Using the data from the ICU study create a dichotomous variable NONWHITE ( if or 3 and if

). Fit the logistic regression of STA on NONWHITE and show that the 95 percent profile likelihood confidence interval for the coefficient for nonwhite has asymmetry of and that this interval is 26% wider than the Wald-based interval. This example points out that even when the sample size and number of events are large , and there can be substantial asymmetry and differences between the two interval estimators. Explain why this is the case in this example.

1 The remainder of this section is more advanced material that can be skipped on first reading of the text.

2 The term coverage of an interval estimator refers to the percent of time confidence intervals computed in a similar manner contain the true parameter value. Research has shown that when the normality assumption does not hold, Wald-based confidence intervals can be too narrow and thus contain the true parameter with a smaller percentage than the stated confidence coefficient.