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Sequential, multiple assignment, randomized trial (SMART) designs are appropriate for comparing adaptive treatment interventions, in which intermediate outcomes (called tailoring variables) guide subsequent treatment decisions for individual patients. Within a SMART design, patients may be re-randomized to subsequent treatments following the outcomes of their intermediate assessments. In this paper, we provide an overview of statistical considerations necessary to design and implement a two-stage SMART design with a binary tailoring variable and a survival final endpoint. A chronic lymphocytic leukemia trial with a final endpoint of progression-free survival is used as an example for the simulations to assess how design parameters, including, choice of randomization ratios for each stage of randomization, and response rates of the tailoring variable affect the statistical power. We assess the choice of weights from restricted re-randomization on data analyses and appropriate hazard rate assumptions. Specifically, for a given first-stage therapy and prior to the tailoring variable assessment, we assume equal hazard rates for all patients randomized to a treatment arm. After the tailoring variable assessment, individual hazard rates are assumed for each intervention path. Simulation studies demonstrate that the response rate of the binary tailoring variable impacts power as it directly impacts the distribution of patients. We also confirm that when the first stage randomization is 1:1, it is not necessary to consider the first stage randomization ratio when applying the weights. We provide an R-shiny application for obtaining power for a given sample size for SMART designs.

When the primary endpoints in randomized clinical trials require long term follow-up or are costly to measure, it is often desirable to assess treatment effects on surrogate instead of clinical endpoints. Prior to adopting a surrogate endpoint for such purposes, the extent of its surrogacy on the primary endpoint must be assessed. There is a rich statistical literature on assessing surrogacy in the overall population, much of which is based on quantifying the proportion of treatment effect on the primary endpoint that is explained by the treatment effect on the surrogate endpoint. However, the surrogacy of an endpoint may vary across different patient subgroups according to baseline demographic characteristics, and limited methods are currently available to assess overall surrogacy in the presence of potential surrogacy heterogeneity. In this paper, we propose methods that incorporate covariates for baseline information, such as age, to improve overall surrogacy assessment. We use flexible semi-non-parametric modeling strategies to adjust for covariate effects and derive a robust estimate for the proportion of treatment effect of the covariate-adjusted surrogate endpoint. Simulation results suggest that the adjusted surrogate endpoint has greater proportion of treatment effect compared to the unadjusted surrogate endpoint. We apply the proposed method to data from a clinical trial of infliximab and assess the adequacy of the surrogate endpoint in the presence of age heterogeneity., Competing Interests: Declaration of conflicting interestsThe authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Platform trials are randomized clinical trials that allow simultaneous comparison of multiple interventions, usually against a common control. Arms to test experimental interventions may enter and leave the platform over time. This implies that the number of experimental intervention arms in the trial may change as the trial progresses. Determining optimal allocation rates to allocate patients to the treatment and control arms in platform trials is challenging because the optimal allocation depends on the number of arms in the platform and the latter typically varies over time. In addition, the optimal allocation depends on the analysis strategy used and the optimality criteria considered. In this article, we derive optimal treatment allocation rates for platform trials with shared controls, assuming that a stratified estimation and a testing procedure based on a regression model are used to adjust for time trends. We consider both, analysis using concurrent controls only as well as analysis methods using concurrent and non-concurrent controls and assume that the total sample size is fixed. The objective function to be minimized is the maximum of the variances of the effect estimators. We show that the optimal solution depends on the entry time of the arms in the trial and, in general, does not correspond to the square root of k allocation rule used in classical multi-arm trials. We illustrate the optimal allocation and evaluate the power and type 1 error rate compared to trials using one-to-one and square root of k allocations by means of a case study., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Background: Multicentre RCTs are widely used by critical care researchers to answer important clinical questions. However, few trials evaluating mortality outcomes report statistically significant results. We hypothesised that the low proportion of trials reporting statistically significant differences for mortality outcomes is plausibly explained by lower-than-expected effect sizes combined with a low proportion of participants who could realistically benefit from studied interventions., Methods: We reviewed multicentre trials in critical care published over a 10-yr period in the New England Journal of Medicine, the Journal of the American Medical Association, and the Lancet. To test our hypothesis, we analysed the results using a Bayesian model to investigate the relationship between the proportion of effective interventions and the proportion of statistically significant results for prior distributions of effect size and trial participant susceptibility., Results: Five of 54 trials (9.3%) reported a significant difference in mortality between the control and the intervention groups. The median expected and observed differences in absolute mortality were 8.0% and 2.0%, respectively. Our modelling shows that, across trials, a lower-than-expected effect size combined with a low proportion of potentially susceptible participants is consistent with the observed proportion of trials reporting significant differences even when most interventions are effective., Conclusions: When designing clinical trials, researchers most likely overestimate true population effect sizes for critical care interventions. Bayesian modelling demonstrates that that it is not necessarily the case that most studied interventions lack efficacy. In fact, it is plausible that many studied interventions have clinically important effects that are missed., (Copyright © 2021 British Journal of Anaesthesia. Published by Elsevier Ltd. All rights reserved.)

Composite endpoints reveal the tendency for statistical convention to arise locally within subfields. Composites are familiar in cardiovascular trials, yet almost unknown in sepsis. However, the VITAMINS trial in patients with septic shock adopted a composite of mortality and vasopressor-free days, and an ordinal scale describing patient status rapidly became standard in COVID studies. Aware that recent use could incite interest in such endpoints, we are motivated to flag their potential value and pitfalls for sepsis research and COVID studies., (© 2020 The Authors. Pharmaceutical Statistics published by John Wiley & Sons Ltd.)

