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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.

In 2016 we published three articles in Pharmaceutical Statistics that gave a practical guide to sample size calculations. In each of the articles there were instructions on how to obtain the App SampSize. This short communication updates these instructions and highlights the updates and added functionality to the App.

For any estimate of response, confidence intervals are important as they help quantify a plausible range of values for the population response. However, there may be instances in clinical research when the population size is finite, but we wish to take a sample from the population and make inference from this sample. Instances where you can have a fixed population size include when undertaking a clinical audit of patient records or in a clinical trial a researcher could be checking for transcription errors against patient notes. In this paper, we describe how confidence interval calculations can be calculated for a finite population. These confidence intervals are narrower than confidence intervals from population samples. For the extreme case of when a 100% sample from the population is taken, there is no error and the calculation is the population response. The methods in the paper are described using a case study from clinical data management.

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.

It is often of interest to measure the agreement between a number of raters when an outcome is nominal or ordinal. The kappa statistic is used as a measure of agreement. The statistic is highly sensitive to the distribution of the marginal totals and can produce unreliable results. Other statistics such as the proportion of concordance, maximum attainable kappa and prevalence and bias adjusted kappa should be considered to indicate how well the kappa statistic represents agreement in the data. Each kappa should be considered and interpreted based on the context of the data being analysed. Copyright © 2014 JohnWiley & Sons, Ltd.

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.

A number of meta-analyses have been undertaken to assess both the safety and efficacy of antidepressants in paediatric and adolescent patients. This article updates the analyses with additionally reported trials. The aim of this analysis was to investigate whether antidepressant treatments are associated with an increased risk of suicide-related outcomes in paediatric and adolescent patients. Also, in the same population, to assess whether antidepressant treatments are beneficial in terms of efficacy. A meta-analysis of randomised controlled trials of antidepressant treatments compared with placebo in paediatric and adolescent patients was undertaken of 6039 individuals participating in 35 randomised controlled trials. For suicide-related outcomes suicidal behaviour, suicidal ideation and suicidal behaviour or ideation were examined. These data presented the additional problem of the events of interest being rare. An analysis was described in this article to account for the rare events that also included studies which had no events on either treatment arm. There were trends to indicate that active treatments increased the risk of these events in absolute terms. For efficacy, the results indicated that antidepressant treatments did have a statistically significant effects compared to placebo but the effect was less for the trials in depression. The results are in the main consistent with previous meta-analyses on a smaller number of trials. There was evidence of an increased risk in suicide-related outcomes on antidepressant treatments, while antidepressant treatments were also shown to be efficacious.

In a non-inferiority trial to assess a new investigative treatment, there may need to be consideration of an indirect comparison with placebo using the active control in the current trial. We can, therefore, use the fact that there is a common active control in the comparisons of the investigative treatment and placebo. In analysing a non-inferiority trial, the ABC of: Assay sensitivity, Bias minimisation and Constancy assumption needs to be considered. It is highlighted how the ABC assumptions can potentially fail when there is placebo creep or a patient population shift. In this situation, the belief about the placebo response expressed in terms of a prior probability in Bayesian formulation could be used with the observed treatment effects to set the non-inferiority limit.

Since the web-based registry ClinicalTrials.gov was launched on 29 February 2000, the pharmaceutical industry has made available an increasing amount of information about the clinical trials that it sponsors. The process has been spurred on by a number of factors including a wish by the industry to provide greater transparency regarding clinical trial data; and has been both aided and complicated by the number of institutions that have a legitimate interest in guiding and defining what should be made available. This article reviews the history of this process of making information about clinical trials publicly available. It provides a reader's guide to the study registries and the databases of results; and looks at some indicators of consistency in the posting of study information. Copyright © 2010 John Wiley & Sons, Ltd.

