Sequential boundaries approach in clinical trials with unequal allocation ratios

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-β) were evaluated for all tests.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.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.One of the key reasons for using sequential methods, instead of single-stage design (SSD), in planning clinical trials is that the expected number of patients is decreased while maintaining the pre-specified significance level and power. Sequential designs have become common practice in interim monitoring of clinical trials because of their ethical and economic advantages. Nowadays, investigators planning a clinical trial have a wide range of sequential methods available to choose. These methods can be categorized in two different types: boundaries approach and repeated significance tests [1-6]. In this paper we have only considered boundaries approach, including triangular test (TT) and double triangular test (DTT), because of their interesting properties [2,7-9]. Sebille and Bellissant presented a nice account of the properties of TT and DTT [7,8,10]. However, the properties of these methods, in some cases, are still unknown. In parti