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(Stroke. 2004;35:1216.)
© 2004 American Heart Association, Inc.
Comments, Opinions, and Reviews |
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 philip.bath{at}nottingham.ac.uk
| Abstract |
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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
1 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 (1ß) 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.
Key Words: stroke randomized controlled trials acute stroke systematic review
| Introduction |
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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 trials 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 |
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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).
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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 (1ß), anticipated rates of primary outcome in control group (p1) and treatment group (p2), and intended absolute treatment effect (P=p2p1). 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.
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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).
| Results |
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Sample Size Calculation
Of the 189 reports, 57 (30%) reported
1 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 (1ß) 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).
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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);13,25 35 were neutral; and 3 were negative: EAST (enlimomab), MAST-E (streptokinase), and ATLANTIS A (alteplase).13,26,27
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Functional Outcome
The anticipated percentage of control subjects having an event for the trials 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
1 (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.
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Forty-eight of 57 (84%) reports gave the desired absolute treatment effect (P), reported either directly or by calculation of the difference between active and control event rates (p2p1). 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 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 trials primary result were: positive, 560 (215 to 15 200, n=4);13,28 neutral, 775 (426 to 1200, n=32); and negative 600 (300 to 600, n=3).13,26,27
| Discussion |
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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 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 (1ß) and to make assumptions about the proportion of subjects achieving the outcome in the control group (p1) and the desired treatment effect (p2p1).33 From these values/numbers, the sample size (N) can be calculated:
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where
(
, ß) 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 (ß=1power) 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 assumption about the anticipated absolute treatment effect (P, where p2=Pp1). 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
5000 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 |
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Received September 10, 2003; revision received January 7, 2004; accepted January 15, 2004.
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