Symmetric association measures in effect-control sampling

In order to measure the association between an exposure variable X and an outcome variable Y, we introduce the effect-control sampling design and we consider the family of symmetric association measures. Focusing on the case of binary exposure and outcome variables, a general estimator of such measures is proposed and its asymptotic properties are also discussed. We define an allocation procedure for a stratified effect-control design, which is optimal in terms of the variance of such an estimator. Finally, small sample behaviour is investigated by Monte Carlo simulation for a measure belonging to the family, which we believe particularly interesting as it possess the appealing property of being normalized.