Adaptive designs in critical care trials: a simulation study

Table 1 Spending functions

Spending function	Function forms
O’Brien-Fleming (OBF)	\(\mathrm{\alpha }(\mathrm{t})=2-2\upphi (\frac{{\mathrm{Z}}_{1-\frac{\mathrm{\alpha }}{2}}}{\sqrt{\mathrm{t}}}) (\mathrm{t}\ne 0)\)
O’Brien-Fleming (OBF)	\(\mathrm{\alpha }(\mathrm{t})= 0 (\mathrm{t }=0)\)
Hwang-Shih-DeCani (HSD)	\(\mathrm{\alpha }(\mathrm{t})=\mathrm{\alpha }(\frac{1-{\mathrm{e}}^{-\mathrm{\gamma t}}}{1-{\mathrm{e}}^{-\upgamma }}) (\upgamma \ne 0)\)
Hwang-Shih-DeCani (HSD)	\(\mathrm{\alpha }(\mathrm{t})=\mathrm{\alpha t }(\upgamma =0)\)

t represents the fraction of information accumulated at the time of the interim analysis (t = 0 at the start of the trial and t = 1 at the time of the final analysis) which represents the proportion of the total sample size; α(t) represents the significance level at t; Z_1-α/2 represents the Z-value at the significance level of (1-α/2); ϕ represents the function that converts the Z-value to the corresponding significance level

ISSN: 1471-2288