right truncated. In addition, one has to cope with overdispersion as well as clustering. Traditional analysis approaches ignore overdispersion and clustering and summarize the data into a continuous score that can be analysed using simple linear models. In this paper, a novel combined frailty model is developed that simultaneously captures all of the aforementioned statistical challenges posed by the data., (Copyright © 2015 John Wiley & Sons, Ltd.)

The success of a seasonal influenza vaccine efficacy trial depends not only upon the design but also upon the annual epidemic characteristics. In this context, simulation methods are an essential tool in evaluating the performances of study designs under various circumstances. However, traditional methods for simulating time-to-event data are not suitable for the simulation of influenza vaccine efficacy trials because of the seasonality and heterogeneity of influenza epidemics. Instead, we propose a mathematical model parameterized with historical surveillance data, heterogeneous frailty among the subjects, survey-based heterogeneous number of daily contact, and a mixed vaccine protection mechanism. We illustrate our methodology by generating multiple-trial data similar to a large phase III trial that failed to show additional relative vaccine efficacy of an experimental adjuvanted vaccine compared with the reference vaccine. We show that small departures from the designing assumptions, such as a smaller range of strain protection for the experimental vaccine or the chosen endpoint, could lead to smaller probabilities of success in showing significant relative vaccine efficacy., (Copyright © 2015 John Wiley & Sons, Ltd.)

In a clinical trial comparing two treatment groups, one commonly-used endpoint is time to death. Another is time until the first nonfatal event (if there is one) or until death (if not). Both endpoints have drawbacks. The wrong choice may adversely affect the value of the study by impairing power if deaths are too few (with the first endpoint) or by lessening the role of mortality if not (with the second endpoint). We propose a compromise that provides a simple test based on the time to death if the patient has died or time since randomization augmented by an increment otherwise. The test applies the ordinary two-sample Wilcoxon statistic to these values. The formula for the increment (the same for experimental and control patients) must be specified before the trial starts. In the simplest (and perhaps most useful) case, the increment assumes only two values, according to whether or not the (surviving) patient had a nonfatal event. More generally, the increment depends on the time of the first nonfatal event, if any, and the time since randomization. The test has correct Type I error even though it does not handle censoring in a customary way. For conditions where investigators would face no easy (advance) choice between the two older tests, simulation results favor the new test. An example using a renal-cancer trial is presented., (Copyright © 2015 John Wiley & Sons, Ltd.)

Background: The objective of phase II cancer clinical trials is to determine if a treatment has sufficient activity to warrant further study. The efficiency of a conventional phase II trial design has been the object of considerable debate, particularly when the study regimen is characteristically cytostatic. At the time of development of a phase II cancer trial, we accumulated clinical experience regarding the time to progression (TTP) for similar classes of drugs and for standard therapy. By considering the time to event (TTE) in addition to the tumor response endpoint, a mixed-endpoint phase II design may increase the efficiency and ability of selecting promising cytotoxic and cytostatic agents for further development., Methods: We proposed a single-arm phase II trial design by extending the Zee multinomial method to fully use mixed endpoints with tumor response and the TTE. In this design, the dependence between the probability of response and the TTE outcome is modeled through a Gaussian copula., Results: Given the type I and type II errors and the hypothesis as defined by the response rate (RR) and median TTE, such as median TTP, the decision rules for a two-stage phase II trial design can be generated. We demonstrated through simulation that the proposed design has a smaller expected sample size and higher early stopping probability under the null hypothesis than designs based on a single-response endpoint or a single TTE endpoint., Conclusions: The proposed design is more efficient for screening new cytotoxic or cytostatic agents and less likely to miss an effective agent than the alternative single-arm design.

