July 11, 2005.

 

Documentation of Power for Randomized Clinical Trials

 

Minn M. Soe, MD, MPH, MCTM : msoe@sph.emory.edu

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)”.