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When designing a clinical trial, one key aspect of the design is the sample size calculation. The sample size calculation tends to rely on a target or expected difference. The expected difference can be based on the observed data from previous studies, which results in bias. It has been reported that large treatment effects observed in trials are often not replicated in subsequent trials. If these values are used to design subsequent studies, the sample sizes may be biased which results in an unethical study. Regression to the mean (RTM) is one explanation for this. If only health technologies which meet a particular continuation criterion (such as p

Sample size calculations for cluster-randomised trials require inclusion of an inflation factor taking into account the intra-cluster correlation coefficient. Often, estimates of the intra-cluster correlation coefficient are taken from pilot trials, which are known to have uncertainty about their estimation. Given that the value of the intra-cluster correlation coefficient has a considerable influence on the calculated sample size for a main trial, the uncertainty in the estimate can have a large impact on the ultimate sample size and consequently, the power of a main trial. As such, it is important to account for the uncertainty in the estimate of the intra-cluster correlation coefficient. While a commonly adopted approach is to utilise the upper confidence limit in the sample size calculation, this is a largely inefficient method which can result in overpowered main trials. In this paper, we present a method of estimating the sample size for a main cluster-randomised trial with a continuous outcome, using numerical methods to account for the uncertainty in the intra-cluster correlation coefficient estimate. Despite limitations with this initial study, the findings and recommendations in this paper can help to improve sample size estimations for cluster randomised controlled trials by accounting for uncertainty in the estimate of the intra-cluster correlation coefficient. We recommend this approach be applied to all trials where there is uncertainty in the intra-cluster correlation coefficient estimate, in conjunction with additional sources of information to guide the estimation of the intra-cluster correlation coefficient.

Melanie L Bell,1 Amy L Whitehead,2 Steven A Julious2 1Department of Epidemiology and Biostatistics, Mel and Enid Zuckerman College of Public Health, University of Arizona, Tucson, AZ, USA; 2Medical Statistics Group, Design, Trials and Statistics, School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK Background: A pilot study can be an important step in the assessment of an intervention by providing information to design the future definitive trial. Pilot studies can be used to estimate the recruitment and retention rates and population variance and to provide preliminary evidence of efficacy potential. However, estimation is poor because pilot studies are small, so sensitivity analyses for the main trial’s sample size calculations should be undertaken.Methods: We demonstrate how to carry out easy-to-perform sensitivity analysis for designing trials based on pilot data using an example. Furthermore, we introduce rules of thumb for the size of the pilot study so that the overall sample size, for both pilot and main trials, is minimized.Results: The example illustrates how sample size estimates for the main trial can alter dramatically by plausibly varying assumptions. Required sample size for 90% power varied from 392 to 692 depending on assumptions. Some scenarios were not feasible based on the pilot study recruitment and retention rates.Conclusion: Pilot studies can be used to help design the main trial, but caution should be exercised. We recommend the use of sensitivity analyses to assess the robustness of the design assumptions for a main trial. Keywords: pilot, feasibility, sample size, power, randomized controlled trial, sensitivity analysis

Background: A key step in the design of a randomised controlled trial (RCT) is the estimation of the number of participants needed. By far the most common approach is to specify a target difference and then estimate the corresponding sample size; this sample size is chosen to provide reassurance that the trial will have high statistical power to detect such a difference between the randomised groups (at the planned statistical significance level). The sample size has many implications for the conduct of the study, as well as carrying scientific and ethical aspects to its choice. Despite the critical role of the target difference for the primary outcome in the design of an RCT, the manner in which it is determined has received little attention. This article reports the protocol of the Difference ELicitation in TriAls (DELTA2) project, which will produce guidance on the specification and reporting of the target difference for the primary outcome in a sample size calculation for RCTs. Methods/design: The DELTA2 project has five components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a 2-day consensus meeting bringing together researchers, funders and patient representatives, as well as one-off engagement sessions at relevant stakeholder meetings (stage 4); and the preparation and dissemination of a guidance document (stage 5). Discussion: Specification of the target difference for the primary outcome is a key component of the design of an RCT. There is a need for better guidance for researchers and funders regarding specification and reporting of this aspect of trial design. The aim of this project is to produce consensus based guidance for researchers and funders.