The planning of an oncology clinical trial with a seamless phase II/III adaptive design is discussed. Two regimens of an experimental treatment are compared to a control at an interim analysis, and the most-promising regimen is selected to continue, together with control, until the end of the study. Because the primary endpoint is expected to be immature at the interim regimen selection analysis, designs that incorporate primary as well as surrogate endpoints in the regimen selection process are considered. The final testing of efficacy at the end of the study comparing the selected regimen to the control with respect to the primary endpoint uses all relevant data collected both before and after the regimen selection analysis. Several approaches for testing the primary hypothesis are assessed with regard to power and type I error rate. Because the operating characteristics of these designs depend on the specific regimen selection rules considered, benchmark scenarios are proposed in which a perfect surrogate and no surrogate is used at the regimen selection analysis. The operating characteristics of these benchmark scenarios provide a range where those of the actual study design are expected to lie. A discussion on family-wise error rate control for testing primary and key secondary endpoints as well as an assessment of bias in the final treatment effect estimate for the selected regimen are also presented., (Copyright © 2015 John Wiley & Sons, Ltd.)

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial., (Copyright © 2014 John Wiley & Sons, Ltd.)

The aim of phase II clinical trials is to determine whether an experimental treatment is sufficiently promising and safe to justify further testing. The need for reduced sample size arises naturally in phase II clinical trials owing to both technical and ethical reasons, motivating a significant part of research in the field during recent years, while another significant part of the research effort is aimed at more complex therapeutic schemes that demand the consideration of multiple endpoints to make decisions. In this paper, our attention is restricted to phase II clinical trials in which two treatments are compared with respect to two dependent dichotomous responses proposing some flexible designs. These designs permit the researcher to terminate the clinical trial when high rates of favorable or unfavorable outcomes are observed early enough requiring in this way a small number of patients. From the mathematical point of view, the proposed designs are defined on bivariate sequences of multi-state trials, and the corresponding stopping rules are based on various distributions related to the waiting time until a certain number of events appear in these sequences. The exact distributions of interest, under a unified framework, are studied using the Markov chain embedding technique, which appears to be very useful in clinical trials for the sample size determination. Tables of expected sample size and power are presented. The numerical illustration showed a very good performance for these new designs., (Copyright © 2014 John Wiley & Sons, Ltd.)

Background: Central to the design of a randomised controlled trial is the calculation of the number of participants needed. This is typically achieved by specifying a target difference and calculating the corresponding sample size, which provides reassurance that the trial will have the required statistical power (at the planned statistical significance level) to identify whether a difference of a particular magnitude exists. Beyond pure statistical or scientific concerns, it is ethically imperative that an appropriate number of participants should be recruited. Despite the critical role of the target difference for the primary outcome in the design of randomised controlled trials, its determination has received surprisingly little attention. This article provides guidance on the specification of the target difference for the primary outcome in a sample size calculation for a two parallel group randomised controlled trial with a superiority question., Methods: This work was part of the DELTA (Difference ELicitation in TriAls) project. Draft guidance was developed by the project steering and advisory groups utilising the results of the systematic review and surveys. Findings were circulated and presented to members of the combined group at a face-to-face meeting, along with a proposed outline of the guidance document structure, containing recommendations and reporting items for a trial protocol and report. The guidance and was subsequently drafted and circulated for further comment before finalisation., Results: Guidance on specification of a target difference in the primary outcome for a two group parallel randomised controlled trial was produced. Additionally, a list of reporting items for protocols and trial reports was generated., Conclusions: Specification of the target difference for the primary outcome is a key component of a randomized controlled trial sample size calculation. There is a need for better justification of the target difference and reporting of its specification.

Evaluation of surrogate end points using patient-level data from multiple trials is the gold standard, where multi-trial copula models are used to quantify both patient-level and trial-level surrogacy. While limited consideration has been given in the literature to copula choice (e.g., Clayton), no prior consideration has been given to direction of implementation (via survival vs. distribution functions). We demonstrate that even with the "correct" copula family, directional misspecification leads to biased estimates of patient-level and trial-level surrogacy. We illustrate with a simulation study and a reanalysis of disease-free survival as a surrogate for overall survival in early stage colon cancer.

