3. Consider a diagnostic test which yielded the results shown in Fig. 1. The nor

Question

3. Consider a diagnostic test which yielded the results shown in Fig. 1. The normalized distributions for the cancer (positive) population is centred at a lower test result value than the healthy (negative) population mean value. The total number of cancer and healthy patients is 1000 for each population. Diagnostic Test cancer hreshole healthy 0.02 14 0.015 0.0121 r 0.008 0.005 50 130150 200 Test Res lt Fig. 1 a. For a decision threshold of 130, determine the number of FP, FN, TP, TN. b. What are the specificity and sensitivity of the diagnostic test? c. If the threshold t is Increased, what happens to the values of sensitivity and specificity?

Explanation / Answer

a and b) For a threshold of 130

c)If the threshold is increases the False positive FP will decrease and False negative FN will increase

This implies that specificity will increase as FP decreases and sensitivity will decrease as FN increases

FP 130-100 30 FN 150-130 20 TP 130-50 80 TN 200-130 70 Specificity TN/(TN+ FP) 0.7 Sensitivity TP/(TP+FN) 0.8

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