Correlated endpoints: simulation, modeling, and extreme correlations

Modeling and simulation of correlated random variables are important for evaluating operating characteristics of experimental designs in various applications, of which clinical trials with multiple endpoints provide an important example. There exist efficient algorithms to address the problem of generating multivariate distributions with given marginals and correlation structure. For model fitting as well as for simulation, it is important to know the feasible range of pairwise correlations, which can be much narrower than the interval [- 1,+ 1] . We provide closed-form expressions for extreme correlations for several classes of bivariate distributions that involve both discrete and continuous endpoints, as well as an algorithm for the construction of such distributions in the discrete case.