Optimal design has been considered in some previous works. Reilly and Pepe (1995) derived a closed-form expression of the optimal design for their mean-score estimator. Since the expression depends on phase-2 **data** which are not available at the design stage, Reilly (1996) suggested to estimate the expression using **data** from a further pilot study. McIsaac and Cook (2015) proposed to save the extra cost by using a multi-wave sampling. The idea is to sample wave 1 with pre-specified sampling probabilities and then combine phase-1 and wave-1 **data** to estimate design components. The later waves can then be sampled adaptively.