This document defines key clinical evaluation statistics used to assess diagnostic tests: Sensitivity measures the percentage of true positive results and specificity measures the percentage of true negative results. The positive predictive value is the probability a positive test result reflects the disease, and the negative predictive value is the probability a negative result correctly rules out the disease. Prevalence refers to the percentage of a population with the disease. Accuracy measures the percentage of correct test outcomes overall.

1. Clinical Evaluation Statistics with Expended Formulas
𝑆𝑒𝑛𝑠𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑇𝑃
𝑇𝑃+𝐹𝑁
=
𝑎
𝑎+𝑐
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 =
𝑇𝑁
𝑇𝑁+𝐹𝑃
=
𝑑
𝑑+𝑏
Test
Result
P
Disease No Disease Total
a = TP b = FP TP+FP = a+b
N
c = FN d = TN FN+TN = c+d
TP+FN = a+c FP+TN = b+d a+b+c+d =
TP+FN+FP+TN
𝑆𝑒𝑛𝑠𝑡𝑖𝑣𝑖𝑡𝑦 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 Prevalence PPV NPV
Prevalence PPV NPV
𝑃𝑃𝑉 =
𝑇𝑃
𝑇𝑂+𝐹𝑃
=
𝑎
𝑎+𝑏
𝑁𝑃𝑉 =
𝑇𝑁
𝑇𝑁 + 𝐹𝑁
=
𝑑
𝑑 + 𝑐
Important
for Post-
Test
Probability
Prevalence=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒
=
𝑇𝑃+𝐹𝑁
𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁

2. Sensitivity / Specificity
Sensitivity is the probability that a person with disease has a positive test.
Sensitivity is also known as the true positive rate.
Specificity is the probability that a non-diseased person
has a negative test. Specificity is also known as the true
negative rate.
𝑆𝑒𝑛𝑠𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑇𝑃
𝑇𝑃 + 𝐹𝑁
× 100 =
𝑎
𝑎 + 𝑐
= 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒
=
𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑇𝑒𝑠𝑡 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑇𝑒𝑠𝑡𝑠 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑃𝑟𝑒𝑠𝑠𝑒𝑛𝑡 𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
=
𝐷𝑒𝑡𝑒𝑐𝑡𝑒𝑑 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝐴𝑙𝑙 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑢𝑛𝑑𝑒𝑟 𝑠𝑡𝑢𝑑𝑦
=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑒𝑠𝑡 𝑅𝑒𝑠𝑢𝑙𝑡𝑠 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
= 𝐻𝑜𝑤 𝑚𝑢𝑐ℎ 𝑎𝑟𝑒 𝑡𝑟𝑢𝑒 𝑝𝑜𝑖𝑠𝑖𝑡𝑖𝑣𝑒
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 =
𝑇𝑁
𝑇𝑁 + 𝐹𝑃
× 100 =
𝑑
𝑑 + 𝑏
= 𝑇𝑟𝑢𝑒 𝑁𝑎𝑔𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒
=
𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
=
𝑁𝑜𝑛−𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝑁𝑜𝑛−𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒+𝑁𝑜𝑛−𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑇𝑒𝑠𝑡 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
=
𝐷𝑒𝑡𝑒𝑐𝑡𝑒𝑑 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝐴𝑙𝑙 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑖𝑛 𝑢𝑛𝑑𝑒𝑟 𝑠𝑡𝑢𝑑𝑦
=
𝑁𝑜𝑛 − 𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑒𝑠𝑡 𝑅𝑒𝑠𝑢𝑙𝑡𝑠 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
= 𝐻𝑜𝑤 𝑀𝑢𝑐ℎ 𝑎𝑟𝑒 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
SnNOUT—a Sensitive test with a Negative result (False Negative) rule OUT
disease.
SpPIN—a Specific test with a Positive result (False
Positive) rules IN disease