Background: The ICH E9(R1) addendum states that the strategy to account for intercurrent events should be included when defining an estimand, the treatment effect to be estimated based on the study objective. The estimator used to assess the treatment effect needs to be aligned with the estimand that accounted for intercurrent events. Regardless of the strategy, missing data resulting from patient premature withdrawal could undermine the robustness of the study results. Informative censoring due to dropouts in an events-based study is one such example. Sensitivity analyses using imputation methods are useful to examine the uncertainty due to informative censoring and address the robustness and strength of the study results., Methods: We assessed the effect of premature patient withdrawal in the PRECISION study, a randomized non-inferiority clinical trial of patients with chronic arthritic pain that compared the cardiovascular safety of three nonsteroidal anti-inflammatory drugs-based treatment policies or paradigms. The protocol-defined use of concomitant or rescue medications was permitted since changes in pain medications due to insufficient analgesia were expected in patients in this long-term study. Anticipating that premature study discontinuations could potentially lead to informative censoring, a supplementary analysis was pre-specified in which censored outcomes due to the premature study discontinuation were imputed based on adverse events that were clinically associated with the primary endpoint (cardiovascular outcome based on the Antiplatelet Trialists Collaboration composite endpoint). Furthermore, tipping point analyses were conducted to test the robustness of the primary analysis results by assuming data censored not at random. The level of increase at which the primary study conclusion would change was estimated., Results: For the analysis of time to first primary endpoint event through 30 months, 4065 out of the 24,081 enrolled patients were lost to follow-up, withdrew consent, or were no longer willing to participate in the study. These withdrawals occurred gradually and resulted in a cumulative total of 5893 censored patient-years of observation (10.2%). The rate of discontinuation and the baseline characteristics of the discontinued patients were similar across the three treatment groups. The non-inferiority conclusion from the primary analysis was confirmed in the supplementary analysis incorporating relevant adverse events. Furthermore, tipping point analyses demonstrated that in order to lose non-inferiority in the primary analysis, the risk of primary endpoint events during the censored observation time would have to increase by more than 2.7-fold in the celecoxib group while remaining constant in the other nonsteroidal anti-inflammatory drugs groups, demonstrating that the scenarios where the study results are invalid appear not plausible., Conclusions: Supplementary and sensitivity analyses presented to address informative censoring in PRECISION helped to further interpret and strengthen the study results.

A clinical trial often has primary and secondary endpoints and comparisons of high and low doses of a study drug to a control. Multiplicity is not only caused by the multiple comparisons of study drugs versus the control, but also from the hierarchical structure of the hypotheses. Closed test procedures were proposed as general methods to address multiplicity. Two commonly used tests for intersection hypotheses in closed test procedures are the Simes test and the average method. When the treatment effect of a less efficacious dose is not much smaller than the treatment effect of a more efficacious dose for a specific endpoint, the average method has better power than the Simes test for the comparison of two doses versus control. Accordingly, for inferences for primary and secondary endpoints, the matched parallel gatekeeping procedure based on the Simes test for testing intersection hypotheses is extended here to allow the average method for such testing. This procedure is further extended to clinical trials with more than two endpoints as well as to clinical trials with more than two active doses and a control.

The design of a clinical trial is often complicated by the multi-systemic nature of the disease; a single endpoint often cannot capture the spectrum of potential therapeutic benefits. Multi-domain outcomes which take into account patient heterogeneity of disease presentation through measurements of multiple symptom/functional domains are an attractive alternative to a single endpoint. A multi-domain test with adaptive weights is proposed to synthesize the evidence of treatment efficacy over numerous disease domains. The test is a weighted sum of domain-specific test statistics with weights selected adaptively via a data-driven algorithm. The null distribution of the test statistic is constructed empirically through resampling and does not require estimation of the covariance structure of domain-specific test statistics. Simulations show that the proposed test controls the type I error rate, and has increased power over other methods such as the O'Brien and Wei-Lachin tests in scenarios reflective of clinical trial settings. Data from a clinical trial in a rare lysosomal storage disorder were used to illustrate the properties of the proposed test. As a strategy of combining marginal test statistics, the proposed test is flexible and readily applicable to a variety of clinical trial scenarios., (© 2019 John Wiley & Sons Ltd.)

A placebo-controlled randomized clinical trial is required to demonstrate that an experimental treatment is superior to its corresponding placebo on multiple coprimary endpoints. This is particularly true in the field of neurology. In fact, clinical trials for neurological disorders need to show the superiority of an experimental treatment over a placebo in two coprimary endpoints. Unfortunately, these trials often fail to detect a true treatment effect for the experimental treatment versus the placebo owing to an unexpectedly high placebo response rate. Sequential parallel comparison design (SPCD) can be used to address this problem. However, the SPCD has not yet been discussed in relation to clinical trials with coprimary endpoints. In this article, our aim was to develop a hypothesis-testing method and a method for calculating the corresponding sample size for the SPCD with two coprimary endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy. In addition, the usefulness of our methods is confirmed by returning to an SPCD trial with a single primary endpoint of Alzheimer disease-related agitation., (© 2019 John Wiley & Sons, Ltd.)

Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well-investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis-specification, in particular, regarding the Neyman-Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation., (© 2019 John Wiley & Sons, Ltd.)

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context., (© 2019 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.)