For the statistical validation of surrogate endpoints, an alternative formulation is proposed for testing Prentice's fourth criterion, under a bivariate normal model. In such a setup, the criterion involves inference concerning an appropriate regression parameter, and the criterion holds if the regression parameter is zero. Testing such a null hypothesis has been criticized in the literature since it can only be used to reject a poor surrogate, and not to validate a good surrogate. In order to circumvent this, an equivalence hypothesis is formulated for the regression parameter, namely the hypothesis that the parameter is equivalent to zero. Such an equivalence hypothesis is formulated as an alternative hypothesis, so that the surrogate endpoint is statistically validated when the null hypothesis is rejected. Confidence intervals for the regression parameter and tests for the equivalence hypothesis are proposed using bootstrap methods and small sample asymptotics, and their performances are numerically evaluated and recommendations are made. The choice of the equivalence margin is a regulatory issue that needs to be addressed. The proposed equivalence testing formulation is also adopted for other parameters that have been proposed in the literature on surrogate endpoint validation, namely, the relative effect and proportion explained.

In an adaptive seamless phase II/III clinical trial interim analysis, data are used for treatment selection, enabling resources to be focused on comparison of more effective treatment(s) with a control. In this paper, we compare two methods recently proposed to enable use of short-term endpoint data for decision-making at the interim analysis. The comparison focuses on the power and the probability of correctly identifying the most promising treatment. We show that the choice of method depends on how well short-term data predict the best treatment, which may be measured by the correlation between treatment effects on short- and long-term endpoints.

This article deals with seven special issues related to the assumptions, applicability, and practical use of formulas for calculating power or sample size, respectively, for comparative clinical trials with time-to-event endpoints, with particular focus on the well-known Freedman and Schoenfeld methods. All problems addressed are illustrated by numerical examples, and recommendations are given on how to deal with them in the planning of clinical trials.

An analytical way to compute predictive probability of success (PPOS) together with credible interval at interim analysis (IA) is developed for big clinical trials with time-to-event endpoints. The method takes account of the fixed data up to IA, the amount of uncertainty in future data, and uncertainty about parameters. Predictive power is a special type of PPOS. The result is confirmed by simulation. An optimal design is proposed by finding optimal combination of analysis time and futility cutoff based on some PPOS criteria.

Surrogate endpoint validation for a binary surrogate endpoint and a binary true endpoint is investigated using the criteria of proportion explained (PE) and the relative effect (RE). The concepts of generalized confidence intervals and fiducial intervals are used for computing confidence intervals for PE and RE. The numerical results indicate that the proposed confidence intervals are satisfactory in terms of coverage probability, whereas the intervals based on Fieller's theorem and the delta method fall short in this regard. Our methodology can also be applied to interval estimation problems in a causal inference-based approach to surrogate endpoint validation.

In a clinical trial where several doses are compared to a control, a multi-stage design that combines both the selection of the best dose and the confirmation of this selected dose is desirable. An example is the two-stage drop-the-losers or pick-the-winner design, where inferior doses are dropped after interim analysis. Selection of target dose(s) can be based on ranking of observed effects, hypothesis testing with adjustment for multiplicity, or other criteria at interim stages. A number of methods have been proposed and have made significant gains in trial efficiency. However, many of these designs started off with all doses with equal allocation and did not consider prioritizing the doses using existing dose-response information. We propose an adaptive staggered dose procedure that allows explicit prioritization of doses and applies error spending scheme that favors doses with assumed better responses. This design starts off with only a subset of the doses and adaptively adds new doses depending on interim results. Using simulation, we have shown that this design performs better in terms of increased statistical power than the drop-the-losers design given strong prior information of dose response.

