Method: The sensitivity (Sn) and specificity (Sp) of the exercise ECG in the diagnosis of coronary artery disease have been found to be approximately 0.68 and 0.77, respectively. The corresponding estimates for SPECT are 0.88 and 0.77. We compare the performance of the two individual tests with their conjoint performance under two assumptions: i) the conjoint test has two outcomes, with a positive test defined by a positive exercise ECG or a positive SPECT (or both), and ii) the conjoint test has four outcomes, defined by the four possible outcomes of the exercise ECG and SPECT. These comparisons are made by plotting the expected value of the amount of information obtained by testing (using the information theory function, mutual information) as a function of pretest probability.
Result: Under the assumption that the exercise ECG and SPECT are independent, (Sn, Sp) for the conjoint two outcome case is (0.96, 0.59). The corresponding pairs for each outcome of the conjoint four outcome case are (0.60, 0.95), (0.08, 0.82), (0.28, 0.82), and (0.04, 0.41). The figure plots the expected value of the amount of information that diagnostic testing provides as a function of pretest probability for the exercise ECG alone (ECG), SPECT alone (SPECT), the conjoint two outcome case (ECG OR SPECT), and the conjoint four outcome case (ECG + SPECT). One bit is the amount of information gained in going from complete uncertainty about the presence of disease (probability = 0.5) to complete certainty about the presence of disease (probability of 0 or 1).
Conclusion: Defining a cardiac stress test as positive if either the exercise ECG or SPECT is positive (two outcome case) will, on average, result in the loss of diagnostic information relative to performing SPECT alone. On the other hand, adding the exercise ECG to SPECT will, on average, increase diagnostic information if posttest probabilities are determined on the basis of the specific combination of results obtained (four outcome case).
