Sample Size Calculations in Acute Stroke Trials: A
Systematic Review of Their Reporting, Characteristics,
and Relationship With Outcome
Chris S. Weaver, RGN; Jo Leonardi-Bee, MSc; Fiona J. Bath-Hextall, PhD; Philip M.W. Bath, FRCP
Downloaded from http://stroke.ahajournals.org/ by guest on June 16, 2017
Background and Purpose—Only a few randomized controlled trials in acute stroke have shown a treatment-related benefit.
Inadequate trial design, especially low sample size, may partly explain this failure. We investigated sample size
calculations (SSCs) in a systematic review of acute stroke trials.
Methods—Full reports of nonconfounded randomized controlled trials that recruited patients within 1 week of stroke onset
and were published before the end of 2001 were identified from the Cochrane Library and other bibliographic databases.
Information on the SSC and outcome event rates was collected for each trial.
Results—Of 189 identified trial reports, 57 (30%) reported ⱖ1 components of the SSC, phase II 14/129 (11%) versus phase
III 43/60 (72%) (P⬍0.001), with 32 (56%) giving all the required parameters. Significance (␣) was mentioned in 54
(96%) reports; 53 used a significance level of ␣⫽0.05. And 55 (98%) reports gave the power (1⫺␤) of the study (median
[25th and 75th percentile] 0.80 [0.80, 0.90]). The anticipated percentage of control subjects having a primary outcome
event was given in 24 (42%) articles: case fatality 21.8% (11.8%, 23.5%, n⫽4) and combined death or disability/
dependency 55.5% (44.5%, 66.3%, n⫽20); 25 studies used other outcomes and 8 studies gave insufficient information.
Four of the 22 trials achieved a control rate within 5% of their prediction. 49 (86%) reports gave the anticipated
treatment effect; case fatality: anticipated 9.5% (1.1%, 12.5%, n⫽6), achieved ⫺0.3% (⫺4.1%, ⫹2.4%); combined
death or disability/dependency: anticipated 13.0% (10.0%, 16.0%, n⫽25), achieved 1.8% (⫺0.5%, ⫹5.4%). The median
calculated sample size was 600 (198, 995, n⫽54).
Conclusions—Too few trial publications report the assumptions underlying their SSC. Most trials were underpowered, ie,
power ⬍0.90, used inappropriate assumptions for event rates, and were grossly overoptimistic in their expectation of
treatment effect. These deficiencies will together have resulted in trials being far too small and reduced their chance of
being able to detect real treatment effects. (Stroke. 2004;35:1216-1224.)
Key Words: stroke 䡲 randomized controlled trials 䡲 acute stroke 䡲 systematic review
A
lthough several hundred trials have been completed in
acute stroke, only a few assessing efficacy have been
positive, eg, relating to aspirin, alteplase, and prourokinase.1–3 Many explanations have been put forward to explain
this situation, eg, findings in animals may be irrelevant to
humans,4,5 drugs are ineffective6 –10 or detrimental,11–13 and
trial design may be suboptimal, using inappropriate outcomes4,14 or statistical analyses.15 To address these problems,
the Stroke Therapy Academic Industry Roundtable (STAIR)
group created guidelines with the aim of improving future
experimental and clinical trials.16 –18
In an earlier study, we found that the reporting of trials was
often suboptimal.19 One result in that systematic review was
that components of the sample size calculation (SSC) were
only published in 33 of 114 trials,19 and that these studies
were mostly small and underpowered. We hypothesized that
a further reason why trials might be failing could relate to
their design in the context of an inadequate sample size.
Conventionally, a trial’s sample size is estimated mathematically from 4 assumptions if a dichotomous outcome measure
is being assessed: (1) anticipated treatment effect; (2) event
rate in the control group; (3) desired power; and (4) desired
significance. Inappropriate choice of values for these parameters would lead to trials being too small. Here, we systematically assess the reporting and parameters used in SSC in
trials of acute stroke.
Materials and Methods
Trial Eligibility
We assessed full and final reports of nonconfounded randomized
controlled trials that recruited patients within 1 week of stroke onset.
Studies published in a peer-reviewed journal by the end of 2001 were
Received September 10, 2003; final revision received January 7, 2004; accepted January 15, 2004.
