Standard Operating Procedure for Calculating Sample Size for Trials

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1 size_v01.doc Page 1 of 8 Standard Operating Procedure for Calculating Sample Size for Trials SOP ID Number: Effective Date: 22/01/2010 Version Number & Date of Authorisation: V01, 15/01/2010 Review Date: 22/01/2012 SOP edocument kept: S:\CLINICAL_TRIALS\SOPs\EFFECTIVE_SOPs_ Guides \SPONSOR SOPs\SPON_S02_SOP for calculation of sample size_v01.docx Page 1 of 8

2 size_v01.doc Page 2 of 8 Revision Chronology: SOP ID Number: Effective Date: Reason for Change: Author: New SOP 22/01/2010 Julie Barber Gareth Ambler Rumana Omar ACRONYMS: JBRU Joint Biomedical Research Unit GCP Good Clinical Practice SOP Standard Operating Procedure BSG Biostatistics Group Page 2 of 8

3 size_v01.doc Page 3 of 8 1. PURPOSE Standard Operating Procedure for Calculating Sample Size for Trials This Standard Operating Procedure (SOP) has been written to describe the procedure for calculating and reporting sample size calculations for a randomised trial protocol. This document is meant for internal use by statisticians in the JBRU Biostatistics Group. 2. JOINT UCLH/UCL BIOMEDICAL RESEARCH UNIT POLICY All SOPs produced from the JBRU must be used in conjunction with local NHS Trust and UCL policies and procedures. The JBRU acts as the representative of the Sponsor and will be the official name used on all SOPs. 3. BACKGROUND A sample size calculation is carried out at the design stage of a trial and reported in the trial protocol. This is to ensure that adequate numbers of patients are recruited to the study to provide the power or precision needed to detect or estimate important treatment effects. The sample size is based on the primary outcome(s) specified for the trial. The method of calculating sample size will depend on the type of primary outcome (e.g. continuous, categorical) and the design of the study (e.g. cross over, parallel group). In calculating sample size it is important to allow for expected loss of patients during the study and non compliance with randomised intervention. In reporting sample size in the protocol and other trial documents it is essential that complete information regarding the calculation is given and estimates used are properly justified. 4. SCOPE OF THIS SOP This SOP applies to calculation of sample size for all randomised trials where members of the Biostatistics Group are the main trial statistician. 5. RESPONSIBLE PERSONNEL The trial statistician should follow this SOP. 6. PROCEDURE 6.1. General detail for calculating sample size Calculation of sample size for a randomised trial will usually involve a power based calculation for the specified primary outcome(s). The method of calculation will depend on the form of the outcome and design of the study. However in most cases the following will apply: o Power will be at least 80% o A 2-sided significance level of 5% will be used except where adjustments are necessary to allow for interim analysis or multiple primary outcomes and in the particular case of equivalence trials (see later). o If appropriate, adjustment will be made for the estimated dropout rate (e.g. inflating by 1/(1-total loss rate)) Page 3 of 8

4 size_v01.doc Page 4 of 8 o If appropriate, adjustment will be made for estimated non compliance (e.g. inflating by 1/(1-total non compliance rate) 2 ) o If appropriate, sample size should be inflated to allow for planned investigations of treatment interactions. In some cases a precision based calculation may be appropriate or complementary to a power based calculation. Precision based calculations are derived from standard formulae for confidence intervals. They require specification of the width of the confidence interval as well as variance estimates Usual power based methods for common trial designs Two parallel groups Continuous outcome Assuming the outcome is approximately Normally distributed and a simple 2 sample t- test will be used to compare the treatment groups, the sample size calculation will follow standard methods that require specification of : o The smallest difference in means of clinical importance (e.g difference in average blood pressure) o Standard deviation(s) (SD) of the measure (if assuming equal SDs the estimate should be relevant to the comparison / control group, for unequal SDs separate estimates are needed for each group) For non Normally distributed data where a Mann-Whitney test is planned, a conservative estimate of sample size may be obtained by dividing the t-test sample size by Continuous outcome with baseline measurements (ANCOVA) In cases where the primary analysis is an analysis of covariance including a baseline covariate, an adjustment should be made to the sample size calculation. This requires an estimate of the correlation between repeated measurements of the primary outcome. Binary outcome For a binary outcome where a simple Chi squared test is planned for analysis the following information will be required to calculate sample size: o smallest effect size of clinical importance (e.g. difference in proportions) o estimate of the prevalence of the disease in the control group Where a Fisher s exact test is planned for analysis an exact method for calculating sample size should be used. Survival outcome For a survival outcome where the basic analysis will involve a log rank test with an assumption of proportional hazards, the following information is required for the sample size calculation: Either o anticipated values for the proportions surviving in the two groups at a chosen timepoint (e.g. 1 year) Or o anticipated values for the proportion surviving in the comparison group and an estimate of the hazard ratio. Or Page 4 of 8

