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Size: 1813
Comment:
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Size: 1814
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
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| + Biopsies have the likelihood of having 46 or more cells (Predicted + equal to number in cell A) or less than 46 cells (Predicted - equal to number in cell B) | + Biopsies have the likelihood of having 46 or more cells (Predicted + equal to number in cell A) or less than 46 cells (Predicted - equal to number in cell B ) |
Haematuria Clinic example
We are interested in seeing if counting the number of MCM cells less than 46 or 46 or more is related to the chance of a positive biopsy. The results of a trial are given below from which we can a high sensitivity but a low positive predictive value (PPV).
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True |
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- Biopsy |
+ Biopsy |
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Pred |
Cell count < 46 (-) |
27 |
0 |
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Cell count 46 or more (+) |
4 |
8 |
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The PPV = P(a positive biopsy given you have a MCM Cell Count of 46 or more) = 8 /(8+4) = 0.67
The Sensitivity = P(a MCM Cell Count of 46 or more given you have a positive biopsy) = 8/(8+0) = 1.00
This is explained by all positive biopsies having MCM cell counts of 46 or more but not all MCM cell counts of 46 or more having positive biopsies (only 2/3rds do).
Another way of seeing this related to the graphical method of Giggerenzer for explaining conditional probabilities is
+ Biopsies have the likelihood of having 46 or more cells (Predicted + equal to number in cell A) or less than 46 cells (Predicted - equal to number in cell B )
- Biopsies have the likelihood of having 46 or more cells (Predicted + equal to number in cell C) or less than 46 cells (Predicted - equal to number in cell D)
PPV = P(Pred + | a + Biopsy) / [P(Pred + | a + Biopsy) + (Pred + | a – Biopsy)] = A / (A+C) = P(True + (+ Biopsy) | a Pred + (46 or more cells))
Sensitivity = P(Pred + | a + Biopsy) / [P(Pred + | a + Biopsy) + P(Pred - | a + Biopsy)] = A / (A+B) = P(Pred + (46 or more cells) | True + (+ Biopsy))