From Institute of Neurosciences (C.S.W., P.M.W.B.), Institute of Clinical Research (J.L.-B.), and School of Nursing (F.J.B.-H.), University of
Nottingham, UK.
Correspondence to Philip Bath, Division of Stroke Medicine, Institute of Neuroscience, University of Nottingham, City Hospital Campus, Nottingham
NG5 1PB, UK. E-mail [email protected]
© 2004 American Heart Association, Inc.
Stroke is available at http://www.strokeaha.org
DOI: 10.1161/01.STR.0000125010.70652.93
1216
Weaver et al
TABLE 1.
Information Sought for Each Trial
Acute Stroke Trials
1217
Results
Year of publication
Trials
Type of trial: phase II (pilot, safety, explanatory, phase III 关efficacy兴)
The searches found 189 trial reports (phase II, n⫽129; phase
III n⫽60) that fulfilled the inclusion criteria. A total of 82 716
patients had been included, with individual trials enrolling
between 12 and 21 106 subjects, median (25th to 75th
percentile), 89 (40 to 294). The studies were reported over a
period from 195621 to the end of 2001. Trial size had
increased during this period (rs⫽0.387, P⬍0.001).
Primary outcome measure
Sample size calculation reported
Predicted rates for primary outcome
Control/placebo group (p1)
Active group (p2)
Absolute treatment effect (p1⫺p2)
Sample size in each treatment group
Achieved rates
Case fatality rate in placebo group
Case fatality rate in treatment group
Combined death or dependency/disability in placebo group
Combined death or dependency/disability in treatment group
Sample size in each treatment group
Downloaded from http://stroke.ahajournals.org/ by guest on June 16, 2017
N of treatment groups
Final trial result for primary outcome—positive, neutral, negative
included. Trials that had been published in abstract-form alone or as
a chapter in a book, had a crossover design, only compared active
treatments, or primarily involved patients with transient ischemic
attack, subarachnoid hemorrhage, or nonstroke conditions were
excluded.
Identification of Acute Stroke Trials
Potential trials for inclusion were identified from the Cochrane
Controlled Trials Register (Cochrane Library, issue 1, 2002). Further
searches were made of the EMBASE and MEDLINE bibliographic
databases, a previous review of acute stroke trials,19 and a book
detailing trials in acute stroke.20 The key words used in searches
were: randomized controlled trial, controlled clinical trial, acute
stroke, ischemic stroke, cerebrovascular disorders, and cerebral
hemorrhage (see Figure 1).
Data Extraction
Each publication was scrutinized and the data were abstracted by 2
authors (C.S.W., J.L.-B.) for information about the trial. Components of the SSC were recorded (Table 1): significance level (␣),
power (1⫺␤), anticipated rates of primary outcome in control group
(p1) and treatment group (p2), and intended absolute treatment effect
(P⫽p2⫺p1). When necessary, relative or proportional effects were
converted to absolute effects. Data were excluded if based on mean
or median scores. Achieved sample size, outcome rates in control
and treatment groups, and actual treatment effect (positive, neutral,
or negative) were also recorded (Table 1). Trials were defined as
phase II if they studied safety, tolerability, feasibility, and/or surrogate measures of outcome, and phase III if they stated that their
primary intention was to assess efficacy, usually judged on death,
combined death and disability/dependency, or impairment. Data
were double-entered (C.S.W., J.L.-B.) into a database (FileMaker
Pro v4.1; Claris, Santa Clara) and cross-checked to ensure accuracy.
Any disagreements about the interpretation of the information in the
report were discussed and resolved by P.M.W.B. A questionnaire
was sent out to all first-named authors to see if they could provide
any further information to the data extracted.
Analysis
Nonparametric descriptors (median, 25th to 75th percentile) and tests
(␹2 with Yates correction, Spearman correlation) were used because
most of the data were of an ordered categorical (ordinal) or binary
(nominal) type. Analysis was performed using the SPSS statistical
package (v10.0.7a for Apple PowerPC; SPSS Corp).
