of observations used in all procedures; the computation time is the maximum computation time for all procedures. There are two empirical coverage probabilities for PSM. The first is from the original confidence region (defined in ); the second is based on the alternative formula (defined in ). In this simple case, we can see from this table that the empirical coverage probabilities of all cases are close to the nominated $95\%$ coverage probability; we also see that they get closer as $d$ becomes smaller. For a given $d$, the total numbers of observations used are similar among SM and PSMs with $M=2, 5$. The case with a higher dimensional vector (${\bm{{\beta}}_{0}}$) tends to use larger data sizes and the computation times are as expected. We basically see that in this simple case, the proposed method can have the same desired properties as the conventional method.

Using the D-optimality criterion in subject selection {#using-the-d-optimality-criterion-in-subject-selection .unnumbered}
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To show the procedure with D-optimality, we set only $M=2$, in addition to the conventional method. We generate data under the same setup as in the earlier case. The purpose of this part of the simulation study is to see the performance of using the 