Refer to Exercise 7-52 and the data in Table 7-32 on cardiac surgery patients. Conduct a risk-adjusted sequential probability ratio test using a false-alarm rate of 0.005. Assume that the chance of failing to detect a decrease in the odds ratio of mortality from 1 to 0.6 is 0.05.

Exercise 7-52

The predicted mortality of cardiac surgery patients in an intensive care unit, based on their APACHE score, is found based on a logistic regression model applied to patients over a four-year period. Table 7-32 shows the predictive pre-operative mortality for 25 recent patients, along with the observed outcome after surgery, where a value of 0 indicates that the patient survived while a value of 1 indicates that the patient died. Construct a risk-adjusted cumulative sum chart for patient mortality to determine if there has been an improvement. (Use the odds ratio under the alternative hypothesis to be R_a = 0.6.) Comment on the performance of the surgical team.

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+ TABLE 7-32 Predicted and Observed Mortality of Patients Predicted Observed Patient Patient Number Mortality Number 0 14 0 15 1 16 0.32 0 17 0.75 ITI 18 0.84 1 19 0.69 0 20 0.82 0 21 0.72 22 0.64 1 23 0 24 0 25 0 1 ·23456 OHLE 7 8 9 10 11 12 13 Mortality 0.28 0.62 0.45 0.36 0.72 0.84 0.26 0.54 0.40 0.74 0.49 0.55 0.37 Predicted Mortality 0.44 0.58 0.62 0.73 0.82 Observed Mortality 0 0 0 0 0 0 1 TOO 000 0 0