Sample Size Calculation
Of the 189 reports, 57 (30%) reported ⱖ1 components of the
SSC (Table 1); 32/57 (56%) reports gave all the required
parameters. Although the first trial in acute stroke was published
in 1956, the first to give a SSC was in 1983.22 The proportion of
trials reporting a SSC increased after the publication of the
CONSORT statement (which recommended that SSC should be
reported in trial publications in 199623). Before CONSORT,
27/135 (20%) included SSC; after CONSORT, 29/54 (54%)
included SSC (␹2⫽19.9 P⬍0.001; see Figure 2). A higher
proportion of phase III trials reported a SSC in comparison with
phase II trials: phase II, 14/129 (11%); phase III, 43/60 (72%)
(␹2⫽70.1, P⬍0.001). A value for significance (␣) was present in
55 of 57 (96%) reports; 54 of these used ␣⫽0.05 whereas 1 used
␣⫽0.025.24 Power (1⫺␤) was given in 56 of 57 (98%) reports;
the median power was 0.80 (25th to 75th percentile 0.80 to 0.90,
range 0.75 to 0.95).
Trial Results
Of the 57 trials, 8 were positive on their primary outcome
(active treatment superior to control), 43 were neutral, and 6
were negative (control superior to active treatment). When
assessing just phase III trials (Tables 2 and 3), 4 were
positive: CAST (aspirin), NINDS (alteplase), STAT (ancrod),
and PROACT II (pro-urokinase);1–3,25 35 were neutral; and 3
were negative: EAST (enlimomab), MAST-E (streptokinase),
and ATLANTIS A (alteplase).13,26,27
Functional Outcome
The anticipated percentage of control subjects having an event
for the trial’s primary outcome was reported in 24 of 57 (42%)
articles: case fatality, 21.8% (11.8% to 23.5%, n⫽4); combined
death or disability/dependency, 55.0% (44.5% to 66.3%, n⫽20).
And 25 studies used another outcome, such as change in
neurological score (n⫽11), ordinal comparison of functional
outcome (n⫽7), rate of spontaneous recanalization (n⫽1), percentage of patients achieving a National Institute of Health
Stroke Scale (NIHSS) score of ⱕ1 (n⫽1), or another approach
(n⫽5). Eight studies gave insufficient information. The median
anticipated rate of combined death and dependency/disability
was 55.0%, with that for death being 21.8%. Table 4 shows the
full results. The achieved rates of death, or combined death and
dependency, in control patients tended to be lower than planned;
slightly ⬎50% of studies came within 20% of their target. Table
5 shows a more detailed examination. Only 7 (12.5%) trials
stated that the control rate estimate was obtained from a previous
study.
Forty-eight of 57 (84%) reports gave the desired absolute
treatment effect (P), reported either directly or by calculation
1218
Stroke
May 2004
TABLE 2. Sample Size Calculations for Acute Stroke Trials Judged by Their Authors to Be Primarily Assessing Efficacy (ie, Phase
III), as Published by the End of 2001 (Ordered by Year of Publication, Earliest First)