5 size_v01.doc Page 5 of 8 o anticipated values for the proportion surviving in the comparison group and estimates of the median survival times in the two groups (assuming an exponential distribution) More than two parallel groups In the case of more than two treatment groups, the sample size for a comparison of two groups should be used and multiplied up to allow for the number of parallel groups planned. An adjusted P-value should be used in this calculation (e.g. based on Bonferroni) to allow for multiple testing Cross over trials Continuous outcome Assuming the outcome is approximately Normally distributed the sample size calculation can be carried out based on a paired t-test. This requires specification of: o the smallest clinically important difference in the outcome o the SD of the differences between repeated measurements for the outcome Binary outcome Assuming a McNemar s test is appropriate for the primary analysis, the sample size calculation will require estimates of: o proportion of discordant pairs o odds ratio (of responding positively on treatment B and negatively on treatment A compared with positively on treatment A and negatively on treatment B) Cluster randomised trials or trials with repeated measurements The sample size obtained for a parallel group study with a single outcome measurement should be inflated by the design effect. This requires estimates of the average cluster size and the intra cluster correlation coefficient Parallel equivalence trial A basic analysis for an equivalence trial usually involves calculation of a 100(1-α)% confidence interval for the true difference in the primary outcome. Calculation of sample size for such trials is based on limiting the probability (power) that the upper limit for the confidence interval will not exceed a pre-specified value of equivalence. For the sample size calculation the following must be specified : o the range of equivalence / maximum allowable difference in primary outcome between groups (ie the difference below which treatments will be considered equivalent) o one sided α this is often set to be quite large e.g. 0.1 or 0.2) o overall response rate / mean, depending on the outcome Other considerations Interim analyses In trials where one or more interim analysis is planned, an appropriate adjustment to the significance level should be made in the sample size calculation (for example using O Brien and Flemings method). In addition details should be given of planned stopping rules Multiple primary endpoints Page 5 of 8

6 size_v01.doc Page 6 of 8 Where multiple primary endpoints are planned the sample size should be calculated for each using a significance level that reflects the number of comparisons to be made (e.g using the Bonferroni method). The largest sample size should then be planned for in the study Software and tables for calculation of sample size Recommended software for carrying out the sample size calculations described above are: 1) Stata 3 (commands sampsi, stpower ) 2) nquery advisor 4 Tables for sample size calculation are available in Machin et al (1997). 1 Dr Gareth Ambler has written a program in Stata for calculation of sample size for Fisher s exact test. Sample size calculation should not be performed using free web based calculators that have not been adequately validated. 6.5 Writing up sample size calculations The paragraph(s) used in trial documents (e.g. in the protocol and ethics form) to describe the sample size calculation should include all information to allow recalculation of the sample size. The following information is essential: o statement of the primary outcome o statement regarding the main method of analysis to be used o a reference to the methodology used for the sample size calculation o detail of all estimated values used in the calculation and source / justification for these (e.g SD used, smallest effect size, dropout rate, power and significance levels) o statement of assumptions made in the calculation (e.g assumptions of Normality, proportional hazards) o statement justifying that the planned recruitment period will be adequate to recruit the required number of patients Example This sample size calculation is based on the primary outcome of time until no benefit of treatment. The main analysis will therefore be a comparison of survival between the intervention and placebo groups, illustrated with Kaplan Meier curves and tested using the log rank test. All analyses will be by intention to treat. The sample size calculation is based on standard equations for the log rank test (reference) [or the sample size calculation has been performed using the statistical software x ]. To calculate sample size we have used estimates from our experience with previous work in this area (reference). This has indicated the proportion of patients expected to benefit in the placebo arm by 12 months would be up to 5% and that a minimum hazard ratio of 2.5 in favour of the intervention would be plausible and of considerable interest. Sample size calculations are inflated to allow for the possibility of up to a 10% withdrawal rate from the study for other reasons. With these assumptions and with 80% power and a 5% significance level, a total of 58 patients (29 per group) are required. The average recruitment rate per month is expected to be 2.5 subjects so that the 24 month recruitment period will ensure adequate numbers are randomised. Page 6 of 8

7 size_v01.doc Page 7 of 8 7. REFERENCES 1. Machin D, Campbell M, Fayers P, Pinol A. Sample size tables for clinical studies. Blackwell Science 1997) 2. Randle R., Wolfe D. Introduction to the theory of nonparametric statistics, Wiley, New York StataCorp Statistical Software: Release College Station, TX: Stata Corporation. 4. nquery Advisor, version 6, Statistical Solutions, USA. 8. APPENDICES 9. TEMPLATES/LOGS ASSOCITATED TO THIS SOP 10. SOP DISSEMINATION AND TRAINING This SOP will be provided to all statisticians of the Biostatistics group by the SOP authors. BSG staff will be requested to read the SOP and will given an opportunity to ask specific questions. BSG statisticians will then sign the SOP training log in section SIGNATURE PAGE Author and Job Title: Rumana Omar, Julie Barber and Gareth Ambler Signature: Date: Authorised by: Name and Job Title Helen Cadiou, QA Manager Signature: Date: Page 7 of 8

8 size_v01.doc Page 8 of SOP TRAINING LOG 1 Name of Staff (Capital letters) Job Title: Department: Training Date I confirm that I understand & agree to work to this SOP SIGNATURE Name of Trainer (if training required) Signature Date Page 8 of 8