3. Positive Predicted Value/Negative Predicted Value
Positive Predicted Value: (PPV) is the probability that a person with a
positive test has disease.
Negative Predicted Value :(NPV) is the probability that a person
with a
negative test does not have disease.
𝑃𝑃𝑉 =
𝑇𝑃
𝑇𝑃 + 𝐹𝑃
=
𝑎
𝑎 + 𝑏
=
𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑇𝑢𝑟𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
=
𝑇𝑒𝑠𝑡 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑃𝑟𝑒𝑠𝑒𝑛𝑡
𝑇𝑒𝑠𝑡 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 + 𝑇𝑒𝑠𝑡 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑁𝑜𝑛 − 𝐷𝑖𝑠𝑒𝑎𝑠𝑒
=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑒𝑠𝑡 𝑅𝑒𝑠𝑢𝑙𝑡𝑠
𝑁𝑃𝑉 =
𝑇𝑁
𝑇𝑁 + 𝐹𝑁
=
𝑑
𝑑 + 𝑐
=
𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
=
𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑁𝑜𝑛 𝐷𝑖𝑠𝑒𝑎𝑠𝑒
𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑁𝑜𝑛 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 + 𝑇𝑒𝑠𝑡 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐷𝑖𝑠𝑒𝑎𝑠𝑒
=
𝑁𝑜𝑛 − 𝐷𝑖𝑠𝑒𝑎𝑠𝑒
𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑇𝑒𝑠𝑡 𝑅𝑒𝑠𝑢𝑙𝑡𝑠
Prevalence
Prevalence: Prevalence refers to the total number of individuals in a population who have a disease or health condition at a specific
period of time, usually expressed as a percentage of the Sample.
Pre test Probability=Prevalence=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
=
𝐻𝑎𝑣𝑒 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑇𝑒𝑠𝑡𝑠 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐻𝑎𝑣𝑒 𝐷𝑖𝑠𝑒𝑎𝑠𝑒 𝑇𝑒𝑠𝑡𝑠 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒
=
𝐴𝑙𝑙 𝑑𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒

4. Accuracy
Accuracy is the degree of degree to true values. over all outcomes
Accuracy =
𝑎 + 𝑑
𝑎 + 𝑏 + 𝑐 + 𝑑
=
𝑇𝑃 + 𝑇𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
=
𝑻𝒆𝒔𝒓 𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝒅𝒊𝒔𝒆𝒂𝒔𝒆 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 + 𝑻𝒆𝒔𝒕 𝑵𝒆𝒈𝒂𝒕𝒊𝒗𝒆 𝑵𝒐𝒏 − 𝑫𝒊𝒔𝒆𝒂𝒔𝒆
𝑨𝒍𝒍 𝑻𝒆𝒔𝒕 𝑹𝒆𝒔𝒖𝒍𝒕𝒔
=
𝑻𝒓𝒖𝒆 𝑶𝒖𝒕𝒄𝒐𝒎𝒆𝒔
𝑻𝒐𝒕𝒂𝒍 𝑶𝒖𝒕𝒄𝒐𝒎𝒆𝒔

5. Positive Likelihood Ratio / Negative Likelihood Ratio
The likelihood ratio for a positive test is the ratio of getting a
positive test result in a diseased person divided by the probability
of getting a positive test result in a non-diseased person. From the
2  2 table, we see that this is the same as saying the ratio of the
true positive rate (sensitivity) over the false positive rate
(1- specificity).
A higher value (much 1) indicates that a positive test is much
more likely to be coming from a diseased person than from a non-
diseased person, increasing our confidence that a person with a
positive result has disease.
The likelihood ratio for a negative test is the ratio of the
probability of getting a negative test result in a diseased person
divided by the probability of getting a negative test result in a
non-diseased person From the 2  2 table, we see that this is the
same as saying the ratio of the false negative rate (1-sensitivity)
divided by the true negative rate (specificity).
A lower value (much 1) indicates that the negative test is much
more likely to be coming from a non-diseased person than from a
diseased person, increasing our confidence that a person with a
negative result does not have disease.
+𝐋𝐇𝐑 =
𝑺𝒆𝒏𝒔𝒕𝒊𝒗𝒊𝒕𝒚
𝟏 − 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄𝒊𝒕𝒚
=
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝟏 −
𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝑻𝑵 + 𝑭𝑷 − 𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝑭𝑷
𝑻𝑵 + 𝑭𝑷
=
𝑻𝒓𝒖𝒆 𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑹𝒂𝒕𝒆
𝑭𝒂𝒍𝒔𝒆 𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑹𝒂𝒕𝒆
=
𝑻𝒆𝒔𝒕 +/𝑫𝒊𝒔𝒆𝒂𝒔𝒆 +
𝑻𝒆𝒔𝒕 +/𝑫𝒊𝒔𝒆𝒂𝒔𝒆 −
= −𝑳𝑯𝑹 =
𝟏 − 𝑺𝒆𝒏𝒔𝒕𝒊𝒗𝒊𝒕𝒚
𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄𝒊𝒕𝒚
=
𝟏 −
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑻𝑷 + 𝑭𝑵 − 𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑭𝑵
𝑻𝑷 + 𝑭𝑵
𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑭𝒂𝒍𝒔𝒆 𝑵𝒆𝒈𝒂𝒕𝒊𝒗𝒆 𝑹𝒂𝒕𝒆𝒔
𝑻𝒖𝒆 𝑵𝒆𝒈𝒂𝒕𝒊𝒗𝒆 𝑹𝒂𝒕𝒆𝒔
=
𝑻𝒆𝒔𝒕 −/𝑫𝒊𝒔𝒆𝒂𝒔𝒆 +
𝑻𝒆𝒔𝒕 −/𝑫𝒊𝒔𝒆𝒂𝒔𝒆 −