Background The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the ‘target difference’ and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups. Objective The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives. Methods The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document. Results Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered. Conclusions Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items. Funding Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC–National Institute for Health Research Methodology Research programme.

Background\ud \ud With millions of pounds spent annually on medical research in the UK, it is important that studies are spending funds wisely. Internal pilots offer the chance to stop a trial early if it becomes apparent that the study will not be able to recruit enough patients to show whether an intervention is clinically effective. This study aims to assess the use of internal pilots in individually randomised controlled trials funded by the Health Technology Assessment (HTA) programme and to summarise the progression criteria chosen in these trials.\ud \ud Methods\ud \ud Studies were identified from reports of the HTA committees’ funding decisions from 2012 to 2016. In total, 242 trials were identified of which 134 were eligible to be included in the audit. Protocols for the eligible studies were located on the NIHR Journals website, and if protocols were not available online then study managers were contacted to provide information.\ud \ud Results\ud \ud Over two-thirds (72.4%) of studies said in their protocol that they would include an internal pilot phase for their study and 37.8% of studies without an internal pilot had done an external pilot study to assess the feasibility of the full study. A typical study with an internal pilot has a target sample size of 510 over 24 months and aims to recruit one-fifth of their total target sample size within the first one-third of their recruitment time. There has been an increase in studies adopting a three-tiered structure for their progression rules in recent years, with 61.5% (16/26) of studies using the system in 2016 compared to just 11.8% (2/17) in 2015. There was also a rise in the number of studies giving a target recruitment rate in their progression criteria: 42.3% (11/26) in 2016 compared to 35.3% (6/17) in 2015.\ud \ud Conclusions\ud \ud Progression criteria for an internal pilot are usually well specified but targets vary widely. For the actual criteria, red/amber/green systems have increased in popularity in recent years. Trials should justify the targets they have set, especially where targets are low.

Background This article on choosing the target difference for a randomised controlled trial (RCT) and undertaking and reporting the sample size calculation has been dual published in the BMJ and BMC Trials journals. A key step in the design of a RCT is the estimation of the number of participants needed in the study. The most common approach is to specify a target difference between the treatments for the primary outcome and then calculate the required sample size. The sample size is chosen to ensure that the trial will have a high probability (adequate statistical power) of detecting a target difference between the treatments should one exist. The sample size has many implications for the conduct and interpretation of the study. Despite the critical role that the target difference has in the design of a RCT, the way in which it is determined has received little attention. In this article, we summarise the key considerations and messages from new guidance for researchers and funders on specifying the target difference, and undertaking and reporting a RCT sample size calculation. Methods The DELTA2 (Difference ELicitation in TriAls) project comprised five major components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a two-day consensus meeting bringing together researchers, funders and patient representatives (stage 4); and the preparation and dissemination of a guidance document (stage 5). Results and Discussion The key messages from the DELTA2 guidance on specifying the target difference are presented. Recommendations for specifying the target difference and the subsequent reporting of the sample size calculation are provided.