Background and Objective: The use of valid surrogate endpoints can accelerate the development of phase III trials. Numerous validation methods have been proposed with the most popular used in a context of meta-analyses, based on a two-step analysis strategy. For two failure time endpoints, two association measures are usually considered, Kendall's τ at individual level and adjusted R2 ([Formula: see text]) at trial level. However, [Formula: see text] is not always available mainly due to model estimation constraints. More recently, we proposed a one-step validation method based on a joint frailty model, with the aim of reducing estimation issues and estimation bias on the surrogacy evaluation criteria. The model was quite robust with satisfactory results obtained in simulation studies. This study seeks to popularize this new surrogate endpoints validation approach by making the method available in a user-friendly R package., Methods: We provide numerous tools in the frailtypack R package, including more flexible functions, for the validation of candidate surrogate endpoints using data from multiple randomized clinical trials., Results: We implemented the surrogate threshold effect which is used in combination with [Formula: see text] to make decisions concerning the validity of the surrogate endpoints. It is also possible thanks to frailtypack to predict the treatment effect on the true endpoint in a new trial using the treatment effect observed on the surrogate endpoint. The leave-one-out cross-validation is available for assessing the accuracy of the prediction using the joint surrogate model. Other tools include data generation, simulation study and graphic representations. We illustrate the use of the new functions with both real data and simulated data., Conclusion: This article proposes new attractive and well developed tools for validating failure time surrogate endpoints., Competing Interests: The authors have declared that no competing interests exist.

In the analysis of composite endpoints in a clinical trial, time to first event analysis techniques such as the logrank test and Cox proportional hazard test do not take into account the multiplicity, importance, and the severity of events in the composite endpoint. Several generalized pairwise comparison analysis methods have been described recently that do allow to take these aspects into account. These methods have the additional benefit that all types of outcomes can be included, such as longitudinal quantitative outcomes, to evaluate the full treatment effect. Four of the generalized pairwise comparison methods, ie, the Finkelstein-Schoenfeld, the Buyse, unmatched Pocock, and adapted O'Brien test, are summarized. They are compared to each other and to the logrank test by means of simulations while specifically evaluating the effect of correlation between components of the composite endpoint on the power to detect a treatment difference. These simulations show that prioritized generalized pairwise comparison methods perform very similarly, are sensitive to the priority rank of the components in the composite endpoint, and do not measure the true treatment effect from the second priority-ranked component onward. The nonprioritized pairwise comparison test does not suffer from these limitations and correlation affects only its variance., (© 2019 John Wiley & Sons, Ltd.)

In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error and proposes methods to improve statistical inference in the presence of measurement error. Three main types of measurement error in continuous endpoints are considered: classical, systematic, and differential. For each measurement error type, a corrected effect estimator is proposed. The corrected estimators and several methods for confidence interval estimation are tested in a simulation study. These methods combine information about error-prone and error-free measurements of the endpoint in individuals not included in the trial (external calibration sample). We show that, if measurement error in continuous endpoints is ignored, the treatment effect estimator is unbiased when measurement error is classical, while Type-II error is increased at a given sample size. Conversely, the estimator can be substantially biased when measurement error is systematic or differential. In those cases, bias can largely be prevented and inferences improved upon using information from an external calibration sample, of which the required sample size increases as the strength of the association between the error-prone and error-free endpoint decreases. Measurement error correction using already a small (external) calibration sample is shown to improve inferences and should be considered in trials with error-prone endpoints. Implementation of the proposed correction methods is accommodated by a new software package for R., (© 2019 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Introduction: In some randomised trials, the primary interest is in the mechanisms by which an intervention exerts its effects on health outcomes. That is, clinicians and policy-makers may be interested in how the intervention works (or why it does not work) through hypothesised causal mechanisms. In this article, we highlight the value of understanding causal mechanisms in randomised trials by applying causal mediation analysis to two randomised trials of complex interventions., Main Body: In the first example, we examine a potential mechanism by which an exercise programme for rheumatoid arthritis of the hand could improve hand function. In the second example, we explore why a rehabilitation programme for ankle fractures failed to improve lower-limb function through hypothesised mechanisms. We outline critical assumptions that are required for making valid causal inferences from these analyses, and provide results of sensitivity analyses that are used to assess the degree to which the estimated causal mediation effects could have been biased by residual confounding., Conclusion: This paper demonstrates how the application of causal mediation analyses to randomised trials can identify the mechanisms by which complex interventions exert their effects. We discuss methodological issues and assumptions that should be considered when mediation analyses of randomised trials are used to inform clinical practice and policy decisions.

Perioperative investigators and professionals increasingly seek to evaluate whether implementing systematic practice changes improves outcomes compared to a previous routine. Cluster randomized trials are the optimal design to assess a systematic practice change but are often impractical; investigators, therefore, often select a before-after design. In this Statistical Grand Rounds, we first discuss biases inherent in a before-after design, including confounding due to periods being completely separated by time, regression to the mean, the Hawthorne effect, and others. Many of these biases can be at least partially addressed by using appropriate designs and analyses, which we discuss. Our focus is on segmented regression of an interrupted time series, which does not require a concurrent control group; we also present alternative designs including difference-in-difference, stepped wedge, and cluster randomization. Conducting segmented regression well requires a sufficient number of time points within each period, along with a robust set of potentially confounding variables. This method compares preintervention and postintervention changes over time, divergences in the outcome when an intervention begins, and trends observed with the intervention compared to trends projected without it. Difference-in-difference methods add a concurrent control, enabling yet stronger inference. When done well, the discussed methods permit robust inference on the effect of an intervention, albeit still requiring assumptions and having limitations. Methods are demonstrated using an interrupted time series study in which anesthesiologists took responsibility for an adult medical emergency team from internal medicine physicians in an attempt to improve outcomes.