Intervention
Primary Poor
Outcome
Alpha
(%)
Power
(%)
Anticipated
Control Rate
(%)
Anticipated
Active Rate
(%)
Calculated
Sample
Size
Follow-up
(mo)
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Trial
Year
Duke
1986
Heparin
Case fatality
5
80
*
30
*
Norris
1986
Dexamethasone
Comparison of TSS
5
90
†
50
104
0.75
IASS-H
1987
Dextran 40
MRS ⬎2
5
95
50
40
1200
6
SSSG
1987
Dextran 40 & venesection
Comparison of SNSS
*
*
*
7
400
3
PANS
1988
pentoxifylline
Comparison of BI
5
80
20
10
250
1
BEST
1988
␤-blocker
Percentage having a poor outcome
5
80
*
20
750
6
TRUST
1990
Nimodipine
BI ⬍60
5
90
40
30
1200
6
ANSG
1992
Nimodipine
Case fatality
5
80
30
21
1252
6
Yu
1992
Glycerol
Change in SNSS
5
95
*
*
6
NEST
1994
Nimodipine
Reduction in BI
2.5
90
85
70
700
3
NAHS
1994
Nimodipine
MRS ⬎2
5
80
40
25
330
12
EST
1994
GM1 ganglioside
Change in CNS
5
80
*
MAST I
1995
Streptokinase
mRS ⬎3
5
95
50
ECASS
1995
Alteplase
BI difference of 15 points
5
80
NINDS
1995
Alteplase
Global test
5
95
*
0.5
12
800
4
40
1500
6
*
*
600
3
*
20
640
3
3
RANTTAS
1996
Tirilazad
BI ⬍60
5
80
*
12
1130
FIST
1996
Flunarizine
MRS ⬎2
5
80
70
50
530
6
MAST-E
1996
Streptokinase
MRS ⬎2
5
95
70
56
600
6
ASK
1996
Streptokinase
BI ⬍60
5
80
50
38
600
3
CAST
1997
Aspirin
Case fatality
5
90
9
20000
1
LUB-INT 9
1997
Lubeluzole
Case fatality
5
80
23.5
14
600
3
PASS
1997
Piracetam
Change in Orgogozo ⬍10
5
80
*
35
900
1
TOAST
1997
ORG 10172
GOS ⬎2 or BI ⬍60
5
90
50
40
1076
3
EAIS
1998
Ebselen
GOS ⬎2
5
80
65
53
260
3
MAHST
1998
Hydroxyethyl starch
Improvement in GNS
5
90
85
80
400
3
LUB-INT 5
1998
Lubeluzole
Case fatality
5
80
23.5
14
722
3
ECASS II
1998
Alteplase
mRS ⬎1
5
80
70
60
800
3
CLASS
1999
Clomethiazole
BI ⬍60
5
90
*
9
1350
3
CSSG
1999
Citicoline
BI ⬍95
5
80
67
51
*
3
PROACT II
1999
Prourokinase
mRS ⬎2
5
80
*
*
180
3
ATLANTIS B
1999
Alteplase
NIHSS ⬎1
5
80
65
56
968
3
GAIN-I
2000
Gavestinel
BI dead–55, 60–90, 95–100
5
90
61
55
1600
3
LUB-INT 13
2000
Lubeluzole
BI ⬍70
5
80
†
†
800
3
CAIS
2000
Nalmefene
BI ⱖ60
5
80
45
30
330
3
TTAISS
2000
rt-PA
Change of NIHSS ⬍4
5
90
70
53
300
3
7.65
STAT
2000
Ancrod
BI ⬍95
5
90
34
15
HAEST
2000
Aspirin and dalteparin
Recurrent stroke
5
80
12
4
*
408
3
0.5
VENUS
2001
Nimodipine
MRS ⬎3
5
80
40
32
1500
3
TAIST
2001
Tinzaparin
MRS ⬎2
5
80
60
50
1410
6
GAIN-A
2001
Gavestinel
BI dead–55
5
90
45
39
1580
3
CSSG
2001
Citicoline
Change in NIHSS ⬍7
5
85
59
49
900
3
AHAIS
2001
Aptiganel
Comparison of mRS
5
80
†
*
900
3
EAST
2001
Enlimomab
MRS ⬎1
5
90
*
†
600
3
BI indicates Barthel Index; CNS, Canadian Neurological Scale; GNS, Global Neurological Scale; GOS, Glasgow Outcome Scale; mRS, modified Rankin Scale; NIHSS,
National Institutes Health Stroke Scale; SNSS, Scandinavian Neurological Stroke Scale; TSS, Toronto Stroke Scale.
*Information not in publication.
†Trial gave mean or median value for an outcome scale.