Background: There is interest in surrogate end points for clinical trials of chronic kidney disease progression because currently established end points-end-stage renal disease (ESRD) and doubling of serum creatinine level-are late events, requiring large clinical trials with long follow-up. Doubling of serum creatinine level is equivalent to a 57% decline in estimated glomerular filtration rate (eGFR). We evaluated type 1 error and required sample size for clinical trials using surrogate end points based on lesser eGFR declines., Study Design: Simulation study., Setting & Participants: Simulations evaluating 3,060 scenarios representative of 19 treatment comparisons in 13 chronic kidney disease clinical trials., Index Tests: Surrogate end points defined as composite end points based on ESRD and either 30% or 40% eGFR declines., Reference Test: Clinical outcome (ESRD) for type 1 error. Established end point (composite of ESRD and 57% eGFR decline) for required sample size., Results: Use of the 40% versus 57% eGFR decline end point consistently led to a reduction in sample size > 20% while maintaining risk for type 1 error < 10% in the presence of a small acute effect (<1.25mL/min/1.73m(2)) for: (1) 2-, 3-, or 5-year trials with a high mean baseline eGFR (67.5mL/min/1.73m(2)), and (2) 2-year trials with an intermediate mean baseline eGFR (42.5mL/min/1.73m(2)). Use of the 30% versus the 40% eGFR decline end point often led to moderately larger reductions in sample size in the absence of an acute effect, but not in the presence of acute effects., Limitations: The complexity of eGFR trajectories prevented evaluation of all scenarios for clinical trials., Conclusions: Use of end points based on 30% or 40% eGFR declines is an appropriate strategy to reduce sample size in certain situations. However, risk for type 1 error is increased in the presence of acute effects, particularly for 30% eGFR declines. The decision to use these end points should be made after thorough evaluation of their expected performance under the conditions of specific clinical trials., (Copyright © 2014 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.)

The use of surrogate endpoints is expected to play an important role in the development of new drugs, as they can be used to reduce the sample size and/or duration of randomized clinical trials. Biostatistical researchers and practitioners have proposed various surrogacy measures; however, (i) most of these surrogacy measures often fall outside the range [0,1] without any assumptions, (ii) these surrogacy measures do not provide a cut-off value for judging a surrogacy level of candidate surrogate endpoints, and (iii) most surrogacy measures are highly variable; thus, the confidence intervals are often unacceptably wide. In order to solve problems (i) and (ii), we propose a new surrogacy measure, a proportion of the treatment effect captured by candidate surrogate endpoints (PCS), on the basis of the decomposition of the treatment effect into parts captured and non-captured by the candidate surrogate endpoints. In order to solve problem (iii), we propose an estimation method based on the half-range mode method with the bootstrap distribution of the estimated surrogacy measures. Finally, through numerical experiments and two empirical examples, we show that the PCS with the proposed estimation method overcomes these difficulties. The results of this paper contribute to the reliable evaluation of how much of the treatment effect is captured by candidate surrogate endpoints., (Copyright © 2014 John Wiley & Sons, Ltd.)

Informative exposure-response modeling of clinical endpoints is important in drug development. There has been much recent progress in latent variable modeling of ordered categorical endpoints, including the application of indirect response (IDR) models and accounting for residual correlations between multiple categorical endpoints. This manuscript describes a framework of latent-variable-based IDR models that facilitate easy simultaneous modeling of a continuous and a categorical clinical endpoint. The model was applied to data from two phase III clinical trials of subcutaneously administered ustekinumab for the treatment of psoriatic arthritis, where Psoriasis Area and Severity Index scores and 20, 50, and 70 % improvement in the American College of Rheumatology response criteria were used as efficacy endpoints. Visual predictive check and external validation showed reasonable parameter estimation precision and model performance.

In HIV-1 clinical trials the interest is often to compare how well treatments suppress the HIV-1 RNA viral load. The current practice in statistical analysis of such trials is to define a single ad hoc composite event which combines information about both the viral load suppression and the subsequent viral rebound, and then analyze the data using standard univariate survival analysis techniques. The main weakness of this approach is that the results of the analysis can be easily influenced by minor details in the definition of the composite event. We propose a straightforward alternative endpoint based on the probability of being suppressed over time, and suggest that treatment differences be summarized using the restricted mean time a patient spends in the state of viral suppression. A nonparametric analysis is based on methods for multiple endpoint studies. We demonstrate the utility of our analytic strategy using a recent therapeutic trial, in which the protocol specified a primary analysis using a composite endpoint approach., (© 2014, The International Biometric Society.)

