Power analyses for correlations from clustered study designs

Power analysis constitutes an important component of modern clinical trials and research studies. Although a variety of methods and software packages are available, almost all of them are focused on regression models, with little attention paid to correlation analysis. However, the latter is arguably a simpler and more appropriate approach for modelling concurrent events, especially in psychosocial research. In this paper, we discuss power and sample size estimation for correlation analysis arising from clustered study designs. Our approach is based on the asymptotic distribution of correlated Pearson-type estimates. Although this asymptotic distribution is easy to use in data analysis, the presence of a large number of parameters creates a major problem for power analysis due to the lack of real data to estimate them. By introducing a surrogacy-type assumption, we show that all nuisance parameters can be eliminated, making it possible to perform power analysis based only on the parameters of interest. Simulation results suggest that power and sample size estimates obtained under the proposed approach are robust to this assumption.