1. What size of trial do I need? Peter T. Donnan Professor of Epidemiology and Biostatistics Co-Director of TCTU Statistics for Health Research

2. Tayside Clinical Trials Unit TCTU now fully registered with UKCRC Trials unitsTCTU now fully registered with UKCRC Trials units Added randomisation serviceAdded randomisation service

3. Outline of Talk Basis of sample size Basis of sample size Effect size Effect size Significance level Significance level or (Type I error - α ) or (Type I error - α ) Type II error ( β) Type II error ( β) Power (1 – type II error) Power (1 – type II error)

4. What size of study do I need? 10 10,000 or

5. Answer As large as possible!As large as possible! Data is information, so the more data the sounder the conclusionsData is information, so the more data the sounder the conclusions In real world, data limited by resources: access to patients, money, time, etc..In real world, data limited by resources: access to patients, money, time, etc..

6. What size of study do I need? Expand the question: What size of study do I need to answer the question posed, given the size of my practice / clinic, or no. of samples, given the amount of resources (time and money) I have to collect the information?

7. What is the question? Efficacy: new drugs (CTIMP), weight loss programme (non- CTIMPEfficacy: new drugs (CTIMP), weight loss programme (non- CTIMP Equivalence (not very common)Equivalence (not very common) Non-inferiority (e.g.me-too drug with less side effects)Non-inferiority (e.g.me-too drug with less side effects)

8. Why bother? 1.You will not get your study past ethics! 2.You will not get your proposal past a statistical review by funders! 3.It will be difficult to publish your results!

9. Why bother? Is the study feasible?Is the study feasible? Is likely sample size enough to show meaningful differences with statistical significance?Is likely sample size enough to show meaningful differences with statistical significance? Does number planned give enough power or need larger number?Does number planned give enough power or need larger number?

10. OBJECTIVES Understand issues involved in estimating sample sizeUnderstand issues involved in estimating sample size Sample size is dependent on design and type of analysisSample size is dependent on design and type of analysis Parameters needed for sample size estimationParameters needed for sample size estimation

11. OBJECTIVES Understand what is necessary to carry out some simple sample size calculationsUnderstand what is necessary to carry out some simple sample size calculations Carry out these calculations with softwareCarry out these calculations with software Note SPSS does not yet have a sample size calculatorNote SPSS does not yet have a sample size calculator

12. What is the measure of outcome? Difference in Change in :Difference in Change in : Depression Scores, physiological measures (BP, Chol), QOL, hospitalisations,mortality, etc….Depression Scores, physiological measures (BP, Chol), QOL, hospitalisations,mortality, etc…. Choose PRIMARY OUTCOMEChoose PRIMARY OUTCOME A number of secondary but not too many!A number of secondary but not too many!

13. Unit of Randomisation 1)Randomisation by patient (Individual Randomisation)- RCT e.g. Crossover trial 2) Randomisation by practice (Cluster randomisation)

14. RANDOMISED CONTROLLED TRIAL (RCT) Gold standard method to assess Efficacy of treatment

15. RANDOMISED CONTROLLED TRIAL (RCT) Random allocation to intervention or control so likely balance of all factors affecting outcome Hence any difference in outcome ‘caused’ by the intervention

16. Randomised Controlled Trial RANDOMISED Eligible subjects Intervention Control

17. INTERVENTION: new drug/therapynew drug/therapy patient educationpatient education Health professional educationHealth professional education organisational changeorganisational change To improve patient care and/or efficiency of care delivery

18. Example RCT of new statin vs. old Evaluate cost-effectiveness of new statin Randomise eligible individuals to either receive new statin or old statin

19. Eligible subjects Evaluate cost-effectiveness of new statin on: Men ? Aged over 50? Cardiovascular disease? Previous MI? Requires precise INCLUSION and EXCLUSION criteria in protocol

20. WHAT IS THE OUTCOME? Improvement in patients’ healthImprovement in patients’ health Reduction in CV hospitalisationsReduction in CV hospitalisations More explicitly a greater reduction in mean lipid levels in those receiving the new statin compared with the old statinMore explicitly a greater reduction in mean lipid levels in those receiving the new statin compared with the old statin Reduction in costsReduction in costs

21. Decide on Effect size? Sounds a bit chicken and egg! Likely size of effect: What is the minimum effect size you will accept as being clinically or scientifically meaningful?