Background: Cluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size. To allow for this, sample sizes are inflated by a modified version of the design effect for clustering. These inflation factors are valid under the assumption that randomisation is stratified by cluster size. We investigate the impact of unequal cluster size when that constraint is relaxed, with particular focus on the stepped-wedge cluster randomised trial, where this is more difficult to achieve., Methods: Assuming a multi-level mixed effect model with exchangeable correlation structure for a cross-sectional design, we use simulation methods to compare the precision for a trial with clusters of unequal size to a trial with clusters of equal size (relative efficiency). For a range of scenarios we illustrate the impact of various design features (the cluster-mean correlation - a function of the intracluster correlation and the cluster size, the number of clusters, number of randomisation sequences) on the average and distribution of the relative efficiency., Results: Simulations confirm that the average reduction in precision, due to varying cluster sizes, is smaller in a stepped-wedge trial compared to the parallel trial. However, the variance of the distribution of the relative efficiency is large; and is larger under the stepped-wedge design compared to the parallel design. This can result in large variations in actual power, depending on the allocation of clusters to sequences. Designs with larger variations in cluster sizes, smaller number of clusters and studies with smaller cluster-mean correlations (smaller cluster sizes or smaller intra-cluster correlation) are particularly at risk., Conclusion: The actual realised power in a stepped-wedge trial might be substantially higher or lower than that estimated. This is particularly important when there are a small number of clusters or the variability in cluster sizes is large. Constraining the randomisation on cluster size, where feasible, might mitigate this effect.

Goal Attainment Scaling is an assessment instrument to evaluate interventions on the basis of individual, patient-specific goals. The attainment of these goals is mapped in a pre-specified way to attainment levels on an ordinal scale, which is common to all goals. This approach is patient-centred and allows one to integrate the outcomes of patients with very heterogeneous symptoms. The latter is of particular importance in clinical trials in rare diseases because it enables larger sample sizes by including a broader patient population. In this paper, we focus on the statistical analysis of Goal Attainment Scaling outcomes for the comparison of two treatments in randomised clinical trials. Building on a general statistical model, we investigate the properties of different hypothesis testing approaches. Additionally, we propose a latent variable approach to generate Goal Attainment Scaling data in a simulation study, to assess the impact of model parameters such as the number of goals per patient and their correlation, the choice of discretisation thresholds and the type of design (parallel group or cross-over). Based on our findings, we give recommendations for the design of clinical trials with a Goal Attainment Scaling endpoint. Furthermore, we discuss an application of Goal Attainment Scaling in a clinical trial in mastocytosis.

The individual causal association (ICA) has recently been introduced as a metric of surrogacy in a causal-inference framework. The ICA is defined on the unit interval and quantifies the association between the individual causal effect on the surrogate (ΔS) and true (ΔT) endpoint. In addition, the ICA offers a general assessment of the surrogate predictive value, taking value 1 when there is a deterministic relationship between ΔT and ΔS, and value 0 when both causal effects are independent. However, when one moves away from the previous two extreme scenarios, the interpretation of the ICA becomes challenging. In the present work, a new metric of surrogacy, the minimum probability of a prediction error (PPE), is introduced when both endpoints are binary, ie, the probability of erroneously predicting the value of ΔT using ΔS. Although the PPE has a more straightforward interpretation than the ICA, its magnitude is bounded above by a quantity that depends on the true endpoint. For this reason, the reduction in prediction error (RPE) attributed to the surrogate is defined. The RPE always lies in the unit interval, taking value 1 if prediction is perfect and 0 if ΔS conveys no information on ΔT. The methodology is illustrated using data from two clinical trials and a user-friendly R package Surrogate is provided to carry out the validation exercise., (© 2018 John Wiley & Sons, Ltd.)

The stratified Cox model is commonly used for stratified clinical trials with time-to-event endpoints. The estimated log hazard ratio is approximately a weighted average of corresponding stratum-specific Cox model estimates using inverse-variance weights; the latter are optimal only under the (often implausible) assumption of a constant hazard ratio across strata. Focusing on trials with limited sample sizes (50-200 subjects per treatment), we propose an alternative approach in which stratum-specific estimates are obtained using a refined generalized logrank (RGLR) approach and then combined using either sample size or minimum risk weights for overall inference. Our proposal extends the work of Mehrotra et al, to incorporate the RGLR statistic, which outperforms the Cox model in the setting of proportional hazards and small samples. This work also entails development of a remarkably accurate plug-in formula for the variance of RGLR-based estimated log hazard ratios. We demonstrate using simulations that our proposed two-step RGLR analysis delivers notably better results through smaller estimation bias and mean squared error and larger power than the stratified Cox model analysis when there is a treatment-by-stratum interaction, with similar performance when there is no interaction. Additionally, our method controls the type I error rate while the stratified Cox model does not in small samples. We illustrate our method using data from a clinical trial comparing two treatments for colon cancer., (© 2019 John Wiley & Sons, Ltd.)

Background: When using a continuous outcome measure in a randomised controlled trial (RCT), the baseline score should be measured in addition to the post-intervention score, and it should be analysed using the appropriate statistical analysis., Methods: We derive the correlation between the change score and baseline score and show that there is always a correlation (usually negative) between the change score and baseline score. We discuss the following correlations and provide the mathematical derivations in the Appendix: Correlation between change score and baseline score Correlation between change score and post score Correlation between change score and average score. The setting here is a parallel, two-arm RCT, but the method discussed in this paper is applicable for any studies or trials that have a continuous outcome measure; it is not restricted to RCTs., Results: We show that using the change score as the outcome measure does not address the problem of regression to the mean, nor does it take account of the baseline imbalance. Whether the outcome is change score or post score, one should always adjust for baseline using analysis of covariance (ANCOVA); otherwise, the estimated treat effect may be biased. We show that these correlations also apply when comparing two measurement methods using Bland-Altman plots., Conclusions: The correlation between baseline and post-intervention scores can be derived using the variance sum law. We can then use the derived correlation to calculate the required sample size in the design stage. Baseline imbalance may occur in RCTs, and ANCOVA should be used to adjust for baseline in the analysis stage.

