This is a repository copy of Practical guide to sample size calculations: an introduction. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/97115/ Version: Accepted Version Article: Flight, L. orcid.org/0000-0002-9569-8290 and Julious, S.A. (2016) Practical guide to sample size calculations: an introduction. Pharmaceutical Statistics , 15 (1). pp. 68-74. ISSN 1539-1604 https://doi.org/10.1002/pst.1709 This is the peer reviewed version of the following article: Flight, L., and Julious, S. A. (2016) Practical guide to sample size calculations: an introduction. Pharmaceut. Statist., 15: 68–74. doi: 10.1002/pst.1709., which has been published in final form at http://dx.doi.org/10.1002/pst.1709. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-820227.html). Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Practical guide to sample size calculations: an introduction Laura Flight1 and Steven. A. Julious1 March 24, 2016 Abstract A sample size justification is a vital step when designing any trial. How- ever, 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. 1 Introduction When planning a study, an essential step is the calculation of the minimum sample size required to meet the study objectives. Estimating the number of participants required to give a meaningful result is not always straightforward. A study with a poorly calculated sample size not only wastes resources but also has ethical implications. Recruiting too many participants runs the risk of more individuals than necessary receiving an inferior treatment. Too few may not give enough evidence to answer the original research question [1]. The motivations for and against a sample size calculation are discussed in Table 1 This paper is the first in a series of three articles. It summarises some important concepts required for sample size estimation. The steps needed to carry out calculations are outlined and demonstrated using the app SampSize. Subsequent papers demonstrate these steps for various trial objectives focussing on trials with a Normal primary endpoint. The series provides a condensed summary of key points and is largely adapted from the work of Julious [2]. 2 SampSize The calculations undertaken throughout the series can be carried out on the app SampSize (developed by the University of Sheffield and epiGenesys) [3]. This app has been developed as an aid to calculating sample sizes without the need for familiarity with alternative statistical packages. The examples emphasise the key components of a sample size calculation, illustrating how the app can be utilised when a sample size is required away from a computer. Formulae and statistical tables are also provided to aid the understanding of the components Table 1: The motivations for carrying out sample size calculations. A sample size justification is a requirement for any clinical investigation. Many journals in their guidelines for authors ask for a sample size justification. For example, the BMJ ask for [7] ‘The sample size calculation (drawing on previous literature) with an estimate of how many participants will be needed for the primary outcome to be statistically, clinically and/or politically significant.’ A sample size justification is required for an ethics submis- sion [8] and by CONSORT [9] and is recommended as an assessment of quality in the reporting of trials [8]-[10]. Why not do a sample size calculation? There is rarely enough information for precise calculations. When designing a study, a statistician will ask for any previ- ous, similar studies to obtain information for a sample size calculation. The information available, however, is often either sparse or suboptimal. This is not surprising. The ra- tionale for the trial being planned is usually to obtain good quality information on an intervention to change prescrib- ing or policy. If there was already good quality information, there would be no need to conduct a trial. Thus, an in- vestigator plans a trial to obtain good quality information but then has poor quality information to plan the trial. Hav- ing pilot information can assist greatly therefore in planning [11],[12]. Even when information is available to assist with sample size estimation, often the main constraints are availability of patients, finance, resources and time. Even given these final points, there should still be a sample size justification in the protocol with a statement that the sample size is based on feasibility disclosed. of a sample size calculation. Details on how to obtain the app are provided in Table 2. 3 Determining the Trial Objective The first step in a sample size calculation is to establish the trial objective. This motivates the type of trial to be conducted. In terms of hypothesis testing, there are four main types of trial: • Superiority trials, Table 2: How to obtain the app SampSize The SampSize app is available on the Apple App Store to download for free and can be used on iPod Touch, iPad and iPhones. The app is also available on the Android Market. It requires Android version 2.3.3 and above. For the calculations in this paper, an iPad is used. • Non-inferiority trials, • Equivalence trials and • Bioequivalence trials. We will not go into detail describing the types of trials in this paper we will do this in the subsequent papers [4],[5]. A distinction therefore needs to be drawn to highlight differences in trials designed to demonstrate ‘superiority’ and trials designed to demonstrate ‘equiv- alence’ or ‘non-inferiority’. This is discussed with an emphasis on how differences in the null and alternative hypotheses can impact on calculations. The types of trial can often be confusing especially when formally writing down the trial in terms of the null and alternative hypotheses. Clinical trials are often named after their alternative hypothesis. For example, in a superior- ity trial, the null hypothesis is that there is no difference between treatments, and the alternative hypothesis is that there is a statistically significant differ- ence. Informally, it is useful to consider the null hypothesis as ‘what we are investigating’, while the alternative is ‘what we wish to show’. A summary of these trial types and their hypotheses is given in Table 3. In addition to trials designed to investigate an effect or lack of trials can be undertaken to investigate possible effects for future investigation such as in pilot or early phase trials [6]. Such trials could be designed using an estimation approach to give a required precision around the estimates of effect. All these trial types can be handled in SampSize (Figure 1). This series will concentrate on superiority, non-inferiority and equivalence trials [4],[5]. It is possible a trial may have multiple objectives. In a clinical trial with three treatment arms, a new treatment, the standard treatment and a placebo treatment, the new drug may be compared with the placebo to test superiority and also to the standard treatment to test for non-inferiority. In this situation, the sample size calculation should be based on the type of trial used to achieve the primary objective. When there are multiple primary objectives (multiplicity), the calculations are more complex. The Committee for Proprietary Medicinal Products (CPMP) has guidance on important points to consider when there is multiplicity in trials [13]. The SampSize app cannot handle calculations with multiple endpoints. Table 3: Summary of hypotheses for different trial objectives available in the SampSize app. Type Description Hypotheses Superiority Determine whether H0 : µA = µB vs. H1 : µA =6 µB there is evidence of a difference in the desired outcome between treat- ment A and treatment B Non-inferiority Determine whether H0 : µA − µB ≤ −dNI vs. H1 : µA − µB > there is evidence that 1/dNI treatment A is not clinically inferior to treatment B in terms of a clinical difference dNI Equivalence Determine whether H0 : µA − µB ≤ −dE or H0 : µA − µB ≥ there is evidence of +dE vs. H1 : −dE < µA − µB > 1/dE no clinically mean- ingful difference dE between treatment A and treatment B Bioequivalence Determine whether H0 : µA/µB ≤ dBE or H0 : µA/µB ≥ there is evidence of 1/dBE vs. H1 : dBE < µA/µB < 1/dBE no clinically mean- ingful difference dBE in the bioavailability between treatment A and treatment B Figure 1: Options available on SampSize for different trial objectives. 3.1 The Type of Trial This series focusses on parallel group designs. In a crossover trial, each patient receives all treatments. Usually, the order in which the participant receives the treatment is randomised.