Background When designing a randomised controlled trial (RCT), an important consideration is the sample size required. This is calculated from several components; one of which is the target difference. This study aims to review the currently reported methods of elicitation of the target difference as well as to quantify the target differences used in Health Technology Assessment (HTA)-funded trials. Methods Trials were identified from the National Institute of Health Research Health Technology Assessment journal. A total of 177 RCTs published between 2006 and 2016 were assessed for eligibility. Eligibility was established by the design of the trial and the quality of data available. The trial designs were parallel-group, superiority RCTs with a continuous primary endpoint. Data were extracted and the standardised anticipated and observed effect size estimates were calculated. Exclusion criteria was based on trials not providing enough detail in the sample size calculation and results, and trials not being of parallel-group, superiority design. Results A total of 107 RCTs were included in the study from 102 reports. The most commonly reported method for effect size derivation was a review of evidence and use of previous research (52.3%). This was common across all clinical areas. The median standardised target effect size was 0.30 (interquartile range: 0.20–0.38), with the median standardised observed effect size 0.11 (IQR 0.05–0.29). The maximum anticipated and observed effect sizes were 0.76 and 1.18, respectively. Only two trials had anticipated target values above 0.60. Conclusion The most commonly reported method of elicitation of the target effect size is previous published research. The average target effect size was 0.3. A clear distinction between the target difference and the minimum clinically important difference is recommended when designing a trial. Transparent explanation of target difference elicitation is advised, with multiple methods including a review of evidence and opinion-seeking advised as the more optimal methods for effect size quantification.

The aim of this document is to provide practical guidance on the choice of target difference used in the sample size calculation of a randomised controlled trial (RCT). Guidance is provided with a definitive trial, one that seeks to provide a useful answer, in mind and not those of a more exploratory nature. The term “target difference” is taken throughout to refer to the difference that is used in the sample size calculation (the one that the study formally “targets”). Please see the glossary for definitions and clarification with regards other relevant concepts. In order to address the specification of the target difference, it is appropriate, and to some degree necessary, to touch on related statistical aspects of conducting a sample size calculation. Generally the discussion of other aspects and more technical details is kept to a minimum, with more technical aspects covered in the appendices and referencing of relevant sources provided for further reading.The main body of this guidance assumes a standard RCT design is used; formally, this can be described as a two-arm parallel-group superiority trial. Most RCTs test for superiority of the interventions, that is, whether or not one of the interventions is superior to the other (See Box 1 for a formal definition of superiority, and of the two most common alternative approaches). Some common alternative trial designs are considered in Appendix 3. Additionally, it is assumed in the main body of the text that the conventional (Neyman-Pearson) approach to the sample size calculation of an RCT is being used. Other approaches (Bayesian, precision and value of information) are briefly considered in Appendix 2 with reference to the specification of the target difference.

A sample size justification is a vital part of any trial design. However, estimating the number of participants required to give a meaningful result is not always straightforward. A number of components are required to facilitate a suitable sample size calculation. In this paper, the steps for conducting sample size calculations for non-inferiority and equivalence trials are summarised. Practical advice and examples are provided that illustrate how to carry out the calculations by hand and using the app SampSize.

Background \ud Substantial amounts of public funds are invested in health research worldwide. Publicly funded randomised controlled trials (RCTs) often recruit participants at a slower than anticipated rate. Many trials fail to reach their planned sample size within the envisaged trial timescale and trial funding envelope.\ud \ud Objectives \ud To review the consent, recruitment and retention rates for single and multicentre randomised control trials funded and published by the UK's National Institute for Health Research (NIHR) Health Technology Assessment (HTA) Programme.\ud \ud Data sources and study selection \ud HTA reports of individually randomised single or multicentre RCTs published from the start of 2004 to the end of April 2016 were reviewed.\ud \ud Data extraction \ud Information was extracted, relating to the trial characteristics, sample size, recruitment and retention by two independent reviewers.\ud \ud Main outcome measures \ud Target sample size and whether it was achieved; recruitment rates (number of participants recruited per centre per month) and retention rates (randomised participants retained and assessed with valid primary outcome data).\ud \ud Results \ud This review identified 151 individually RCTs from 787 NIHR HTA reports. The final recruitment target sample size was achieved in 56% (85/151) of the RCTs and more than 80% of the final target sample size was achieved for 79% of the RCTs (119/151). The median recruitment rate (participants per centre per month) was found to be 0.92 (IQR 0.43–2.79) and the median retention rate (proportion of participants with valid primary outcome data at follow-up) was estimated at 89% (IQR 79–97%).\ud \ud Conclusions \ud There is considerable variation in the consent, recruitment and retention rates in publicly funded RCTs. Investigators should bear this in mind at the planning stage of their study and not be overly optimistic about their recruitment projections.

