The name is absent

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in the proposed model. Thus the alternative model is (2.2)-(2.5) with G = I and
random cutpoints θ? through θχ_j (^ɪ = 0 is fixed). We used the posterior MCMC
implementation of Cowles (1996). We summarized the marginal posterior distribu-
tions for the cell probabilities as in Table 2.2 (not shown). We find that for only 10
out of the 32 cell probabilities the central 95% posterior credible intervals contain the
simulation truth. To assess the efficiency of the posterior MCMC for the proposed
model versus the ordinal probit regression we recorded serial autocorrelations of the
Markov chain simulations. We find comparable values (not shown). In summary,
we conclude that the proposed model and the conventional ordinal probit regression
lead to comparable results with slightly more flexibility of the proposed model. We
caution against over-interpreting the comparison. The simulated data set is relatively
large with n — 1000, and the reported comparison is based on only one simulated
data set.

Finally we investigated robustness of posterior inference with respect to choices
of the prior hyperparameters. To explore prior sensitivity we considered several al-
ternative choices. Shifting the values of all c⅛_jg to either 1/3 or 3 did not change
inference appreciably. Similarly, using a non informative prior, p(β) oc 1, for the re-
gression parameter did not substantially affect the inference. Overall, we found that
the posterior estimates are quite robust with respect to prior specification.

2.6.2 A Phase III Clinical Trial of Retinoid Isotretinoin

We applied the proposed model for inference in the phase III clinical trial introduced
in Section 2. As in the simulation study, we chose ΛΓ(O,1) priors for the ordinal probit
parameters. The size of the mixture was fixed at G = 2 with equal a priori weights
by setting a_jg = 1. A vague hyperprior centered at 0 with the variance of = IO⁴
was imposed on φ. The cutpoints were chosen following the default choices. The
variances were set to the default choices σ? = 1, σl = 4 and = 16.

Saving every 10^th iteration after a 10,000 iteration burn-in, a Monte Carlo poste-

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