July 11, 2005.

 

Documentation of Power for Cross-sectional 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 Cross-Sectional 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 prevalence of disease (or) coverage (eg. vaccination status) among exposed and non-exposed group are entered ranging from 0 to 100%.

 

The result of the calculation is shown next:

 

 

 

The interpretation of power in this cross-sectional study is as follows: If, in truth, exposed group differs from non-exposed group in their prevalence of disease given the above values, this study would have a 67% 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)];

 

·        Prevalence ratio calculation

 

PR = ( p1/p2 );

 

 

The notations for the formulae are:

Δ = difference of prevalence of disease between exposed group and non-exposed group;  

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

p1= prevalence of disease (coverage) among exposed group;

p2= prevalence of disease (coverage) 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)