July 11, 2005.
Documentation of Power for Cross-sectional Studies
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)