Optimal allocation of time points for the random effects model

In this article the problem of the optimal selection and allocation of time points in repeated measures experiments is considered. D-optimal designs for linear regression models with a random intercept and first order autoregressive serial correlations are computed numerically and compared with designs having equally spaced time points. When the order of the polynomial is known and the serial correlations are not too small, the comparison shows that for any fixed number of repeated measures, a design with equally spaced time points is almost as efficient as the D-optimal design. When, however, there is no prior knowledge about the order of the underlying polynomial, the best choice in terms of efficiency is a D-optimal design for the highest possible relevant order of the polynomial. A design with equally-spaced time points is the second best choice.