In this paper, we shall provide simple methods where nonstatisticians can evaluate sample size calculations for most large simple trials, as an important part of the peer review process, whether a grant, an Institutional Review Board review, an internal scientific review committee, or a journal referee. Through the methods of the paper, not only can readers determine if there is a major disparity, but they can readily determine the correct sample size. It will be of comfort to find in most cases that the sample size computation is correct, but the implications can be major for the minority where serious errors occur. We shall provide three real examples, one where the sample size need was seriously overestimated, one (HIP PRO-test of a device to prevent hip fractures) where the sample size need was dramatically underestimated, and one where the sample size was correct. The HIP PRO case is especially troubling as it went through an NIH study section and two peer reviewed journal reports without anyone catching this sample size error of a factor of more than five-fold., (© 2013 Wiley Periodicals, Inc.)

In recent times, there has been great pressure on physiotherapists to become accountable for their practices and to provide evidence for effectiveness of their treatment. Therefore, it has become necessary to integrate standardised outcome measures (OMs) into clinical practice and boost evidence-based practice. The aim of this study was to determine the extent of use of outcome measures among physiotherapists in India and to identify the commonly used measures. A survey was conducted using a questionnaire consisting of 23 closed-ended questions. It was administered face-to-face and via email to Indian physiotherapists working with musculoskeletal patients. The response rate was 54% (n = 81). The results indicated 80% of the respondents used OMs with impairment-based measures being the most commonly used. Education qualifications, years of work experience and workplace setting were not significantly associated with utilisation of OMs. Various benefits and barriers to use of OMs were also identified. The findings of this study give insight into possible changes that could be incorporated in clinical practice and educational system for developing a standardised level of assessing patients and to tailor future implementation strategies.

The use of two or more primary correlated endpoints is becoming increasingly common. A mandatory approach when analyzing data from such clinical trials is to control the family-wise error rate (FWER). In this context, we provide formulas for computation of sample size and for data analysis. Two approaches are discussed: an individual method based on a union-intersection procedure and a global procedure, based on a multivariate model that can take into account adjustment variables. These methods are illustrated with simulation studies and applications. An R package known as rPowerSampleSize is also available.

In clinical trials, there always is the possibility to use data-driven adaptation at the end of a study. There prevails, however, concern on whether the type I error rate of the trial could be inflated with such design, thus, necessitating multiplicity adjustment. In this project, a simulation experiment was set up to assess type I error rate inflation associated with switching dose group as a function of dropout rate at the end of the study, where the primary analysis is in terms of a longitudinal outcome. This simulation is inspired by a clinical trial in Alzheimer's disease. The type I error rate was assessed under a number of scenarios, in terms of differing correlations between efficacy and tolerance, different missingness mechanisms, and different probabilities of switching. A collection of parameter values was used to assess sensitivity of the analysis. Results from ignorable likelihood analysis show that the type I error rate with and without switching was approximately the posited error rate for the various scenarios. Under last observation carried forward (LOCF), the type I error rate blew up both with and without switching. The type I error inflation is clearly connected to the criterion used for switching. While in general switching, in a way related to the primary endpoint, may impact the type I error, this was not the case for most scenarios in the longitudinal Alzheimer trial setting under consideration, where patients are expected to worsen over time.

We present a Bayesian adaptive design for a confirmatory trial to select a trial's sample size based on accumulating data. During accrual, frequent sample size selection analyses are made and predictive probabilities are used to determine whether the current sample size is sufficient or whether continuing accrual would be futile. The algorithm explicitly accounts for complete follow-up of all patients before the primary analysis is conducted. We refer to this as a Goldilocks trial design, as it is constantly asking the question, "Is the sample size too big, too small, or just right?" We describe the adaptive sample size algorithm, describe how the design parameters should be chosen, and show examples for dichotomous and time-to-event endpoints.