Weaver et al
Acute Stroke Trials
TABLE 3. Outcomes for Acute Stroke Trials Judged by Their Authors to Be Primarily Assessing Efficacy
(ie, Phase III), as Published by the End of 2001 (Ordered by Year of Publication, Earliest First)*
Case
Fatality
Death
Dependency
Trial
Control (%)
Active (%)
ARR (%)
RRR (%)
Control (%)
Active (%)
ARR (%)
RRR (%)
Duke
7.1
15.2
ⴚ8.1
ⴚ114.1
*
*
*
*
Norris
28.3
27.7
0.6
2.1
IASS-H
27.4
27.6
⫺0.2
⫺0.7
*
*
*
*
52.2
54.2
⫺2.0
⫺3.8
SSSG
12.6
15.8
⫺3.2
⫺25.4
*
*
*
*
PANS
10.3
11.9
⫺1.6
⫺15.5
*
*
*
*
BEST
23.0
33.2
ⴚ10.2
ⴚ44.3
36.0
43.6
⫺7.6
⫺21.1
TRUST
24.7
28.5
⫺3.8
⫺15.4
42.3
45.3
⫺3.0
⫺7.1
ANSG
15.9
15.0
0.9
5.7
*
*
*
*
Yu
29.8
32.1
⫺2.3
⫺7.7
*
*
*
*
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NEST
19.6
21.7
⫺2.1
⫺10.7
*
*
*
*
NAHS
12.6
16.5
⫺3.9
⫺30.9
43.7
44.9
⫺1.2
⫺2.7
*
*
5.7
8.4
EST
19.7
20.8
⫺1.1
⫺5.6
*
*
MAST I
28.8
30.5
⫺1.7
⫺5.9
67.9
62.2
ECASS
15.8
22.4
ⴚ6.6
ⴚ41.8
*
*
*
NINDS
21.0
17.0
4.0
19.0
80.0
69.0
11.0
13.8
RANTTAS
13.6
15.6
⫺2.0
⫺14.7
28.6
34.1
⫺5.5
⫺19.2
FIST
25.7
33.6
⫺7.9
⫺30.7
65.3
67.1
⫺1.8
⫺2.8
MAST-E
38.3
46.8
ⴚ8.5
ⴚ22.2
81.8
79.5
2.3
2.8
ASK
20.5
36.2
ⴚ15.7
ⴚ76.6
44.6
48.3
⫺3.7
⫺7.7
CAST
*
4.2
3.6
0.6
14.3
32.9
31.6
1.3
4.0
LUB-INT 9
25.2
20.7
4.5
17.9
58.7
52.6
6.1
10.4
PASS
19.2
23.9
⫺4.7
⫺24.5
*
*
*
*
TOAST
6.1
6.6
⫺0.5
⫺8.2
26.3
24.8
1.5
5.7
EAIS
10.1
6.6
3.5
34.7
66.0
55.0
11.0
16.7
MAHST
16.8
13.5
3.3
19.6
*
*
*
*
LUB-INT 5
21.4
20.8
0.6
2.8
*
*
*
*
ECASS II
10.5
10.3
0.2
1.9
63.4
59.6
3.8
5.9
CLASS
19.7
19.5
0.2
0.1
45.2
44.0
1.2
2.7
CSSG
17.0
17.0
0.0
0.0
*
*
*
*
PROACT II
27.0
25.0
2.0
7.4
83.0
74.0
9.0
10.8
6.9
11.0
ⴚ4.1
59.4
66.0
65.5
0.5
0.8
GAIN-I
18.8
20.4
⫺1.6
⫺8.5
47.0
47.0
0.0
0.0
LUB-INT 13
22.4
22.5
⫺0.1
⫺0.4
53.5
57.2
⫺3.7
⫺6.9
CAIS
15.6
16.0
⫺0.4
⫺2.6
37.7
33.1
4.6
12.2
7.0
22.5
ⴚ15.5
ⴚ221.4
*
*
STAT
23.0
25.4
⫺2.4
⫺10.4
64.2
HAEST
16.4
17.9
⫺1.5
⫺9.1
ATLANTIS B
TTAISS
*
*
57.2
7.0
10.9
64.8
66.1
⫺1.3
⫺2.0
VENUS
8.7
6.2
2.5
28.7
27.1
31.5
⫺4.4
⫺16.2
TAIST
15.1
15.0
0.1
0.7
54.3
54.8
⫺0.5
⫺0.9
GAIN-A
19.4
22.5
⫺3.1
⫺16.0
41.7
41.4
0.3
0.7
CSSG
18.0
17.0
1.0
5.6
60.0
60.0
0.0
0.0
AHAIS
19.2
24.4
⫺5.2
⫺27.1
*
*
*
*
EAST
16.2
22.2
ⴚ6.0
ⴚ37.0
66.5
73.0
ⴚ6.5
ⴚ9.8
ARR indicates absolute risk reduction; RRR, relative risk reduction. Significant results are in bold print.
* Information not in publication.
