Title: Sample size estimation in a single randomised clinical trial with or without interimanalyses
1Sample size estimation in a single randomised
clinical trialwith or withoutinterim-analyses
- Jørn Wetterslev M.D., Ph.D.
- Copenhagen Trial Unit
- Centre for Clinical Intervention Research
- Rigshospitalet
2Presentation
- The risk of type I and type II errors
- Sample size continuous outcome measure
- Sample size binary outcome measure
- Practical approach
- Expansion of sample size in multicentre trials
with interim analyses and heterogeneity
3Type I error risk
- The probability that you find a difference of a
given size (or more) given the null hypothesis,
that there is no difference, is true a
4Type II error risk
- The probability that you discard a difference of
a given size (or more) even though the
alternative hypothesis, that there is a
difference, is true ß
5Sample size in a randomised clinical trials
- The number of participants to be included in
the trial to detect or reject an anticipated
intervention effect µ with the chosen error risks - Type 1 error ?
- Type 2 error ? (power 1- ?)
-
6t-test statistic
- Continuous variable X N(X, SD2)
-
-
µ
X1 - X2
t
( )
?
SD
7Sample size in a RCT with a continuous outcome
measure
- The number of participants N to be included in
the trial to detect or reject an anticipated
intervention effect µ with a variance of ? with
the chosen ? and power 1- ? - N 2 ?
-
(Z2aZß)2 ? ?
µ2
8Sample size in a RCT with a continuous outcome
measure
- Equal group size and sample size N
- with ? 0.05 and ? 0.20
- N 32 ? 32 ?
-
2
2
SD
Noise
µ
Signal
9Sample size (SS) randomised clinical trial with
binary outcome equal group sizes
- SS 4 (Z?/2 Z?)2 ? / ?2
- ? PC - PE intervention effect
- ? P (1- P) the variance P (PCPE) / 2
- PC and PE
- event rates in control and intervention group
10Sample size in RCT with equal group size Type I
error risk 0.05 and power0.10
16(RR1)pCont(RR21) pCont (1RR)2
N
With RR pIntervent / pCont
11Sample size in a RCT with a binary outcome
measure and equal group sizes
- The number of participants N to be included in
the trial to detect or reject an estimated
intervention effect µ with an stimated variance
of ? with a chosen - ? 0.05 and power 1- ? 1- 0.20
- N 4 ? 64 ?
-
16 ? ? 2
2
?
µ
µ2
12Sample size in a RCT with a binary outcome measure
- Sample size N
- with ? 0.05 and ? 0.20
- N 64 ? 64 ?
-
2
2
?
Noise
µ
Signal
13Practical approach
- It is easy to calculate N if µ and ? are known
(true effect and true variance), - but they never
are !!! - Estimating or guessing a µ for µ and ? for ? is
difficult and may in the first trial be
impossible - If a trial is preceeded by numerous trials a
meta-analysis is a prerequisite to make estimates
of a realistic interventon effect µ and variance
?
14Practical approach
- Power and sample size calculater at
- http//biostat.mc.vanderbilt.edu/twiki/bin/view/Ma
in/PowerSampleSize
15Sample size in randomised trials with interim
analyses
-
- Multiple tests on accumulating data
- Heterogeneity in multicentre trials
16Expansion of fixed sample size by multiple
looks in interim analyses
- Multiple analyses of accumulating data may
overinterpret results of interim analyses - The total type I error risk doing repetitive
- significance testing on accumulating data with
- a 5
17Group sequential boundaries same group size
Z 1.96
Z - 1.96
18Sample size adjustment in sequential designs
a 0.05 1-ß 0.80
- Calculate the adjusted sample size by
multiplying of fixed sample size with a factor
from a relevant table (choice of a-spending) - Pococks design
19Group sequential boundaries same group size
Z 1.96
Z - 1.96
20Adjusting sample sizefor multiple
looksOBrien-Flemming
Sample size adjustment factor Mk a 0.05
1-ß0.80
- Calculate the adjusted maximum sample size by
multiplying fixed sample size with the adjusting
factor from appropriate tables (choice of
a-spending)
21Expected proportion of maximumfixed sample size
OBrien-Flemming
Percentage of fixed sample size a 0.05 1-ß
0.80
- The percentage of the maximum sample size
expected on average in trials with the - OBrien- Flemming design
22Adjusting sample sizefor multiple
looksOBrien-Flemming
Sample size adjustment factor Mk a 0.05
1-ß 0.80
- Calculate the adjusted maximum sample size by
multiplying fixed sample size with the adjusting
factor from appropriate tables (choice of
a-spending)
23Adjusted multiple looks sample size (M SS)
- Calculated setting µ and ? to relevant values
possibly found in evidence based on other
interventions in that area
24Sample size in a multicentre trial
-
- If you do not account for variability in the
number of recruited participants and the estimate
of the intervention effect between the sites in a
multicenter trial it may increase type I error
risk and reduce power - Valerij Fedorov og Byron Jones (GSK Pfizer)
- Statistical Methods in Medical Research
200514205-48
25A priori heterogeneity- adjusted multiple looks
sample size (APHM SS)
- Calculated setting µ and ? to a clinically
relevant value possibly found in evidence based
on other interventions in that area
26A priori heterogeneity adjusted multiple sample
size (APHM SS)
- Calculated setting µ and ? to
- clinical relevant values or realistic estimates
27Conclusions
- Estimate or calculate relevant or anticipated
intervention effect - Estimate or calculate relevant variance
- Calculate fixed sample size (without interim
looks) - Adjust for multiple looks when interim analyses
are planned - Adjust for anticipated heterogeneity between
sites in multicenter trials
28Type 1 error risk and power
- Type 1 error risk Pr?t?gt c ?
- when the effect of the intervention 0
- c ?-1(1 - ?/2) ( 1.96)
- Power Pr ?t?gt c 1 - ?
- when the effect of the intervention ? 0
- and ? Type 2 error risk