July 11, 2005.

Documentation of Power for Cohort Studies

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 cohort studies. 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 exposed group and that for non-exposed group are entered.

· The risk of disease among exposed and non-exposed group are entered ranging from 0 to 100%.

The result of the calculation is shown below:

The interpretation of power in this cohort study is as follows: If, in truth, exposed group differs from non-exposed group in their disease outcome given the above values, this study would have 85% 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 risk of disease between exposed group and non-exposed group;

κ = ratio of sample size: non-exposed group / exposed group;

p1= risk of disease among exposed group;

p2= risk of disease among non-exposed group;

p = (p1*n1+p2*n2) / (n1+n2);

q= 1-p;

n1= available sample size among exposed group;

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)