Example comparing software for evaluating sample sizes for log rank test
We give a worked examples comparing the total number of participants required using the Schoenfeld (1983) formula, WINPEPI and web calculator software.
Using the formula of Schoenfeld (1983) for 80% power and a type I error of 5% and comparing equal sized groups
Number of amyloid events = $$ 4 (1.96 + 0.84)2 / [log (log(0.75)/log(0.37))] 2 ^$$ = 20.39.
In particular for comparing equally sized groups from Collett (1983)
The total number of people required (Machin et al.) = [S(1)+S(0)]/2 x number of deaths
(with the number of deaths worked our using WINPEPI or the Schoenfeld (1983) formula)
where S(0) and S(1) are the two survival probabilities being compared at a particular time.
[1/[1 - (0.75+0.37)/2]] x 20.39 = 47 participants needed in total to compare survival rates of 0.75 and 0.37 with 80% power and a type I error rate of 5%.
Using Compare2 in WINPEPI with a hazard ratio of log(0.75)/log(0.37)=0.29 and 80% power, type I error of 5% and equal sized group gives the required umber of amyloid events as 26 for the log rank test. Multiplying by a factor of [1/[1 - (0.75+0.37)/2]] gives a total 59 participants required. The web calculator inputting survival rates of 0.75 and 0.37 gives a total of 60 required.