Following publication of the original article [1], we have been notified of a few mistakes

Summary To enable an assessment of the costs and benefits of a new health technology one should use a range of outcome measures, including medical, psychosocial and economic. Therefore, unless a patient-reported outcome as well as clinical outcome is assessed in a study, the effect of a health technology on the patient will remain unknown as two therapies may have similar clinical consequences but different impacts upon the quality of the life of the patients. An important issue when designing a study with a new patient-reported outcome is the quantification of an effect size. Through a case study we highlight how simple calculations can enable the estimation of the effect sizes if there is information on established outcomes. This is done by mapping changes on the new scale to clinically relevant and important changes on established scales. We recommend the approaches described in this paper be considered for the quantification of important treatment effects when designing a clinical trial with a new patient-reported outcome measure.

Pilot studies are small‐scale studies conducted to gather information and provide a foundation for the design of a definitive trial. They do not seek to estimate treatment efficacy or effectiveness themselves but may be used to assess whether a definitive trial is feasible and how it can be carried out. The objectives of a study can be met only if a sufficient number of participants are recruited. A formal power calculation is not usually necessary for a pilot study where the focus is on estimation – for example, of feasibility parameters or the population variance – and the precision of these estimates. However, the sample size should still be justified as appropriate to meet the aims of the trial. The appropriate analysis of a pilot study would usually be a descriptive summary of the parameters of interest, addressing the original trial objectives. The analysis should not contain hypothesis testing for which the trial is not powered. The interpretation of the results should be in line with the feasibility of the planned main trial. The decision‐making process and changes made to the trial design based on the pilot study should be documented, and results presented in accordance with the CONSORT extension for pilot trials. Every effort should be made to publish the trial for transparency and to allow learning to be shared within the research community.

Adaptive designs have the potential to improve efficiency in the evaluation of new medical treatments in comparison to traditional fixed sample size designs. However, they are still not widely used in practice in clinical research. Little research has been conducted to investigate what adaptive designs are being undertaken. This review highlights the current state of registered adaptive designs and their characteristics. The review looked at phase II, II/III and III trials registered on ClinicalTrials.gov from 29 February 2000 to 1 June 2014, supplemented with trials from the National Institute for Health Research register and known adaptive trials. A range of adaptive design search terms were applied to the trials extracted from each database. Characteristics of the adaptive designs were then recorded including funder, therapeutic area and type of adaptation. The results in the paper suggest that the use of adaptive designs has increased. They seem to be most often used in phase II trials and in oncology. In phase III trials, the most popular form of adaptation is the group sequential design. The review failed to capture all trials with adaptive designs, which suggests that the reporting of adaptive designs, such as in clinical trials registers, needs much improving. We recommend that clinical trial registers should contain sections dedicated to the type and scope of the adaptation and that the term ‘adaptive design’ should be included in the trial title or at least in the brief summary or design sections. Electronic supplementary material The online version of this article (doi:10.1186/s13063-016-1273-9) contains supplementary material, which is available to authorized users.

Non-inferiority trials are motivated in the context of clinical research where a proven active treatment exists and placebo-controlled trials are no longer acceptable for ethical reasons. Instead, active-controlled trials are conducted where a treatment is compared to an established treatment with the objective of demonstrating that it is non-inferior to this treatment. We review and compare the methodologies for calculating sample sizes and suggest appropriate methods to use. We demonstrate how the simplest method of using the anticipated response is predominantly consistent with simulations. In the context of trials with binary outcomes with expected high proportions of positive responses, we show how the sample size is quite sensitive to assumptions about the control response. We recommend when designing such a study that sensitivity analyses be performed with respect to the underlying assumptions and that the Bayesian methods described in this article be adopted to assess sample size.