1219
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Stroke
May 2004
TABLE 4. Outcomes for Acute Stroke Trials Judged by Their Authors to Be Primarily Assessing Efficacy (ie, Phase III),
as Published by the End of 2001 but Who Did Not Use a SSC in Their Trial Design (Ordered by Year of Publication,
Earliest First)
Case Fatality
Death or Dependency
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Control
(%)
Active
(%)
ARR
(%)
RRR
(%)
Control
(%)
Active
(%)
ARR
(%)
RRR
(%)
36
52.6
76.5
⫺23.9
⫺45.4
*
*
*
*
1976
100
27.1
25.0
2.1
7.7
50.0
63.5
⫺13.5
⫺27.0
1976
79
33.3
32.1
1.2
3.6
74.1
60.7
13.4
18.1
Mulley
1978
118
78.9
68.9
10.0
12.7
89.5
83.6
5.9
6.6
Ohtomo
1985
350
2.2
0.0
2.2
36.5
29.0
7.5
20.5
Tazaki
1988
267
8.1
4.6
3.5
43.2
†
†
†
†
IASS-H⫹D
1989
502
24.4
18.8
5.6
23.0
†
Kornhuber
1993
422
9.5
11.8
ⴚ2.3
ⴚ24.2
†
†
†
†
NGAST
1994
482
10.3
8.4
1.9
18.4
†
†
†
†
INWEST
1994
295
33.0
42.7
ⴚ4.7
ⴚ29.4
†
†
FISS
1995
308
7.6
7.4
0.2
2.6
64.7
48.8
Trial
Year
Dyken
1956
Matthews
Geismar
Size
100
†
†
15.9
24.6
IST
1997
19435
22.0
22.0
0.0
0.0
63.2
62.1
1.1
1.7
RANTTAS II
1998
111
32.7
18.9
13.8
42.2
53.4
35.8
17.6
33.0
ASSIST
1999
567
17.1
22.1
ⴚ5.0
ⴚ29.2
†
†
†
†
CLASS-H
2000
201
10.7
19.8
⫺9.1
⫺85.0
38.2
40.6
⫺2.4
⫺6.3
Ogun
2001
40
85.0
80.0
5.0
5.9
*
*
*
*
CTST
2001
36
26.0
26.0
0.0
0.0
*
*
*
*
ARR indicates absolute risk reduction; RRR, relative risk reduction. Significant results are in bold print.
* Information not in publication.
† Trial gave mean or median value for an outcome scale.
of the difference between active and control event rates
(p2⫺p1). The intended reduction in 6 trials using case fatality
was 9.5% (1.1% to 12.5%) whereas the achieved result was
⫺0.3% (⫺4.1% to ⫹2.4%). Similarly, the intended reduction
in 24 trials using combined death and disability/dependency
was 12.0% (10.0% to 15.3%), with the final result being 1.9%
(⫺0.5% to ⫹5.4%). The remaining 18 studies did not use
these primary outcomes.
The median calculated sample size was 600 (199 to 995,
n⫽54); 3 trial reports did not give the result of their SSC. The
TABLE 5.
calculated sample size by type of trials was: phase II, 69 (40
to 116, n⫽11); phase III, 722 (400 to 1200, n⫽39). For phase
III studies, the calculated sample size by the trial’s primary
result were: positive, 560 (215 to 15 200, n⫽4);1–3,28 neutral,
775 (426 to 1200, n⫽32); and negative 600 (300 to 600,
n⫽3).13,26,27
Discussion
The relative failure to find effective treatments for acute
stroke has led to much speculation as to the causes. A
Functional Outcome in Phase III Trials by Treatment Group
Death
(n⫽4)
Death or Dependency
(n⫽20)
Anticipated rate (%)
21.8 (11.8, 23.5)
55.0 (44.5, 66.3)
Achieved rate (%)
15.7 (5.4, 24.3)
53.3 (36.3, 65.2)
Group
Control
Trials with SSC
Prediction
All phase III trials
Trials within 5%
0 (0%)
4 (22%)
Trials within 20%
2 (50%)
13 (65%)
No. of studies
59
41
Achieved rate (%)
19.2 (11.0, 25.2)
54.1 (40.4, 64.9)
Active
Trials with SSC
All phase III trials
Anticipated rate (%)
12.0 (8.2, 14.0)
40.0 (30.5, 51.8)
Achieved rate (%)
15.9 (5.7, 20.5)
52.8 (28.6, 65.1)
No. of studies
59
41
Achieved rate (%)
20.4 (15.0, 25.0)
53.2 (38.6, 63.7)
No. (%) or median (25–75 percentiles).
