Robustness properties of A-, D-, and E-optimal designs for polynomial growth models with autocorrelated errors

Optimal designs for polynomial growth models for longitudinal data with autocorrelated errors determine the optimal allocation and number of time points. A-, D-, and E-optimal designs for linear, quadratic and cubic growth models with four or less time points on the time interval [0,2] are given and four robustness properties of these designs are examined. The first considers the robustness against using too many time points. It is shown that the design with the number of time points equal to the number of regression coefficients is optimal, and that the efficiency of a design decreases when the number of time points increases. The second robustness property deals with the consequences of using an incorrect order of the polynomial. The efficiency of a design is shown to be generally higher if the assumed order of the polynomial is closer to the true order. The third robustness property deals with the robustness against an incorrect value of the autocorrelation coefficient. Results show that the optimal designs are very robust. The fourth robustness property considers the robustness of optimal designs with respect to other optimality criteria. The optimal designs are shown to be very robust to the other two optimality criteria.