Concerns about potentially misleading reporting of pharmaceutical industry research have surfaced many times. The potential for duality (and thereby conflict) of interest is only too clear when you consider the sums of money required for the discovery, development and commercialization of new medicines. As the ability of major, mid-size and small pharmaceutical companies to innovate has waned, as evidenced by the seemingly relentless decline in the numbers of new medicines approved by Food and Drug Administration and European Medicines Agency year-on-year, not only has the cost per new approved medicine risen: so too has the public and media concern about the extent to which the pharmaceutical industry is open and honest about the efficacy, safety and quality of the drugs we manufacture and sell. In 2005 an Editorial in Journal of the American Medical Association made clear that, so great was their concern about misleading reporting of industry-sponsored studies, henceforth no article would be published that was not also guaranteed by independent statistical analysis. We examine the precursors to this Editorial, as well as its immediate and lasting effects for statisticians, for the manner in which statistical analysis is carried out, and for the industry more generally.

In this paper we set out what we consider to be a set of best practices for statisticians in the reporting of pharmaceutical industry-sponsored clinical trials. We make eight recommendations covering: author responsibilities and recognition; publication timing; conflicts of interest; freedom to act; full author access to data; trial registration and independent review. These recommendations are made in the context of the prominent role played by statisticians in the design, conduct, analysis and reporting of pharmaceutical sponsored trials and the perception of the reporting of these trials in the wider community.

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.

It is a common belief that individual variation in response to treatment is an important explanation for the variation in observed outcomes in clinical trials. If such variation is large, it seems reasonable to suppose that progress in treating disease will be advanced by classifying patients according to their abilities or not to ‘respond’ to particular treatments. We consider that there is currently a lost opportunity in drug development. There is a great deal of talk about individual response to treatment and tailor-made drugs. However, relatively little work is being done to formally investigate, using suitable designs, where individual response to treatment may be important. Through a case study from a replicate cross-over study we show how, given suitable replication, it is possible to isolate the component of variation corresponding to patient-by-treatment interaction and hence investigate the possibility of individual response to treatment.

Biostatisticians have frequently uncritically accepted the measurements provided by their medical colleagues engaged in clinical research. Such measures often involve considerable loss of information. Particularly, unfortunate is the widespread use of the so-called 'responder analysis', which may involve not only a loss of information through dichotomization, but also extravagant and unjustified causal inference regarding individual treatment effects at the patient level, and, increasingly, the use of the so-called number needed to treat scale of measurement. Other problems involve inefficient use of baseline measurements, the use of covariates measured after the start of treatment, the interpretation of titrations and composite response measures. Many of these bad practices are becoming enshrined in the regulatory guidance to the pharmaceutical industry. We consider the losses involved in inappropriate measures and suggest that statisticians should pay more attention to this aspect of their work.

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.

This paper describes how simple decision science techniques can be used to optimize the clinical development plan for a given compound. Using a case study from the stroke therapeutic area it is shown how methods such as decision trees can be utilized to describe, and adjudicate on, individual development plans. Terminology pertinent to decision sciences is described and areas where it is recommended statisticians should focus are highlighted. 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.

This is a teaching paper intended as a quick introduction to some of the key concepts in the design of pharmaceutical trials for those new to the industry. Since the first ‘modern’ randomized clinical trial was reported in 1948 by the Medical Research Council, clinical trials have become a central component in the assessment of new therapies. The primary objective of any clinical trial is to obtain an unbiased and reliable assessment of a given regimen response independent of any known or unknown prognostic factors. The essential principals of trial design can be thought of as the ABC of allocation at random, blinding and controlled. In addition, the three Rs of endpoint selection – representative, reliability and reproducibility – are relevant in this context. This paper briefly describes the basic concepts for clinical trials and highlights possible points to consider. It draws heavily on the principles highlighted in the International Conference on Harmonisation guidelines as well as recommendations in the CONSORT statement. Copyright © 2002 John Wiley & Sons, Ltd.