In the past, many clinical trials have withdrawn subjects from the study when they prematurely stopped their randomised treatment and have therefore only collected 'on-treatment' data. Thus, analyses addressing a treatment policy estimand have been restricted to imputing missing data under assumptions drawn from these data only. Many confirmatory trials are now continuing to collect data from subjects in a study even after they have prematurely discontinued study treatment as this event is irrelevant for the purposes of a treatment policy estimand. However, despite efforts to keep subjects in a trial, some will still choose to withdraw. Recent publications for sensitivity analyses of recurrent event data have focused on the reference-based imputation methods commonly applied to continuous outcomes, where imputation for the missing data for one treatment arm is based on the observed outcomes in another arm. However, the existence of data from subjects who have prematurely discontinued treatment but remained in the study has now raised the opportunity to use this 'off-treatment' data to impute the missing data for subjects who withdraw, potentially allowing more plausible assumptions for the missing post-study-withdrawal data than reference-based approaches. In this paper, we introduce a new imputation method for recurrent event data in which the missing post-study-withdrawal event rate for a particular subject is assumed to reflect that observed from subjects during the off-treatment period. The method is illustrated in a trial in chronic obstructive pulmonary disease (COPD) where the primary endpoint was the rate of exacerbations, analysed using a negative binomial model., (© 2018 John Wiley & Sons, Ltd.)

Surrogate endpoints need to be statistically evaluated before they can be used as substitutes of true endpoints in clinical studies. However, even though several evaluation methods have been introduced over the last decades, the identification of good surrogate endpoints remains practically and conceptually challenging. In the present work, the question regarding the existence of a good surrogate is addressed using information-theoretic concepts, within a causal-inference framework. The methodology can help practitioners to assess, given a clinically relevant true endpoint and a treatment of interest, the chances of finding a good surrogate endpoint in the first place. The methodology focuses on binary outcomes and is illustrated using data from the Initial Glaucoma Treatment Study. Furthermore, a newly developed and user friendly R package Surrogate is provided to carry out the necessary calculations.

Development of new pharmacological treatments for osteoarthritis that address unmet medical needs in a competitive market place is challenging. Bayesian approaches to trial design offer advantages in defining treatment benefits by addressing clinically relevant magnitude of effects relative to comparators and in optimizing efficiency in analysis. Such advantages are illustrated by a motivating case study, a proof of concept, and dose finding study in patients with osteoarthritis. Patients with osteoarthritis were randomized to receive placebo, celecoxib, or 1 of 4 doses of galcanezumab. Primary outcome measure was change from baseline WOMAC pain after 8 weeks of treatment. Literature review of clinical trials with targeted comparator therapies quantified treatment effects versus placebo. Two success criteria were defined: one to address superiority to placebo with adequate precision and another to ensure a clinically relevant treatment effect. Trial simulations used a Bayesian dose response and longitudinal model. An interim analysis for futility was incorporated. Simulations indicated the study had ≥85% power to detect a 14-mm improvement and ≤1% risk for a placebo-like drug to pass. The addition of the second success criterion substantially reduced the risk of an inadequate, weakly efficacious drug proceeding to future development. The study was terminated at the interim analysis due to inadequate analgesic efficacy. A Bayesian approach using probabilistic statements enables clear understanding of success criteria, leading to informed decisions for study conduct. Incorporating an interim analysis can effectively reduce sample size, save resources, and minimize exposure of patients to an inadequate treatment., (© 2018 John Wiley & Sons, Ltd.)

In pharmaceutical/clinical development, two-stage seamless adaptive designs are commonly considered. Such designs include a two-stage phase I/II or phase II/III adaptive trial that combines one phase IIb study for dose-finding or treatment selection and one phase III study for efficacy confirmation into a single study. At the end of stage 1, promising dose(s) will be selected based on pre-specified selection criteria. In practice, since there is little power with limited subjects available at interim, commonly considered selection criteria for critical decision-making include (i) conditional power, (ii) precision analysis, (iii) predictive probability of success, and (iv) probability of being the best dose or treatment. The selected promising dose(s) will then proceed to the next stage for efficacy confirmation. In this article, we introduce, compare, and evaluate these criteria. Simulation studies and a numeric example are given to illustrate those criteria. Besides, we attempt to address some concerns for the two-stage seamless adaptive clinical trial.

The draft addendum to the ICH E9 regulatory guideline asks for explicit definition of the treatment effect to be estimated in clinical trials. The draft guideline also introduces the concept of intercurrent events to describe events that occur post-randomisation that may affect efficacy assessment. Composite estimands allow incorporation of intercurrent events in the definition of the endpoint. A common example of an intercurrent event is discontinuation of randomised treatment and use of a composite strategy would assess treatment effect based on a variable that combines the outcome variable of interest with discontinuation of randomised treatment. Use of a composite estimand may avoid the need for imputation which would be required by a treatment policy estimand. The draft guideline gives the example of a binary approach for specifying a composite estimand. When the variable is measured on a non-binary scale, other options are available where the intercurrent event is given an extreme unfavourable value, for example comparison of median values or analysis based on categories of response. This paper reviews approaches to deriving a composite estimand and contrasts the use of this estimand to the treatment policy estimand. The benefits of using each strategy are discussed and examples of the use of the different approaches are given for a clinical trial in nasal polyposis and a steroid reduction trial in severe asthma., (© 2018 John Wiley & Sons, Ltd.)