We show that the proportion of estimates of mean effects in future trials that would be expected to fall within the 95% confidence interval of a current trial is 83.4% for a large sample size — assuming that the sample size for a future trial is the same as for the current trial. Using the results from this paper you can predict the results for future trials from those observed in the current trial.

The study was done to assess the feasibility of conducting a trial evaluating the use of an intradialytic oral nutritional supplement (ONS) on nutritional status. The study design is a single centre, parallel group, external pilot randomised controlled trial (RCT). The setting was at a haemodialysis unit in Sheffield, UK. The aim was to recruit 30 trial participants to allow at least 12 evaluable patients per arm, but the actual study sample consisted of 10 adults with a body mass index (BMI) ≤22 kg/m2, receiving thrice weekly haemodialysis. All participants received nutritional advice from a renal dietitian as per usual practice. The intervention included the provision of an intradialytic ONS. Feasibility outcomes included recruitment to time and retention of participants along with palatability of ONS. Secondary outcomes were clinical parameters to obtain variance and estimates of effect size to inform the sample size calculation for a definitive trial. Recruitment was undertaken for a fixed period of 6 weeks. Rates were lower than expected mainly due to ineligibility with only 7% of screened patients (19/265) being eligible and 4% (10/265) of these being recruited. Due to the small proportion of patients eligible for the trial, all haemodialysis patients at the specified unit were assessed for eligibility. Data completion rates were low for session questionnaires (23%). Sample sizes derived from variance in secondary outcome measure of handgrip strength and adjusted for a dropout rate of 20% indicate that 189 patients would be required for a definitive RCT, requiring 19 UK haemodialysis units to participate. A definitive RCT is feasible with some adaptation to exclusion criteria and methodology. The exclusion criteria could be adapted to include an increase in upper limit for BMI. The use of questionnaires at each dialysis session may not be feasible but the inclusion of appetite and supplement consumption data collection at the main assessments would provide similar outcome data. Quality of life assessment using SF-12 would be acceptable. ISRCTN37431579 .

A sample size justification is a vital step when designing any trial. However, estimating the number of participants required to give a meaningful result is not always straightforward. A number of components are required to facilitate a suitable sample size calculation. In this paper, the general steps are summarised for conducting sample size calculations with practical advice and guidance on how to utilise the app SampSize.

A sample size justification is a vital part of any investigation. However, estimating the number of participants required to give meaningful results is not always straightforward. A number of components are required to facilitate a suitable sample size calculation. In this paper, the steps for conducting sample size calculations for superiority trials are summarised. Practical advice and examples are provided illustrating how to carry out the calculations by hand and using the app SampSize.

When designing a clinical trial an appropriate justification for the sample size should be provided in the protocol. However, there are a number of settings when undertaking a pilot trial when there is no prior information to base a sample size on. For such pilot studies the recommendation is a sample size of 12 per group. The justifications for this sample size are based on rationale about feasibility; precision about the mean and variance; and regulatory considerations. The context of the justifications are that future studies will use the information from the pilot in their design. Copyright © 2005 John Wiley & Sons, Ltd.

An estimated sample size is a function of three components: the required power, the predetermined Type I error rate, and the specified effect size. For Normal data the standardized effect size is taken as the difference between two means divided by an estimate of the population standard deviation. However, in early phase trials one may not have a good estimate of the population variance as it is often based on the results of a few relatively small trials. The imprecision of this estimate should be taken into account in sample size calculations. When estimating a trial sample size this paper recommends that one should investigate the sensitivity of the trial to the assumptions made about the variance and consider being adaptive in one's trial design. Copyright © 2004 John Wiley & Sons Ltd.