22. Likely Effect size? Change in Percentage with Total Cholesterol < 5 mmol/l NewOldDifferenceNewOldDifference 40%20%20%40%20%20% 30%20%10%30%20%10% 25%20%5%25%20%5%

23. Variability of effect? Variability of size of effect: Obtained from previous published studies and/or Obtained from pilot work prior to main study

24. Variability of effect? For a comparison of two proportions the variability of size of effect is dependent on: 1) the size of the study and 1) the size of the study and 2) the size of the proportions or percentages

25. How many subjects? 1) Likely size of effect 1) Likely size of effect  2) Variability of effect 2) Variability of effect  3) Statistical significance level3) Statistical significance level 4) Power4) Power 5) 1 or 2-sided tests5) 1 or 2-sided tests

26. Hypothesis Testing Goal is to keep ,  reasonably small

27. Statistical significance or type I error (  ) Type I error – rejecting null hypothesis when it is true: False positive (Prob=  ) Generally use 5% level (  = 0.05) i.e. accept evidence that null hypothesis unlikely with p< 0.05 May decrease this for multiple testing e.g. with 10 tests accept p < 0.005

28. 1 or 2-sided? Generally use 2-sided significance tests unless VERY strong belief one treatment could not be worse than the other e.g. Weakest NSAID compared with new Cox-2 NSAID

29. How many subjects? 1) Likely size of effect 1) Likely size of effect  2) Variability of effect 2) Variability of effect  3) Statistical significance level 3) Statistical significance level  4) Power4) Power 5) 1 or 2-sided tests 5) 1 or 2-sided tests 

30. Power and type II error Type II error (False negative): Not rejecting the null hypothesis (non-significance) when it is false Probability of type II error -  Power = 1 - , typically 80%

31. Type I and Type II errors ErrorProb. Screening Type I (  )False 1-specificity positive Type II(  )False1-sensitivity negative Analogy with sensitivity and specificity

32. Power Acceptable power 70% - 99% If sample size is not a problem go for 90% or 95% power; If sample size could be problematic go for lower power but still sufficient e.g. 80%

33. Power In some studies finite limit on the possible size of the study then question is rephrased: What likely effect size will I be able to detect given a fixed sample size?

34. How many subjects? 1) Likely size of effect 1) Likely size of effect  2) Variability of effect 2) Variability of effect  3) Statistical significance level 3) Statistical significance level  4) Power 4) Power  5) 1 or 2-sided tests 5) 1 or 2-sided tests 

35. Sample size for difference in two proportions Number needed for comparison depends on statistical test used For comparison of two proportions or percentages use Chi-Squared (  2 ) test

36. Comparison of two proportions Number in each arm = Where p 1 and p 2 are the percentages in group 1 and group 2 respectively

37. Assume 90% power and 5% statistical significance (2-sided) Number in each arm = z  = 1.96 (5% significance level, 2-sided) z 2β = 1.28 ( 90% power) are obtained from Normal distribution

38. Assume 40% reach lipid target on new statin and 20% on old drug Number in each arm = 105 Total = 210

39. Comparison of two proportions Repeat for different effects NewOldDifferencenTotalNewOldDifferencenTotal 40%20%20%105 21040%20%20%105 210 30%20%10%30%20%10% 25%20% 5%25%20% 5% 1964 3928 472 944 n.b. Halving effect size increases size by factor 4!

40. Increase in sample size with decrease in difference

41. Increase in power with sample size

42. Comparison of two means has a similar formula Number in each arm = Where and are the means in group 1 and group 2 respectively and  is the assumed standard deviation

43. Allowing for loss to follow-up / non-compliance The number estimated for statistical purposes may need to be inflated if likely that a proportion will be lost to follow-up For example if you know approx. 20% will drop-out inflate sample size by 1/(1-0.2) = 1.25

44. Software and other sample size estimation The formula depends on the nature of the outcome and likely statistical test Numerous texts with sample size tables and formula Software – nQuery Advisor® IBM SPSS SamplePower ~1600$

45. SUMMARY In planning consider: design, type of intervention, outcomes, sample size, power, and ethics together at the design stage

46. SUMMARY Invaluable information is gained from pilot work and also more likely to be funded (CSO, MRC, NIHR, etc.) Sample size follows from type of analysis which follows from design

47. SUMMARY Pilot also gives information on recruitment rate You may need to inflate sample size due to: Loss of follow-up/ drop-out Low compliance

48. Remember the checklist 1) Likely size of effect 1) Likely size of effect  2) Variability of effect 2) Variability of effect  3) Statistical significance level 3) Statistical significance level  4) Power 4) Power  5) 1 or 2-sided tests 5) 1 or 2-sided tests 

49. SUMMARY Remember in Scientific Research: Size Matters