July 11, 2005.

Documentation of Power for Unmatched Case-Control 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 unmatched case-control 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 cases (disease group) and that for controls (non-disease group) are entered.

· The ‘percent of subjects with exposure’ among cases and controls are entered ranging from 0 to 100%.

The result of the calculation is shown next:

The interpretation of power in this unmatched case-control study is as follows: If, in truth, cases differ from controls in their exposure, given the above values, this study would have a 72% 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)];

· Odds ratio calculation

OR = p1 * (1-p2) / p2 * (1-p1)

The notations for the formulae are:

Δ = difference of proportions of exposure between case and control= | p2-p1|;

κ = ratio of sample size: controls / cases;

p1= percent (proportion) of exposure among cases;

p2= percent (proportion) of exposure among controls;

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

q= 1-p;

n1= available sample size among cases;

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 table 6.9 in “James Schlesselman. Case-control studies: Design, Conduct, Analysis (1982)”.