Health Related Quality of Life (HRQoL) instruments are increasingly important in evaluating health care, especially in cancer trials. When planning a trial, one essential step is the calculation of a sample size, which will allow a reasonable chance (power) of detecting a pre-specified difference (effect size) at a given level of statistical significance. It is almost mandatory to include this calculation in research protocols. Many researchers quote means and standard deviations to determine effect sizes, and assume the data will have a Normal distribution to calculate their required sample size. We have investigated the distribution of scores for two commonly used HRQoL instruments completed by lung cancer patients, and have established that scores do not have the Normal distribution form. We demonstrate that an assumption of Normality can lead to unrealistically sized studies. Our recommendation is to use a technique that is based on the fact that the HRQoL data are ordinal and makes minimal but realistic assumptions. © 2000 Cancer Research Campaign

Paired data occur in crossover trials and matched case-control studies, and it is rare to find studies reporting sample size calculations associated with these types of studies, despite recommendations from editors that sample size calculations should be justified. In this article we describe some simple formulas and strategies for calculating the number of patients that should be entered into a matched or paired study when the outcome measures are continuous, binary, or ordinal.

The problem of calculating the number of subjects in a paired or matched study in which the outcome variable is ordinal is discussed. A common approach in the case of a two category variable is to calculate the required number of discordant pairs, and then divide this by the expected proportion of discordant pairs to obtain the total sample size. An approximate solution for the number of discordant pairs is proposed for ordinal data and compared to sample sizes estimated through simulation. It is shown that the sample sizes are underestimated when the number of categories is two, but that the approximation improves as the number of categories increases. Comparison of the required discordant sample size when there are two categories with the required sample size for more than two categories would suggest that the loss of power is not great if a categorical variable is collapsed into only two categories. However, the total sample size required is likely to be greater with only two categories, since the expected proportion of discordant to concordant pairs increases. Since the expected number of discordant pairs is likely to decrease as the number of categories increases, this suggests that as a rule of thumb the required discordant sample size for the two category case be used as an approximation to the total required sample size when the number of categories is greater than two.

Background Randomised controlled trials (RCTs) are the gold standard assessment for health technologies. A key aspect of the design of any clinical trial is the target sample size. However, many publicly-funded trials fail to reach their target sample size. This study seeks to assess the current state of recruitment success and grant extensions in trials funded by the Health Technology Assessment (HTA) program and the UK Medical Research Council (MRC). Methods Data were gathered from two sources: the National Institute for Health Research (NIHR) HTA Journal Archive and the MRC subset of the International Standard Randomised Controlled Trial Number (ISRCTN) register. A total of 440 trials recruiting between 2002 and 2008 were assessed for eligibility, of which 73 met the inclusion criteria. Where data were unavailable from the reports, members of the trial team were contacted to ensure completeness. Results Over half (55%) of trials recruited their originally specified target sample size, with over three-quarters (78%) recruiting 80% of their target. There was no evidence of this improving over the time of the assessment. Nearly half (45%) of trials received an extension of some kind. Those that did were no more likely to successfully recruit. Trials with 80% power were less likely to successfully recruit compared to studies with 90% power. Conclusions While recruitment appears to have improved since 1994 to 2002, publicly-funded trials in the UK still struggle to recruit to their target sample size, and both time and financial extensions are often requested. Strategies to cope with such problems should be more widely applied. It is recommended that where possible studies are planned with 90% power.

A sample size justification should be given for all clinical investigations. However, sometimes the objective of a trial is to estimate an effect with a view to planning a later definitive study. This paper describes the calculations for designing studies where one wishes to adopt an estimation approach through using confidence intervals around the overall response. Calculations are given for data anticipated to take a Normal form. Copyright © 2004 John Wiley & Sons, Ltd.