One of the most critical decision points in clinical development is Go/No-Go decision-making after a proof-of-concept study. Traditional decision-making relies on a formal hypothesis testing with control of type I and type II error rates, which is limited by assessing the strength of efficacy evidence in a small isolated trial. In this article, we propose a quantitative Bayesian/frequentist decision framework for Go/No-Go criteria and sample size evaluation in Phase II randomized studies with a time-to-event endpoint. By taking the uncertainty of treatment effect into consideration, we propose an integrated quantitative approach for a program when both the Phase II and Phase III trials share a common endpoint while allowing a discount of the observed Phase II data. Our results confirm the argument that an increase in the sample size of a Phase II trial will result in greater increase in the probability of success of a Phase III trial than increasing the Phase III trial sample size by equal amount. We illustrate the steps in quantitative decision-making with a real example of a randomized Phase II study in metastatic pancreatic cancer.

In clinical trials, where the outcome of interest is the occurrence of an event over a fixed time period, estimation of the event proportion at interim analysis can form a basis for decision-making such as early trial termination, sample size re-estimation, and/or dropping inferior treatment arms. In addition to derivation of mean squared error under an exponential time-to-event distribution, we performed a simulation study to examine the performance of five estimators of the event proportion when time to the event is assessable. The simulation results showed advantages of the Kaplan-Meier estimator over others in terms of robustness, and the bias and variability of the event proportion estimate. An example was given to illustrate how the estimators affect dropping treatment arms in a multi-arm multi-stage adaptive trial. We recommended the use of the Kaplan-Meier estimator and discourage the use of other estimators that discard the inherent time-to-event information.

A clinical endpoint bioequivalence (BE) study is often used to establish bioequivalence (BE) between a locally acting generic drug (T) and an innovator drug (R), which is a double-blind, randomized three-arm (T, R and placebo: P) parallel clinical trial. BE is established if two superiority tests (T vs. P, R vs. P) and one equivalence test (T vs. R) all pass. An accurate estimate of the nuisance parameter (e.g. variance) is vital in determining an accurate sample size to attain sufficient power. However, due to potential study design variations between NDA and Abbreviated NDA (ANDA) studies and high variability of clinical endpoints, variance may be over- or under-estimated, resulting in unnecessary extra costs or underpowered studies. Traditionally, clinical endpoint BE studies use a fixed study design. In this work, we propose four sample size re-estimation approaches based on a nuisance parameter and recommend one approach after comparing various operating characteristics by simulation. The proposed adaptive design with sample size re-estimation provides a more accurate estimate of sample size without wasting resources or under-powering the study and controls the Type 1 error rate under a negligible level, both for the family-wise alpha and individual alpha for superiority and equivalence tests.

In studies with recurrent event endpoints, misspecified assumptions of event rates or dispersion can lead to underpowered trials or overexposure of patients. Specification of overdispersion is often a particular problem as it is usually not reported in clinical trial publications. Changing event rates over the years have been described for some diseases, adding to the uncertainty in planning. To mitigate the risks of inadequate sample sizes, internal pilot study designs have been proposed with a preference for blinded sample size reestimation procedures, as they generally do not affect the type I error rate and maintain trial integrity. Blinded sample size reestimation procedures are available for trials with recurrent events as endpoints. However, the variance in the reestimated sample size can be considerable in particular with early sample size reviews. Motivated by a randomized controlled trial in paediatric multiple sclerosis, a rare neurological condition in children, we apply the concept of blinded continuous monitoring of information, which is known to reduce the variance in the resulting sample size. Assuming negative binomial distributions for the counts of recurrent relapses, we derive information criteria and propose blinded continuous monitoring procedures. The operating characteristics of these are assessed in Monte Carlo trial simulations demonstrating favourable properties with regard to type I error rate, power, and stopping time, ie, sample size., (© 2018 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.)

Disease modification is a primary therapeutic aim when developing treatments for most chronic progressive diseases. The best treatments do not simply affect disease symptoms but fundamentally improve disease course by slowing, halting, or reversing disease progression. One of many challenges for establishing disease modification relates to the identification of adequate analytic tools to show differences in a disease course following intervention. Traditional approaches rely on the comparisons of slopes or noninferiority margins. However, it has proven difficult to conclusively demonstrate disease modification using such approaches. To address these challenges, we propose a novel adaptation of the delayed start study design that incorporates posterior probabilities identified by hierarchical Bayesian inference approaches to establish evidence for disease modification. Our models compare the size of treatment differences at the end of the delayed start period with those at the end of the early start period. Simulations that compare several models are provided. These include general linear models, repeated measures models, spline models, and model averaging. Our work supports the superiority of model averaging for accurately characterizing complex data that arise in real world applications. This novel approach has been applied to the design of an ongoing, doubly randomized, matched control study that aims to show disease modification in young persons with schizophrenia (the Disease Recovery Evaluation and Modification (DREaM) study). The application of this Bayesian methodology to the DREaM study highlights the value of this approach and demonstrates many practical challenges that must be addressed when implementing this methodology in a real world trial., (© 2018 John Wiley & Sons, Ltd.)