6. Pre-Test-Odds+ Pre Test Probability /Post Test ± Odds +Post Test
Probability
Pre test Probability=Prevalence=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
=
𝐴𝑙𝑙 𝑑𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑚𝑝𝑙𝑒
Post Test 𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 Odds= 𝑷𝒐𝒔𝒕 − 𝑻𝒆𝒔𝒕 = 𝑷𝒓𝒆𝒕𝒆𝒔𝒕 𝑶𝒅𝒅𝒔 ×
𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑳𝒊𝒌𝒍𝒊𝒉𝒐𝒐𝒅 𝒓𝒂𝒕𝒊𝒐
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
×
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
𝑭𝑷
𝑻𝑵 + 𝑭𝑷
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
×
𝑻𝑷
𝑻𝑷 + 𝑭𝑵
×
𝑻𝑵 + 𝑭𝑷
𝑭𝑷
=
𝑻𝑷
𝑭𝑷
Post Test 𝑵𝒆𝒈𝒂𝒕𝒊𝒗𝒆 Odds= 𝑷𝒐𝒔𝒕 − 𝑻𝒆𝒔𝒕 = 𝑷𝒓𝒆𝒕𝒆𝒔𝒕 𝑶𝒅𝒅𝒔 ×
𝑵𝒆𝒈𝒂𝒕𝒊𝒗𝒆 𝑳𝒊𝒌𝒍𝒊𝒉𝒐𝒐𝒅 𝒓𝒂𝒕𝒊𝒐
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
×
𝑭𝑵
𝑻𝑷 + 𝑭𝑵
𝑻𝑵
𝑻𝑵 + 𝑭𝑷
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
×
𝑭𝑵
𝑻𝑷 + 𝑭𝑵
×
𝑻𝑵 + 𝑭𝑷
𝑻𝑵
=
𝑭𝑵
𝑻𝑵

7. Pre-Test 𝑶𝒅𝒅𝒔 =
𝐏𝐫𝐞𝐯𝐚𝐥𝐞𝐧𝐜𝐞
𝟏−𝐏𝐫𝐞𝐯𝐚𝐥𝐞𝐧𝐜𝐞
=
𝑇𝑃+𝐹𝑁
𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁
1−
𝑇𝑃+𝐹𝑁
𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁 − 𝑇𝑃 − 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
=
𝑇𝑃 + 𝐹𝑁
𝑇𝑁 + 𝐹𝑃
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑁𝑜𝑡 − 𝐷𝑖𝑠𝑒𝑎𝑠𝑒𝑑
=
𝐷𝑖𝑠𝑒𝑎𝑠𝑒 +/𝑇𝑒𝑠𝑡 ∓
𝐷𝑖𝑠𝑒𝑎𝑠𝑒 −/𝑇𝑒𝑠𝑡 ±
Post-Test 𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑷𝒓𝒐𝒃𝒊𝒃𝒊𝒍𝒊𝒕𝒚 =
𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑷𝒐𝒔𝒕𝒆𝒔𝒕 𝑶𝒅𝒅𝒔
𝑷𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝑷𝒐𝒔𝒕𝒆𝒔𝒕 𝑶𝒅𝒅𝒔+𝟏
=
𝑻𝑷
𝑭𝑷
𝑻𝑷
𝑭𝑷
+ 𝟏
=
𝑻𝑷
𝑭𝑷
𝑻𝑷 + 𝑭𝑷
𝑭𝑷
=
𝑻𝑷
𝑭𝑷
×
𝑭𝑷
𝑻𝑷 + 𝑭𝑷
=
𝑻𝑷
𝑻𝑷 + 𝑭𝑷
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