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Correspondence |
Vancouver Hospital and the University of British Columbia, Vancouver, Canada, E-mail: PeterT.Choi{at}vch.ca
The letter from Dr. Siddiqui et al. highlights several issues regarding the conduct of clinical trials. First, as the authors indicate, the probability of drawing 37 treatment and five placebo envelopes is extremely rare and suggests a systematic error in the generation of the allocation sequence. Although pre-numbered plastic bags were placed in the envelopes and mixed, the actual act of random allocation occurred with the selection of the envelopes. From this letter, we cannot determine whether the envelopes were withdrawn in a sequential order or not.
The use of a computer-generated allocation sequence could decrease the potential for a systematic error. Each envelope would contain either treatment or placebo tablets, depending on the sequence, and would be withdrawn sequentially. Free random allocation programs are available online. For example, one Windows-compatible program can be found at http://mahmoodsaghaei.tripod.com/softwares/randalloc.html#SampleSize.1
Second, with a small sample size as in this study (final n = 120), simple randomization can lead to imbalances between treatment and control groups even though the ratio of the treatment subjects relative to placebo subjects approaches unity as the number of randomized subjects increases.2 This can lead to problems with interim analyses. In this study, after 42 envelopes, 17 to 25 treatment envelopes would be drawn 95% of the time; 15 to 27 treatment envelopes would be drawn 99% of the time. The probabilities of observing a ratio of 1.5:1 (25 treatment:17 placebo or 25 placebo:17 treatment) and 1.8:1 (27 treatment:15 placebo or 27 placebo:15 treatment) are 0.096 and 0.022, respectively. Thus, the likelihood of observing some imbalance during the interim analysis would not be rare after 42 envelopes.
Block randomization would diminish the imbalance. In block randomization, patients are divided into several blocks of equal sizes and equal allocation of treatment and placebo is assigned within each block.2 To minimize the ability to guess the allocation sequence, the size of the blocks can be assigned randomly (random permuted block randomization). One disadvantage of this method is the unmasking of the allocation of the last patient in a block if all previous patients in the block are unmasked. Details of this and other methods of randomization are reviewed by Zelen.2
Third, there are limitations in performing an unblinded interim analysis. While the authors properly established an a priori plan for interim analysis, in general, a data monitoring and safety committee (DMSC), which is independent of the investigators, should perform the interim analysis. Data reviewed by the DSMC include information on the management of the trial (e.g., recruitment rates, descriptive statistics of demographics and baseline characteristics of the study population), safety data, and efficacy data.3 Stopping rules, the level of statistical significance required to suggest benefit or harm, should be used to guide decisions of stopping a trial early. The DMSC should remain blinded to the treatment allocation unless the interim analysis suggests a high potential of stopping the study. In this study, blinded analysis by an independent DMSC would have reduced the threat to allocation concealment now faced by the investigators.
Lastly, analysis of interim data can inflate the false positive error rate unless the appropriate statistical methods are used. The ethical, clinical and statistical issues related to interim analysis have been addressed by other authors.3,4
References
1 Saghaei M. Random allocation software, version 1.0. May 2000 [cited 20 April 2006]. Available from URL; http://mahmoodsaghaei.tripod.com/softwares/randalloc.html#SampleSize.
2 Zelen M. The randomization and stratification of patients to clinical trials. J Chronic Dis 1974; 27: 365–75.[Medline]
3 Armitage P. Interim analysis in clinical trials. Stat Med 1991; 10: 925–37.[Medline]
4 Facey KM, Lewis JA. The management of interim analyses in drug development. Stat Med 1998; 17: 1801–9.[Medline]
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