Weaver et al
Figure 1. *Includes all phase II and phase III trials.
Downloaded from http://stroke.ahajournals.org/ by guest on June 16, 2017
consistent theme is that trial design has been suboptimal,
although this statement has been difficult to quantify. We
show here that issues relating to the size of trials may explain
some trial failures. In particular, most trial publications failed
to report the SSC in its entirety, thereby making it impossible
to repeat the calculation and assess the assumptions used.
Furthermore, those trials reporting aspects of SSC were often
underpowered, assumed unrealistic event rates and intervention effects, or used inappropriate primary outcomes (eg,
death).
Alarmingly, most trials did not report a SSC. It is common,
although not correct, for small “phase II” trials to not perform
or report a SSC on the grounds that dose, safety, feasibility,
and/or tolerability are being assessed in a few tens of patient.
Nevertheless, such acute stroke trials should, ideally, have a
primary outcome (eg, adverse events in a dose escalation
trial29 or the effect of treatment on a surrogate measure such
as blood pressure30,31); therefore, they should base their
sample size on SSC. In some cases, no pilot data exist and the
aim of the trial is to develop this for use in the design of a
future larger trial, in which case SSC may not be possible.
Surprisingly, only three-quarters of “phase III” trials, in
which efficacy was being studied, presented SSC, although
all the trials stated they had a primary outcome. The 1996
CONSORT statement requires that trial reports reported a
Figure 2. Reporting of SSCs by year of publication. The
CONSORT statement23 was published in 1996.
Acute Stroke Trials
1221
SSC,23 a message reinforced in the recently updated
CONSORT statement.32 We found that significantly more
trials published a SSC after publication of the CONSORT
statement.
Many forms of SSCs can be used when designing a clinical
trial. An important determinant is whether the outcome is
continuous (eg, blood pressure), ordinal (ordered categorical,
eg, modified Rankin Scale), or binary (nominal, eg, death) in
nature. Continuous and ordinal data can be “collapsed” to
produce binary data by inserting cut-off points, eg, combined
death or dependency can be defined as a modified Rankin
Scale ⬎2, although this reduces statistical power. We found
that the majority of acute stroke trials reporting a SSC
performed an analysis based on a dichotomous outcome. In
this situation, the Trialists needed to choose levels for
significance (␣) and power (1⫺␤) and to make assumptions
about the proportion of subjects achieving the outcome in the
control group (p1) and the desired treatment effect (p2⫺p1).33
From these values/numbers, the sample size (N) can be
calculated:
N⫽
冕
␳1⫻共100⫺␳1兲⫹␳2⫻共100⫺␳2兲
⫻ 共␣, ␤兲
共␳2⫺␳1兲2
where 兰(␣, ␤) is a function of the cumulative distribution
function of a standardized normal deviate.33
This formula can be adapted to include adjustments for
small sample sizes (Yate correction), multiple active groups,
groups of different sizes, and multiple comparisons; all of
these extensions lead to an increased sample size. Only 1 of
the trials using a binary sample size formula extended this to
account for multiple comparisons.24
Statistical convention sets significance at an arbitrary level
of ␣⫽0.0534 and all but 1 trial24 used this figure. Most trials
used a power of 0.80, although this ranged from 0.75 to 0.95.
Many authorities recommend that a power of 0.90 should be
used in clinical efficacy (phase III) studies. The power of the
study relates to the probability (␤⫽1⫺power) of missing a
genuine difference between the treatment and control groups.
It is questionable whether it is worthwhile for Trialists,
funding sources (whether academic, charity, government, or
commercial), or ethics committees to support studies in which
there is a 20% chance of missing a significant effect, ie, in
which the power is only 0.80, because an effective drug could
be discarded and lost forever if a trial was falsely neutral
(type-II error).