Two-period two-treatment (2×2) crossover designs are commonly used in clinical trials. For continuous endpoints, it has been shown that baseline (pretreatment) measurements collected before the start of each treatment period can be useful in improving the power of the analysis. Methods to achieve a corresponding gain for censored time-to-event endpoints have not been adequately studied. We propose a method in which censored values are treated as missing data and multiply imputed using prespecified parametric event time models. The event times in each imputed data set are then log-transformed and analyzed using a linear model suitable for a 2×2 crossover design with continuous endpoints, with the difference in period-specific baselines included as a covariate. Results obtained from the imputed data sets are synthesized for point and confidence interval estimation of the treatment ratio of geometric mean event times using model averaging in conjunction with Rubin's combination rule. We use simulations to illustrate the favorable operating characteristics of our method relative to two other methods for crossover trials with censored time-to-event data, ie, a hierarchical rank test that ignores the baselines and a stratified Cox model that uses each study subject as a stratum and includes period-specific baselines as a covariate. Application to a real data example is provided., (Copyright © 2018 John Wiley & Sons, Ltd.)

Background: Most phase-3 trials feature time-to-first event end points for their primary and secondary analyses. In chronic diseases, where a clinical event can occur >1 time, recurrent-event methods have been proposed to more fully capture disease burden and have been assumed to improve statistical precision and power compared with conventional time-to-first methods., Methods: To better characterize factors that influence statistical properties of recurrent-event and time-to-first methods in the evaluation of randomized therapy, we repeatedly simulated trials with 1:1 randomization of 4000 patients to active versus control therapy, with true patient-level risk reduction of 20% (ie, relative risk=0.80). For patients who discontinued active therapy after a first event, we assumed their risk reverted subsequently to their original placebo-level risk. Through simulation, we varied the degree of between-patient heterogeneity of risk and the extent of treatment discontinuation. Findings were compared with those from actual randomized clinical trials., Results: As the degree of between-patient heterogeneity of risk increased, both time-to-first and recurrent-event methods lost statistical power to detect a true risk reduction and confidence intervals widened. The recurrent-event analyses continued to estimate the true relative risk (0.80) as heterogeneity increased, whereas the Cox model produced attenuated estimates. The power of recurrent-event methods declined as the rate of study drug discontinuation postevent increased. Recurrent-event methods provided greater power than time-to-first methods in scenarios where drug discontinuation was ≤30% after a first event, lesser power with drug discontinuation rates of ≥60%, and comparable power otherwise. We confirmed in several actual trials of chronic heart failure that treatment effect estimates were attenuated when estimated via the Cox model and that increased statistical power from recurrent-event methods was most pronounced in trials with lower treatment discontinuation rates., Conclusions: We find that the statistical power of both recurrent-events and time-to-first methods are reduced by increasing heterogeneity of patient risk, a parameter not included in conventional power and sample size formulas. Data from real clinical trials are consistent with simulation studies, confirming that the greatest statistical gains from use of recurrent-events methods occur in the presence of high patient heterogeneity and low rates of study drug discontinuation.

In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model and the amount of censored data. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analysis. It is also essential that treatment allocation involves randomization-to mitigate various experimental biases and enable valid statistical inference at the end of the trial. In this work, we perform a comparison of several adaptive randomization procedures that can be used for implementing D-optimal designs for dose-response studies with time-to-event outcomes with small to moderate sample sizes. We consider single-stage, two-stage, and multi-stage adaptive designs. We also explore robustness of the designs to experimental (chronological and selection) biases. Simulation studies provide evidence that both the choice of an allocation design and a randomization procedure to implement the target allocation impact the quality of dose-response estimation, especially for small samples. For best performance, a multi-stage adaptive design with small cohort sizes should be implemented using a randomization procedure that closely attains the targeted D-optimal design at each stage. The results of the current work should help clinical investigators select an appropriate randomization procedure for their dose-response study.

Frequentist design for two-arm randomized Phase II clinical trials with outcomes from the exponential dispersion family was proposed previously, where the total sample sizes are minimized under multiple constraints on the standard errors of the estimated group means and their difference. This design was generalized from an approach specific for dichotomous outcomes. The two previous approaches measure the central tendency of each group and treatment effect based on mean and difference in means. Other measures such as median or hazard ratio are more appropriate under certain situations. In addition, the frequentist approaches assume that unknown parameters are fixed values. This does not reflect the reality that uncertainty always exists for unknowns. Compared to the frequentist methods, the Bayesian approach offers a flexible way to measure central tendency and treatment effect, and incorporate uncertainty in parameters of interest into considerations. In this article, we generalize a Bayesian design for Phase II clinical trials with endpoints in the exponential family from the two previously developed frequentist approaches. The proposed design minimizes the total sample sizes under pre-specified constraints on the expected length of posterior credible intervals for measures of treatment effect and central tendency in each group. The design is applicable for trials with fixed or optimal randomization allocation ratio and can be applied under adaptive procedure. Examples of method implementations are provided for different types of endpoints from the exponential family in both fixed and adaptive settings.

The win ratio was first proposed in 2012 by Pocock and his colleagues to analyze a composite endpoint while considering the clinical importance order and the relative timing of its components. It has attracted considerable attention since then, in applications as well as methodology. It is not uncommon that some clinical trials require a stratified analysis. In this article, we propose a stratified win ratio statistic in a similar way as the Mantel-Haenszel stratified odds ratio, derive a general form of its variance estimator with a plug-in of existing or potentially new variance/covariance estimators of the number of wins for the two treatment groups, and assess its statistical performance using simulation studies. Our simulations show that our proposed Mantel-Haenszel-type stratified win ratio performs similarly to the Mantel-Haenszel stratified odds ratio for the simplified situation when the win ratio reduces to the odds ratio, and our proposed stratified win ratio is preferred compared to the inverse-variance weighted win ratio and unweighted win ratio particularly when the data are sparse. We also formulate a homogeneity test following Cochran's approach that assesses whether the stratum-specific win ratios are homogeneous across strata, as this method is used frequently in meta-analyses and a better test for the win ratio homogeneity is not available yet.

