Hi Mike,
I performed calculation for the conditional power based on the interim results dated Feb 23, 2015. At that
time, there were 141 events (out of 247 total events), and the z statistics from the log-rank test was 0.675.
The conditional probability following the observed trend at the interim is 2.4%. Based on the statistical
significance level of 0.01 (one-sided) and 84% power, the conditional power following the original trend
(based on the assumption in the sample size estimation) is 38.0%. I didn’t calculate anything in between
because it will be below 38.0%.
Calculate conditional power
1) Information fraction under 2:1 randomization: interim 99 events : 42 events, final 155 events : 92
events, information fraction = (1/155 + 1/92)/(1/99 + 1/42)=0.51
2) Log-rank Z statistics at 141 events = 0.675
3) B statistics at 0.51 = B(0.51) = 0.675 X sqrt(0.51) = 0.675 x 0.714 = 0.482
4) Z(type I error = 0.01) = 2.325, Z(type II error = 0.15)=1
5) Conditional power based on the interim trend = P (z ≥ (2.325 – B(0.51)/0.51))/sqrt (1-0.51)) = P (z ≥
(2.325 – 0.945)/0.7)) = P (z ≥ 1.97) = 2.4%
6) Conditional power based on the original trend = P (z ≥ (2.325 – 0.482 – (2.325 + 1) x (1-0.51))/0.7) = P
(z ≥ 0.305)= 38.0%
5/15/2015 Update
1) Information fraction under 2:1 randomization: interim 109 events : 48 events, final 155 events : 92
events, information fraction = (1/155 + 1/92)/(1/109 + 1/48)=0.58
2) Log-rank Z statistics at 157 events = 0.515
3) B statistics at 0.58 = B(0.58) = 0.515 X sqrt(0.58) = 0.515 x 0.762 = 0.392
4) Z(type I error = 0.01) = 2.325, Z(type II error = 0.15)=1
5) Conditional power based on the interim trend = P (z ≥ (2.325 – B(0.58)/0.58))/sqrt (1-0.58)) = P (z ≥
(2.325 – 0.676)/0.648)) = P (z ≥ 2.54) = 0.55%
6) Conditional power based on the original trend = P (z ≥ (2.325 – 0.392 – (2.325 + 1) x (1-0.58))/0.648) =
P (z ≥ 0.828)= 20.4%
7) Conditional power based on the mid-point between the interim trend and the original trend = P (z ≥
(2.325 – 0.392 – 0.5 x(0.676+3.325) x (1-0.58))/sqrt (1-0.58)) = P (z ≥ 1.69) = 4.6%
7/15/2015 Update
1) Information fraction under 2:1 randomization: interim 108 events : 48 events, final 155 events : 92
events, information fraction = (1/155 + 1/92)/(1/108 + 1/48)=0.58
2) Log-rank Z statistics at 157 events = 0.448 (sqrt of chi-square value from sas output)
3) B statistics at 0.58 = B(0.58) = 0.448 X sqrt(0.58) = 0.448 x 0.762 = 0.341
4) Z(type I error = 0.01) = 2.325, Z(type II error = 0.15)=1.03
5) Conditional power based on the interim trend = P (z ≥ (2.325 – B(0.58)/0.58))/sqrt (1-0.58)) = P (z ≥
(2.325 – 0.587)/0.648)) = P (z ≥ 2.68) = 0.37% 
6) Conditional power based on the original trend = P (z ≥ (2.325 – 0.341 – (2.325 + 1) x (1-0.58))/0.648) =
P(z ≥ (2.325-1.75)/0.648=P(z ≥ 0.887)= 18.75%
7) Conditional power based on the mid-point between the interim trend and the original trend = P (z ≥
(2.325 – 0.341 – 0.5 x(B(0.58)/0.58+3.325) x (1-0.58))/sqrt (1-0.58)) = P (z ≥ 1.794) = 3.6%
Note: the mid-point is calculated as the mid-point between z(type I
error) + z(type II error) and B(0.58)  projected to the final time
point.