The most difficult part of setting parameters for the SSC is
choosing appropriate event rates for the control and active
groups. The control rate (p1) should usually be obtained from
recent historical data relating to a group of stroke patients
similar to those likely to be enrolled into the planned trial, eg,
from stroke registers or similar trials. However, estimating
event rates from registers is fraught, because outcome tends
to be worse than in trials,35 so analysis of data in registers
should be restricted to trial-eligible patients. Either way,
Trialists should report and reference how they chose the
estimate for control event rate.
The event rate in the treatment group (p2) is usually
determined from the control group event rate (p1) and an
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Stroke
May 2004
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assumption about the anticipated absolute treatment effect (P,
where p2⫽P⫺p1). Almost all trials reporting P (or both p1
and p2) grossly overestimated the anticipated absolute treatment effect in reducing combined death and dependency/
disability; the median value across the trials reporting SSC
was 12%. Of the 2 “proven” treatments for acute stroke, only
alteplase achieved this treatment effect while aspirin managed slightly ⬎1%.1,2,36 It is clear that future trials must
assume smaller treatment effects and that the chosen figure
will depend on a number of factors. First, drugs acting early
in the pathophysiological cascade of acute stroke are likely to
be more efficacious than agents acting later, eg,
thrombolytics versus antithrombotics and neuroprotectants.
Second, expensive drugs (costing hundreds or thousands of
euro) will probably need to demonstrate larger effects than
inexpensive agents (costing a few euro) if they are to be used
widely. Which treatment rate is appropriate is unclear, but a
survey of stroke physicians suggested that an absolute reduction in combined death and dependency/disability of 5%
absolute risk reduction would be worthwhile clinically. In
general, efficacy should be judged on the basis of reducing
death or dependency rather than death alone, because the
former is of more relevance to patients, their carers, and
society. Using death and dependency as the primary outcome
will also tend to limit sample size as compared with death
because, all other things being equal, event rates of ⬇50%
maximize statistical power.
An adjustment may be necessary during the trial limiting
recruitment to particular groups of patients, eg, severe or mild
impairment, to ensure that the overall outcome rate (average
of p1 and p2) approximates to that assumed in the SSC, as
performed in the TAIST trial.7 In this respect, it is vital to
estimate severity using a standardized and validated stroke
impairment scale, eg, Scandinavian Stroke Scale. Ensuring
that the SSC assumptions are achieved is further complicated
because the relationship between severity and outcome is
changing, ie, outcome has improved with time for a given
severity, as seen when comparing the ECASS and ECASS II
trials.37,38 Unfortunately, most trials in our analysis did not
report their assumptions relating to control event rates; when
these data were given, rates of 55% for combined death or
disability/dependency and 22% for death were assumed on
average.
Combining the need for increasing power and reducing the
anticipated treatment effect means that future efficacy trials
will need to be substantially larger than recent studies. Such
studies may need to include ⱖ5000 patients, assuming
significance of 0.05, power of 0.90, control event rate of 50%,
and absolute treatment effect of 5%.39 Because the total cost
of future trials cannot increase dramatically in real terms, a
balance between recruiting more patients and collecting less
data on each patient will need to be found. Modern approaches to randomization and data registration, eg, based on
the Internet,40 will also help in reducing costs.
In summary, Trialists should ensure, and editors and
referees should insist, that publications give detailed information on the SSC in acute stroke trials. When designing
trials, SSC should use appropriate parameters as detailed
here. Combining this approach and improving the rigor of
other design issues will help increase the success rate of
future trials.
Acknowledgments
The full list of trials included in this systematic review is given at
www.nottingham.ac.uk/stroke-medicine/acutetrialslist.htm. We
thank those who responded to our request for further information on
their trials. P.M.W.B. is Stroke Association Professor of Stroke
Medicine. The Division of Stroke Medicine receives core funding
from The Stroke Association. P.M.W.B. was a member of the
STAIR III group.18 No pharmaceutical company was involved in the
design, execution, or interpretation of this study. The work was
presented, in part, at the 10th European Stroke Conference, Lisbon,
May 2001.41
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Stroke. 2004;35:1216-1224; originally published online March 18, 2004;
doi: 10.1161/01.STR.0000125010.70652.93
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