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The median coverage probability of the Wald intervals does not change much for σ1 = 0.5, while the median coverage of the LT interval decreases to 89%.

For ordinal data the median coverage probability of the LT interval increases only from 95.3 % to 95.4 %, but the range becomes as large as the range of the Wald intervals.

However, the LT has still a median coverage probability of 95% for a case-control ratio of 1 2, and becomes slightly liberal for a case-control ratio of 1 9.

For continuous data, the median coverage probability of the LT and of the Wald interval is about 95%, while the median coverage of the Wald-cc interval is 96%, and the range of the LT interval is smaller than the range of the Wald intervals.

In contrast the Wald intervals are slightly liberal even for a case-control ratio of 1 2 (median coverage probability of 93% for the Wald and 94% for the Wald-cc interval), and become very liberal for a case-control ratio of 1 9 (median coverage 76% respectively 78%).

Similar(55)

Therefore, the low 95% coverage probability was probably due to the under estimated standard error.

In each case, the relative bias of the optimal threshold estimate stemming from the mean, the median, and the mode of the posterior distribution were calculated, as well as the mean width, and the coverage probability of the 95% credible interval obtained with the quantile or the HPD method.

Figure 8 Coverage probability comparisons.

The performance of the proposed CIs are evaluated by simulation studies in terms of the empirical coverage probability, the empirical coverage width, and the ratio of the mesial non-coverage probability and non-coverage probability.

Next, we compute the coverage probability for CUEs.

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