Applet Exercise Refer to Exercises 2.125 and 2.126. Suppose now that the disease is not

Chapter 2, Problem 2.127

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Applet Exercise Refer to Exercises 2.125 and 2.126. Suppose now that the disease is not particularly rare and occurs with probability .4 a If, as in Exercise 2.125, a test has sensitivity = specificity = .90, what is the positive predictive value of the test? b Why is the value of the positive predictive value of the test so much higher that the value obtained in Exercise 2.125? [Hint: Compare the size of the numerator and the denominator used in the fraction that yields the value of the positive predictive value.] c If the specificity of the test remains .90, can the sensitivity of the test be adjusted to obtain a positive predictive value above .87? d If the sensitivity remains at .90, can the specificity be adjusted to obtain a positive predictive value above .95? How? e The developers of a diagnostic test want the test to have a high positive predictive value. Based on your calculations in previous parts of this problem and in Exercise 2.126, is the value of the specificity more or less critical when developing a test for a rarer disease?