Consider the ICU data described in Section 1.6.1 and use as the outcome variable vital status (STA) and infection probable at ICU admission (INF) as a covariate. (a) Demonstrate that the value of the...

Consider the ICU data described in Section 1.6.1 and use as the outcome variable vital status (STA) and infection probable at ICU admission (INF) as a covariate.

(a) Demonstrate that the value of the log-odds ratio obtained from the cross classification of STA by INF is identical to the estimated slope coefficient from the logistic regression of STA on INF. Verify that the estimated standard error of the estimated slope coefficient for INF obtained from the logistic regression package is identical to the square root of the sum of the inverse of the cell frequencies from the cross-classification of STA by INF. Use either set of computations, contingency table, or logistic regression, to obtain the 95% confidence interval for the odds ratio.

(b) For purposes of illustration, use a data transformation statement to recode, for this problem only, the variable INF as follows: 4 = No and 2 = Yes. Perform the logistic regression of STA on INF (recoded). Use the four-step method to calculate the estimate of the odds ratio of INF = Yes versus INF = No. Use the results from the fitted logistic regression model to obtain the 95% confidence interval for the odds ratio. Note that they are the same limits as obtained in Exercise 1(a).