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

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

3. Tayside Clinical Trials Unit
TCTU fully registered with UKCRC Trials units, 2017
Sir Kent Woods, Emeritus Professor at the University of Leicester and Chair of the International Review Committee said:
“The International Registration Review Committee is delighted to see the clear impact of this programme on the quality of conduct of clinical trials research in the UK.”

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

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

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

7. 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?

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

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

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

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

12. OBJECTIVES
Understand what is necessary to carry out some simple sample size calculations
Carry out these calculations with software
Note SPSS does have a sample size calculator but expensive!

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

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

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

16. 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

17. Randomised Controlled Trial
Eligible subjects
Intervention
Control

18. To improve patient care and/or efficiency of care delivery
INTERVENTION:
To improve patient care and/or efficiency of care delivery
new drug/therapy
patient education
Health professional education
organisational change

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

20. 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

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

22. (Minimum Clinically Important Difference)
Decide on Effect size?
(Minimum Clinically Important Difference)
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?

23. Likely Effect size?
Change in Percentage with Total Cholesterol < 5 mmol/l
New Old Difference
40% 20% 20%
30% 20% 10%
25% 20% 5%

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

25. 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
2) the size of the proportions or percentages

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

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 
2) Variability of effect 
3) Statistical significance level 
4) Power
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
Analogy with sensitivity and specificity
Error Prob. Screening
Type I () False 1-specificity positive
Type II () False 1-sensitivity negative

32. Hypothesis Testing
Goal is to keep a, b reasonably small

33. 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%

34. 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?

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

36. 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

37. Comparison of two proportions
Number in each arm =
Where p1 and p2 are the percentages in group 1 and group 2 respectively

38. Assume 90% power and 5% statistical significance (2-sided)
Number in each arm =
z = 1.96 (5% significance level, 2-sided) z2β = 1.28 ( 90% power) are obtained from Normal distribution

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

40. Comparison of two proportions
Repeat for different effects
New Old Difference n Total
40% 20% 20%
30% 20% 10%
25% 20% 5%
n.b. Halving effect size increases size by factor 4!

41. Increase in sample size with decrease in difference

42. Increase in power with sample size

43. 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

44. 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

45. 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$
G Power – free
- free

46. nQuery Advisor® Software

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

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

49. 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

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

51. SUMMARY
Remember in Scientific Research:
Size Matters