Comparison of the two-sided single triangular test to the double triangular test

Comparative clinical trials are designed to determine whether a new treatment has either superior or different efficacy than a standard, that is, if theta represents a measure of treatment difference, to test the null hypothesis H-0: theta = 0 against the alternative hypothesis H-1 of either superior (theta > 0, one-sided) or different (theta not equal 0, two-sided with H-1(+): theta > 0 and H-1(-): theta < 0) efficacy. The triangular test (TT), a group sequential method, allows for early stopping of such trials. Its one-sided version (single TT) and two-sided version (double TT) were implemented in the first release of PEST soft-ware. The third release of PEST proposed a modification of the single TT, allowing rejection of H-0 in favor of H-1(-) when very early data show strong inferiority of the new treatment as compared with the standard. Thus, our aim was to compare this modified single TT, referred to as a two-sided test in PEST 3, with the double TT and two-sided single-stage design (SSD). The statistical properties of the SSD and double TT were perfectly similar under all hypotheses. The modified single TT was underpowered as compared to the two others (the probability of falsely accepting H-0 strictly under H-1(-) was 0.65 instead of 0.05), but the average sample number function was lower than the one of the double TT under all H-1(-) hypotheses (-56% strictly under Hi). We conclude that the modified single TT offers a two-sided conclusion with many fewer patients than the double TT, but at the expense of a strong decrease in power under H-1(-). Control Clin Trials 2001; 22:503-514 (C) Elsevier Science Inc. 2001.