Background: Durability of response is a clinically relevant dimension of the treatment effect in randomized clinical trials; it is often measured by comparing among the responders the duration of response between the treatment arms. However, since the comparison groups are defined by response (a post-randomization event), it is subject to analysis-by-responder bias, especially if the proportion of responders differs between the arms., Methods: Two simple methods are developed that use tumor shrinkage measurements in order to lessen analysis-by-responder bias by generating more comparable patient subsets in the control and experimental arms of the trial. These subsets are then used to estimate between-arm differences in response duration. In the subtraction method, responding patients with the least tumor shrinkage in the treatment arm with more responders are removed from the patient subset for that arm. In the addition method, non-responding patients with the most tumor shrinkage in the treatment arm with fewer responders are added to the patient subset for that arm. In both methods, the numbers of patients subtracted or added are such that the proportion of patients in the modified patient subset is the same as the proportion of responders in the other treatment arm., Results: The methods are demonstrated on a hypothetical dataset where they are shown to eliminate analysis-by-responder bias, and on two published analyses of randomized trials that compared the duration of response between the treatment arms., Conclusions: The proposed methods can lessen the analysis-by-responder bias. These methods to compare duration of response between treatment arms may provide a useful exploratory analysis to measure treatment efficacy among responders., (© The Author 2017. 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.)

Background: Pre-planned futility analyses are commonly used in oncology studies. The LUME-Lung 2 study (NCT00806819; 1199.14) was stopped early based on a pre-planned, non-binding futility analysis of investigator-assessed progression-free survival (PFS), although subsequent analysis showed that the primary endpoint of improvement in centrally reviewed PFS was met. Retrospective analyses were conducted to understand the discrepancy between interim futility and final analyses., Materials and Methods: LUME-Lung 2 investigated nintedanib in combination with pemetrexed versus placebo‒pemetrexed for the treatment of patients with advanced or recurrent non-squamous non-small cell lung cancer who had relapsed or failed one prior line of chemotherapy. Pre-planned futility analysis was carried out by the Data Monitoring Committee (DMC) after 50% of the events for the primary PFS analysis (713 events) had occurred; the threshold for futility was a conditional power of < 20%. Conditional/predictive powers and hazard ratios were calculated retrospectively after varying percentages of events had occurred for both investigator- and centrally reviewed PFS., Results: At the time of the pre-planned futility analysis, the conditional power was 10.3% and the predictive power was 18.5%; no safety issues were identified. Retrospective analysis showed that the conditional and predictive powers fluctuated considerably over time for both investigator- and centrally reviewed PFS and that the power only dropped by a notable amount, and below the futility threshold, at the time of the futility analysis., Conclusions: Retrospective investigations suggest that, had the DMC analysis been carried out at another time point, or had centrally reviewed PFS data been used, the futility outcome may have been different and the trial may have been continued. The design of futility analyses requires careful consideration and confirming negative futility outcomes by second analysis may be appropriate., Trial Number: NCT00806819., (© The Author 2017. 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.)

Clinical trials with multiple primary time-to-event outcomes are common. Use of multiple endpoints creates challenges in the evaluation of power and the calculation of sample size during trial design particularly for time-to-event outcomes. We present methods for calculating the power and sample size for randomized superiority clinical trials with two correlated time-to-event outcomes. We do this for independent and dependent censoring for three censoring scenarios: (i) the two events are non-fatal; (ii) one event is fatal (semi-competing risk); and (iii) both are fatal (competing risk). We derive the bivariate log-rank test in all three censoring scenarios and investigate the behavior of power and the required sample sizes. Separate evaluations are conducted for two inferential goals, evaluation of whether the test intervention is superior to the control on: (1) all of the endpoints (multiple co-primary) or (2) at least one endpoint (multiple primary). Copyright © 2017 John Wiley & Sons, Ltd., (Copyright © 2017 John Wiley & Sons, Ltd.)

Background: Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters. The most common frameworks used to analyse data from these types of trials are generalised estimating equations and generalised linear mixed models. A topic of much research into these methods has been their application to cluster randomised trial data and, in particular, the number of clusters required to make reasonable inferences about the intervention effect. However, for stepped wedge trials, which have been claimed by many researchers to have a statistical power advantage over the parallel cluster randomised trial, the minimum number of clusters required has not been investigated., Methods: We conducted a simulation study where we considered the most commonly used methods suggested in the literature to analyse cross-sectional stepped wedge cluster randomised trial data. We compared the per cent bias, the type I error rate and power of these methods in a stepped wedge trial setting with a binary outcome, where there are few clusters available and when the appropriate adjustment for a time trend is made, which by design may be confounding the intervention effect., Results: We found that the generalised linear mixed modelling approach is the most consistent when few clusters are available. We also found that none of the common analysis methods for stepped wedge trials were both unbiased and maintained a 5% type I error rate when there were only three clusters., Conclusions: Of the commonly used analysis approaches, we recommend the generalised linear mixed model for small stepped wedge trials with binary outcomes. We also suggest that in a stepped wedge design with three steps, at least two clusters be randomised at each step, to ensure that the intervention effect estimator maintains the nominal 5% significance level and is also reasonably unbiased.

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.

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.)

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: 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.

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.)