Computing likelihood ratios from sensitivity and specificity

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Often, the literature reports diagnostic test characteristics as sensitivity and specificity rather than likelihood ratios. You could compute them by constructing a two by two table as we did above.
 
  SLE  No SLE  
Positive
ANA
2822 6798  
Negative
ANA
58 90322  
  2880 97120 100000
Going back to the original definition of likelihood ratio, we can compute the probability of a positive ANA test in patients with SLE: (2822 / 2880) or 0.98. We can also compute the probability of a positive ANA test in patients without SLE: (6798 / 97120) or 0.07. The likelihood ratio for a positive ANA is then 0.98 / 0.07 or 14. Using an analagous approach, you should be able to compute the likelihood ratio for a negative ANA (0.02). In more general terms:

LR+ = Sensitivity / (1 - Specificity)

LR- = (1 - Sensitivity) / (Specificity)

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