Statistics - explanations and formulas

These ratios tell you how much the odds of a disease increase when a test is positive (LR+) or how much the odds of a disease decrease when a test is negative (LR-)

• Likelihood ratios are independent of prevalence

• Can be calculated from the sensitivity and specificity (formulas below)

Positive likelihood ratio -– How likely is the disease present if a test is positive  

• • It should be > 1, the higher the better

  • LR + > 10 is an ideal test

  • LR+ < 2 is no change

-  You can calculate it out from the sens/spec;  LR+  =  sens / (1-spec)

Negative likelihood ratio – How likely is the disease not present with a negative test

• • It should be < 1, the lower the better

  • LR- <  0.1 is an ideal test

  • LR-  > 0.5 is no change

-    LR−  = (1-sens) / spec

This example can be seen in this article: Asciutto KC, Ernstson A, Forslund O, Borgfeldt C. Self-sampling with HPV mRNA analyses from vagina and urine compared with cervical samples. J Clin Virol. 2018 Apr;101:69-73. doi: 10.1016/j.jcv.2018.02.002. Epub 2018 Feb 6. PMID: 29433016.

Positive likelihood ratio -– How likely is the disease present if a test is positive  

• It should be > 1, the higher the better
• LR + > 10 is an ideal test
• LR+ < 2 is no change

-  You can calculate it out from the sens/spec;  LR+  =  sens / (1-spec)

                                                                 0.84/(1-0.74) = 3.23

Negative likelihood ratio – How likely is the disease not present with a negative test

• It should be < 1, the lower the better
• LR- <  0.1 is an ideal test
• LR-  > 0.5 is no change

-    LR−  = (1-sens) / spec

(1-0.84)/0.74=0.22