Computing power in case-control association studies through the use of quadratic approximations: application to meta-statistics.

In the framework of case-control studies many different test statistics are available to measure the association of a marker with a given disease. Nevertheless, choosing one particular statistic can lead to very different conclusions. In the absence of a consensus for this choice, a tempting option is to evaluate the power of these different statistics prior to make any decision. We review the available methods dedicated to power computation and assess their respective reliability in treating a wide range of tests on a wide range of alternative models. Considering Monte-Carlo, non-central chi-square and Delta-Method estimates, we evaluate empirical, asymptotic and numerical approaches. Additionally we introduce the use of the Delta-Method, extended to order 2, intended to provide better results than the traditional order-1 Delta-Method. Supplementary data can be found at: http://stat.genopole.cnrs.fr/software/dm2.