A study of the detection of skin cancer invoked the use of Raman spectroscopy to enhance the detection process. Suppose we have 1000 patients who have been visually examined and identified as having suspect lesions. Under normal testing, biopsies would be performed on all 1000 patients.
In the study, the lesions, after visual detection, are investigated using the Raman spectroscopy test for which the sensitivity is 90%. Only lesions that are tested positive are then sent for further biopsies.
(a) Demonstrate how to construct a natural frequency tree OR a binary classification table for the 1000 patients. Assume a prevalence of skin cancers in patients who have suspect lesions from visual inspection to be 45%. Show all your working in developing your answer.