It has been widely recognized that interim analyses of accumulating data in a clinical trial can inflate type I error. Different methods, from group sequential boundaries to flexible alpha spending functions, have been developed to control the overall type I error at prespecified level. These methods mainly apply to testing the same endpoint in multiple interim analyses. In this article, we consider a group sequential design with preplanned endpoint switching after unblinded interim analyses. We extend the alpha spending function method to group sequential stopping boundaries when the parameters can be different between interim, or between interim and final analyses.

A discrete random effects model (Lan and Pinheiro, 2012) was proposed recently for multiregional clinical trials for continuous responses. This article elucidates further the application of this model to time-to-event and binary responses. We provide some guidelines on how to design multiregional trials and also show how the same model lends itself naturally to meta-analysis.

Use of surrogate outcome to improve the inference in biomedical problems is an area of growing interest. Here, we consider a setup where both the true and surrogate endpoints are binary and we observe all the surrogate endpoints along with a few true endpoints. In a two-treatment setup we study the surrogate-augmented Mantel-Haenszel estimator based on observations from different groups when the group effect is present. We compare the Mantel-Haenszel estimator with the one obtained by maximizing profile likelihood in a surrogate augmented setup. We observe that the performances of these estimators are very close.

Objective: To obtain the impacts of experimental design on benchmark dose (BMD), and the result was applied to test the computer simulation by software Slob (optimal method to calculate the BMD: for a certain sample capacity, to add the experimental groups by reducing the amount of animals in each group) , consequently, this method can be widely used in the future., Methods: Eighty adult female SD rats were ig given dimethoate 0.5, 1, 2, 4, 8, 16 and 32 mg/kg for 21 d, respectively. Rats were sacrificed, and acetylcholinesterase (AChE) activity in the hippocampus, cerebral cortex and serum of rats was determined after dimethoate was ig given to rats for 21 d. And then, the software package PROAST28.1 was applied to calculate the BMD. The four does groups of 10 animals (4 x 10 design) and 8 x 5 design were selected from 8 x 10 design to study the impacts of experimental design on BMD., Results: Comparing with the normal control, the significant decline of AChE in hippocampus was observed in 2, 4, 8, 16 and 32 mg/kg groups (P < 0.05), whereas the significant decrease was obtained in 0.5, 1, 2, 4, 8, 16 and 32 mg/kg groups (P < 0.05). Taking the 8 x 10 design as the standard, the confidence interval of BMD calculated by both of 4 x 10 design and 8 x 5 design covered the BMD by 8 x 10 design. And also, confidence interval of BMD, calculated by design scheme 1, 2, 3, 4 and 6 of 4 x 10 design, wider than that of 8 x 5 design, but its scheme 5 narrower than 8 x 5 design., Conclusion: To add experimental groups in a certain sample capacity was the optimal method to calculate BMD, but was not the common toxicity experimental design (e. g. set four groups including control, low-dose, moderate-dose, high-dose group).

Two common features of clinical trials, and other longitudinal studies, are (1) a primary interest in composite endpoints, and (2) the problem of subjects withdrawing prematurely from the study. In some settings, withdrawal may only affect observation of some components of the composite endpoint, for example when another component is death, information on which may be available from a national registry. In this paper, we use the theory of augmented inverse probability weighted estimating equations to show how such partial information on the composite endpoint for subjects who withdraw from the study can be incorporated in a principled way into the estimation of the distribution of time to composite endpoint, typically leading to increased efficiency without relying on additional assumptions above those that would be made by standard approaches. We describe our proposed approach theoretically, and demonstrate its properties in a simulation study.

