The study team is interested in whether a diagnostic test based on both CYFRA 21-1 and CEA is an improvement over tests based solely on one of the markers. Suppose that a patient is classified as having lung cancer if at least one of the markers is above the cutoffs used in parts i. and ii.; i.e., a patient tests positive for lung cancer if CYFRA 21-1 level is greater than 3.3 ng/mL, CEA level is greater than 5.0 ng/mL, or both are elevated.

i. Compute the sensitivity and specificity of this diagnostic test. State any assumptions necessary to make the calculation and comment on whether those assumptions seem reasonable.

ii. Does the diagnostic test based on both markers represent an improvement over the tests in parts i. and ii. for use in high-risk patients? Explain your answer, referencing numerical results to support your reasoning.