Summary. The two-line model when the location of the changepoint is known is introduced, with an F-test to detect a change in the regression coefficient. The situation when the changepoint is unknown is then introduced and an algorithm proposed for parameter estimation. It is demonstrated that when the location of the changepoint is not known the F-test does not conform to its expected parametric distribution. Nonparametric bootstrap methods are proposed as a way of overcoming the problems encountered. Finally, a physiology example is introduced where the regression change represents the change from aerobic to anaerobic energy production.

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.

Meta-analysis is important in the evaluation of therapies for integrating the results of individual studies in order to advance or inform clinical research. In this special issue, different aspects of metaanalysis are reviewed using case studies to illustrate the methodologies being described. There can be issues when evaluating evidence when the events being observed are rare. Lane compares available methods for binary data considering different summary measures such as riskdifference, relative-risk and odds-ratio scale as well as fixed and random-effect methods in the assessment. The paper also highlights the benefit of how graphical approaches can add value. A case study is presented by Julious to highlight issues in evaluating evidence for safety and efficacy, which updates previous analyses with additionally reported trials. These data also consider the problem of the event of interest being rare. Graphical approaches are highlighted to investigate the assumptions in a meta-analysis. Often, however, a direct comparison of two therapies is not possible and indirect comparisons need to be made through a network meta-analysis. A sparsely connected network of 10 treatments for the treatment of diabetes is used by Senn et al. to make points about approaches to analysis. Graphical approaches, both of the network and of the results, are again described to summarise the data. Indirect comparisons are also used in the assessment, and design, of non-inferiority studies. In non-inferiority clinical trials, a test treatment is compared to an active-control rather than to placebo – when randomising to placebo is unethical or not feasible. A critical question is whether the test treatment would have been superior to placebo, had placebo been used in the non-inferiority trial. This question, as highlighted by Schmidli et al., can only be addressed indirectly, based on information from relevant historical trials with data on active-control and placebo. As highlighted multivariate meta-analysis is becoming increasingly popular. The advantages and limitations of multivariate meta-analysis have been discussed. The main limitation being computational complexity and hence, in a timely paper, Mavridis and Salanti review the statistical methods and the related software for multivariate meta-analysis. Pooling evidence from individual trials is important in the evaluation of research. For the individual trials adaptive designs have been recommended. However, there can be issues in pooling evidence when trials have stopped early. Bassler et al. review controversies associated with randomised controlled trials stopped early for apparent benefit and discussed how pooled effects from meta-analyses including trials stopped early could potentially overestimate an effect.

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.

An important part of the evaluation of a therapy is an investigation of the assumption of homogeneity of its effect across pre-defined subpopulations. In this paper we describe simple graphical presentations that could be used to assess the homogeneity of treatment effect and identify outliers. The emphasis in the paper is on meta-analysis but the methods described can be generalized to other investigations.

When designing a clinical trial there is a need to design a study that achieves the objectives of a trial both efficiently and with minimum resources. This paper describes seven trial designs that could possibly be used in clinical development and highlights how a design although not optimal for an individual study may be optimal for a wider clinical program. Copyright © 2011 John Wiley & Sons, Ltd.

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.

The main aim of many studies in clinical pharmacology is to describe the pharmacokinetic activity of a given compound. This pharmacokinetic activity for an individual is then evaluated through a series of summary parameters, such as area under the concentration-time curve (AUC), maximum concentration (Cmax) and the rate constant lambda, and it is evaluated across individuals by descriptive statistics of these parameters, such as the mean and range and a measure of spread such as the standard deviation. How the pharmacokinetic parameters are derived is described here. It is demonstrated that the assumption of an exponential half-life is often fundamental to the derivation of pharmacokinetic parameters. Given this fact, one would think it logical that data are analyzed with the appropriate statistics on the log-scale and not by summary statistics, such as arithmetic means, on the original scale. Why arithmetic means are used to describe the data is explored and the special nature of the log-transformation highlighted.