July 11, 2005.
Documentation of Power for Randomized Clinical Trials
Kevin M. Sullivan, PhD, MPH, MHA: cdckms@sph.emory.edu
This module estimates power for randomized clinical trials. The data input screen is as follows:
The input values requested are:
· Two sided confidence intervals (%) that can be chosen are 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 98, 99, 99.5, 99.8, 99.9, 99.95, 99.98 & 99.99.
·
The available sample size for Treatment Group 1 and that for Treatment
Group 2 are entered.
·
The percent (proportion) of outcome in Treatment Group 1 and Treatment
Group 2 are entered ranging from 0 to 100%.
The result of the
calculation is shown next:
The interpretation of power in this clinical trial is as follows: If, in truth, Treatment Group 1 differs from Treatment Group 2 in their outcome given the above values, this study would have 83% chance of detecting a difference without continuity correction.
The formulae for the estimation of power are as follows:
·
Power
with normal approximation:
·
Power with
continuity correction:
Where n' = n1 - [( κ +1) / ( κ . Δ)];
·
Risk ratio
calculation
RR = ( p1/p2 );
The notations for the formulae are:
Δ = difference of percent of outcome between Treatment Group-1 and Treatment Group-2;
κ = ratio of sample size: Treatment Group-2 / Treatment Group-1;
p1= percent of outcome in Treatment Group-1;
p2= percent of outcome in Treatment Group-2;
p = (p1*n1+p2*n2) / (n1+n2);
q= 1-p;
n1= sample size of Treatment Group-1;
References:
· James Schlesselman. Case-control studies: Design, Conduct, Analysis (1982). (Formula 6.9 is used for estimation of power)
· Sahai H and KHurshid A. Formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two-sample design: A review. Statistics in Medicine, 1996 vol. 15, 1-21. ((In addition to formula 6.9 mentioned above, formula 23 is used to calculate power with continuity correction)
Acknowledgement:
Data in input screen are obtained from example 10.28 in “Bernard Rosner. Fundamentals of Biostatistics (5th edition)”.