Sample size calculations are now mandatory for many research protocols, but the ones useful in common situations are not all easily accessible. This paper outlines the ways of calculating sample sizes in two group studies for binary, ordered categorical, and continuous outcomes. Formulas and worked examples are given. Maximum power is usually achieved by having equal numbers in the two groups. However, this is not always possible and calculations for unequal group sizes are given.

Study objective Recruitment to clinical trials is a challenging but essential activity in emergency medicine. Conventional fixed-sample trials may continue to recruit patients after efficacy has been demonstrated or when further recruitment is futile. Adaptive trials make use of emerging information to modify aspects of a trial or terminate it prematurely, potentially resulting in savings in terms of sample size, time, and cost. We aim to use sequential testing procedures to reanalyze data from a fixed-sample trial, the Randomised Assessment of Treatment Using Panel Assay of Cardiac Markers (RATPAC) trial, and investigate the potential for adaptive designs to reduce unnecessary recruitment. Methods The trial was reanalyzed with a triangular group sequential design, with interim analyses planned every 3 months. Patients were analyzed in the order in which they entered the original trial. Results We found that the RATPAC trial could potentially have stopped 1 year earlier, with 722 patients enrolled compared with 2,243 patients in the original trial, making a potential saving of approximately $390,000. Estimates of effect were similar, and the qualitative conclusions of the original and group sequential RATPAC trials were in agreement. However, the group sequential approach is not without limitations and would have resulted in less precise estimates of effect and less information available for the subsequent evaluation of secondary endpoints. Conclusion Sequential designs are well suited in emergency medicine because of the rapidly obtained outcomes and the need to avoid unnecessary recruitment. We recommend that group sequential designs be considered for clinical trials in emergency medicine.

This article gives an overview of sample size calculations for a single response and a comparison of two responses in a parallel group trial where the outcome is binary. Sample size derivation is given for trials where the objective is to demonstrate: superiority, equivalence, non-inferiority and estimation to a given precision. For each type of trial the null and alternative hypotheses are described and how the impact these have on the sample size calculations. For each type of trial the calculations are highlighted through worked examples. Sample size tables for the different types of trials and worked examples are given to assist in future calculations.

The topic of this paper was prompted by a study for which one of us was the statistician. It was submitted to Annals of Internal Medicine. The paper had positive reviewer comment; however, the statistical reviewer stated that for the analysis to be acceptable for publication, the missing data had to be accounted for in the analysis through the use of baseline in a last observation carried forward imputation. We discuss the issues associated with this form of imputation and recommend that it should not be undertaken as a primary analysis.

One of the most important steps in the design of a pharmaceutical clinical trial is the estimation of the sample size. For a superiority trial the sample size formula (to achieve a stated power) would be based on a given clinically meaningful difference and a value for the population variance. The formula is typically used as though this population variance is known whereas in reality it is unknown and is replaced by an estimate with its associated uncertainty. The variance estimate would be derived from an earlier similarly designed study (or an overall estimate from several previous studies) and its precision would depend on its degrees of freedom. This paper provides a solution for the calculation of sample sizes that allows for the imprecision in the estimate of the sample variance and shows how traditional formulae give sample sizes that are too small since they do not allow for this uncertainty with the deficiency being more acute with fewer degrees of freedom. It is recommended that the methodology described in this paper should be used when the sample variance has less than 200 degrees of freedom.

This article gives an overview of sample size calculations for parallel group and cross-over studies with Normal data. Sample size derivation is given for trials where the objective is to demonstrate: superiority, equivalence, non-inferiority, bioequivalence and estimation to a given precision, for different types I and II errors. It is demonstrated how the different trial objectives influence the null and alternative hypotheses of the trials and how these hypotheses influence the calculations. Sample size tables for the different types of trials and worked examples are given. Copyright © 2004 John Wiley & Sons, Ltd.

