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Sensitivity is also called the True Positive Rate
Specificity is also called the True Negative Rate
Sensitivity = TP rate
Specificity = TN rate

1 = TP rate + FN rate
therefore 1 - Sensitivity = FN rate
or Sensitivity = 1 - FN rate

1 = TN rate + FP rate
therefore 1 - Specificity = FP rate
or Specificity = 1 - FP rate

Increasing Prevalence increases positive predictive value and deceases the negative predictive value but it has nothing to do with sensitivity or specificity.

The Receiver operating Curve plots sensitivity(TP rate) in the Y axis and 1-Specificity (FP rate) in the X axis, area under the curve will be the accuracy of the test.
 
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