title: Sequential boundaries approach in clinical trials with unequal allocation ratios.
abstract: BACKGROUND
  In clinical trials, both unequal randomization design and sequential analyses have ethical and economic advantages. In the single-stage-design (SSD), however, if the sample size is not adjusted based on unequal randomization, the power of the trial will decrease, whereas with sequential analysis the power will always remain constant. Our aim was to compare sequential boundaries approach with the SSD when the allocation ratio (R) was not equal.
  
  
  METHODS
  We evaluated the influence of R, the ratio of the patients in experimental group to the standard group, on the statistical properties of two-sided tests, including the two-sided single triangular test (TT), double triangular test (DTT) and SSD by multiple simulations. The average sample size numbers (ASNs) and power (1-beta) were evaluated for all tests.
  
  
  RESULTS
  Our simulation study showed that choosing R = 2 instead of R = 1 increases the sample size of SSD by 12% and the ASN of the TT and DTT by the same proportion. Moreover, when R = 2, compared to the adjusted SSD, using the TT or DTT allows to retrieve the well known reductions of ASN observed when R = 1, compared to SSD. In addition, when R = 2, compared to SSD, using the TT and DTT allows to obtain smaller reductions of ASN than when R = 1, but maintains the power of the test to its planned value.
  
  
  CONCLUSIONS
  This study indicates that when the allocation ratio is not equal among the treatment groups, sequential analysis could indeed serve as a compromise between ethicists, economists and statisticians.
authors.affiliation: Department of Biostatistics and Epidemiology, Faculty of Health, Shiraz University of Medical Sciences, Shiraz, Iran. pjbiostat@yahoo.co.uk
authors.forename: Peyman
authors.initials: P
authors.lastname: Jafari
authors.forename: Seyyed Mohammad Taghi
authors.initials: SM
authors.lastname: Ayatollahi
authors.forename: Javad
authors.initials: J
authors.lastname: Behboodian
mesh_terms: D002986:Clinical Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D018401:Sample Size; D013223:Statistics as Topic / Q000379:methods*