Background Publicly funded trials regularly fail to recruit their target sample size or find a significant positive result. Adaptive clinical trials which may partly mediate against the problems are not often applied. In this paper we investigate the potential of a form of adaption in a clinical trial - a futility analysis - to see if it has potential to improve publicly funded trials. Methods Outcome data from trials funded by two UK bodies, the Health Technology Assessment (HTA) programme and the UK Medical Research Council (MRC), were collected. These data were then used to simulate each trial with a single futility analysis using conditional power, undertaken after 50% to 90% of the patients had been recruited. Thirty-three trials recruiting between 2002 and 2008 met the inclusion criteria. Stopping boundaries of conditional powers of 20%, 30% and 40% were considered and outcomes included the number of trials successfully stopped and number of patients saved. Results Inclusion of a futility analysis after 75% of the patients had been recruited would have potentially resulted in 10 trials, which went on to have negative results, correctly stopping for futility using a stopping boundary of 30%. A total of 807 patients across all the trials would potentially have been saved using these futility parameters. The proportion of studies successfully recruiting would also have increased from 45% to 64%. Conclusions A futility assessment has the potential to increase efficiency, save patients and decrease costs in publicly funded trials. While there are logistical issues in undertaking futility assessments we recommend that investigators should aim to include a futility analysis in their trial design wherever possible.

This paper describes the methods appropriate for calculating sample sizes for clinical trials assessing quality of life (QOL). An example from a randomized trial of patients with small cell lung cancer completing the Hospital Anxiety and Depression Scale (HADS) is used for illustration. Sample size estimates calculated assuming that the data are either of the Normal form or binary are compared to estimates derived using an ordered categorical approach. In our example, since the data are very skewed, the Normal and binary approaches are shown to be unsatisfactory: binary methods may lead to substantial over estimates of sample size and Normal methods take no account of the asymmetric nature of the distribution. When summarizing normative data for QOL scores the frequency distributions should always be given so that one can assess if non-parametric methods should be used for sample size calculations and analysis. Further work is needed to discover what changes in QOL scores represent clinical importance for health technology interventions.

Background There is little published guidance as to the sample size required for a pilot or feasibility trial despite the fact that a sample size justification is a key element in the design of a trial. A sample size justification should give the minimum number of participants needed in order to meet the objectives of the trial. This paper seeks to describe the target sample sizes set for pilot and feasibility randomised controlled trials, currently running within the United Kingdom. Methods Data were gathered from the United Kingdom Clinical Research Network (UKCRN) database using the search terms ‘pilot’ and ‘feasibility’. From this search 513 studies were assessed for eligibility of which 79 met the inclusion criteria. Where the data summary on the UKCRN Database was incomplete, data were also gathered from: the International Standardised Randomised Controlled Trial Number (ISRCTN) register; the clinicaltrials.gov website and the website of the funders. For 62 of the trials, it was necessary to contact members of the research team by email to ensure completeness. Results Of the 79 trials analysed, 50 (63.3%) were labelled as pilot trials, 25 (31.6%) feasibility and 14 were described as both pilot and feasibility trials. The majority had two arms (n = 68, 86.1%) and the two most common endpoints were continuous (n = 45, 57.0%) and dichotomous (n = 31, 39.2%). Pilot trials were found to have a smaller sample size per arm (median = 30, range = 8 to 114 participants) than feasibility trials (median = 36, range = 10 to 300 participants). By type of endpoint, across feasibility and pilot trials, the median sample size per arm was 36 (range = 10 to 300 participants) for trials with a dichotomous endpoint and 30 (range = 8 to 114 participants) for trials with a continuous endpoint. Publicly funded pilot trials appear to be larger than industry funded pilot trials: median sample sizes of 33 (range = 15 to 114 participants) and 25 (range = 8 to 100 participants) respectively. Conclusion All studies should have a sample size justification. Not all studies however need to have a sample size calculation. For pilot and feasibility trials, while a sample size justification is important, a formal sample size calculation may not be appropriate. The results in this paper describe the observed sample sizes in feasibility and pilot randomised controlled trials on the UKCRN Database.