Modeling clinical endpoints as a function of change in antiretroviral therapy (ART) attempts to answer one simple but very challenging question: was the change in ART beneficial or not? We conceive a similar scientific question of interest in the current manuscript except that we are interested in modeling the time of ART regimen change rather than a comparison of two or more ART regimens. The answer to this scientific riddle is unknown and has been difficult to address clinically. Naturally, ART regimen change is left to a participant and his or her provider and so the date of change depends on participant characteristics. There exists a vast literature on how to address potential confounding and those techniques are vital to the success of the method here. A more substantial challenge is devising a systematic modeling strategy to overcome the missing time of regimen change for those participants who do not switch to second-line ART within the study period even after failing the initial ART. In this article, we adopt and apply a statistical method that was originally proposed for modeling infusion trial data, where infusion length may be informatively censored, and argue that the same strategy may be employed here. Our application of this method to therapeutic HIV/AIDS studies is new and interesting. Using data from the AIDS Clinical Trials Group (ACTG) Study A5095, we model immunological endpoints as a polynomial function of a participant's switching time to second-line ART for 182 participants who already failed the initial ART. In our analysis, we find that participants who switch early have somewhat better sustained suppression of HIV-1 RNA after virological failure than those who switch later. However, we also found that participants who switched very late, possibly censored due to the end of the study, had good HIV-1 RNA suppression, on average. We believe our scientific conclusions contribute to the relevant HIV literature and hope that the basic modeling strategy outlined here would be useful to others contemplating similar analyses with partially missing treatment length data., (© 2013, The International Biometric Society.)

Purpose: To conduct a synthesis of the literature on methods to evaluate the impacts of FDA regulatory actions and identify best practices for future evaluations., Methods: We searched MEDLINE for manuscripts published between January 1948 and August 2011 that included terms related to FDA, regulatory actions, and empirical evaluation; the review additionally included FDA-identified literature. We used a modified Delphi method to identify preferred methodologies. We included studies with explicit methods to address threats to validity and identified designs and analytic methods with strong internal validity that have been applied to other policy evaluations., Results: We included 18 studies out of 243 abstracts and papers screened. Overall, analytic rigor in prior evaluations of FDA regulatory actions varied considerably; less than a quarter of studies (22%) included control groups. Only 56% assessed changes in the use of substitute products/services, and 11% examined patient health outcomes. Among studies meeting minimal criteria of rigor, 50% found no impact or weak/modest impacts of FDA actions and 33% detected unintended consequences. Among those studies finding significant intended effects of FDA actions, all cited the importance of intensive communication efforts. There are preferred methods with strong internal validity that have yet to be applied to evaluations of FDA regulatory actions., Conclusions: Rigorous evaluations of the impact of FDA regulatory actions have been limited and infrequent. Several methods with strong internal validity are available to improve trustworthiness of future evaluations of FDA policies., (Copyright © 2013 John Wiley & Sons, Ltd.)

Purpose: Although several techniques for modification of atrial fibrillation (AF) substrate, such as linear ablation and complex fractionated atrial electrograms (CFAEs) ablation, have been proposed for longstanding persistent AF (LS-AF) and improved the outcome, there was still a certain recurrence rate, even if current ablation endpoints of these techniques were completely achieved. The purpose of this study was to describe the determinants of recurrent AF in patients who obtained current ablation endpoints with LS-AF., Methods and Results: In all, 208 consecutive patients who obtained current ablation endpoints with LS-AF were studied. The current ablation endpoints were defined as complete pulmonary vein isolation, bidirectional block of lines, and disappearance of CFAEs. After a follow-up of 19.9 ± 4.1 months, the patients were classified as AF recurrence group and non-AF recurrence group (including patients with sinus rhythm and atrial tachycardia), and 34 (16 %) patients were in the AF recurrence group. The patients in AF recurrence group had higher rates of right atrium (RA) enlargement (67.7 vs. 45.4 %, p = 0.018) and ≥2 procedure times (58.8 vs. 27.0 %, p < 0.001), longer AF duration (82.4 ± 44.8 vs. 50.8 ± 42.8 months, p < 0.001), and larger left atrium (LA) diameter (49.4 ± 6.2 vs. 46.5 ± 5.3 mm, p = 0.007). In the multivariate analysis, RA enlargement, ≥2 procedure times, and AF duration were independent predictors of AF recurrence., Conclusion: RA enlargement, ≥2 procedure times, and AF duration played important roles in AF recurrence in patients who obtained current ablation endpoints. For these patients with AF recurrence who had already underwent ≥2 procedure times, enlarged RA may contribute to other AF foci and/or substrate, and the ablation strategy may be transformed from LA to RA in the next ablation procedures.