FAQ/gallowayeg - CBU statistics Wiki

Upload page content

You can upload content for the page named below. If you change the page name, you can also upload content for another page. If the page name is empty, we derive the page name from the file name.

File to load page content from
Page name
Comment
Type the odd characters out in each group: abz2a 125t7 HhHaHh year.s 5433r21 worl3d

location: FAQ / gallowayeg

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).

True

- Biopsy

+ Biopsy

Pred

Cell count < 46 (-)

27

0

Cell count 46 or more (+)

4

8

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 Gigerenzer (2003) for explaining conditional probabilities is

Positive Biopsies have the likelihood of having 46 or more cells (Predicted positive equal to number in cell A) or less than 46 cells (Predicted negative equal to number in cell B )

Negative Biopsies have the likelihood of having 46 or more cells (Predicted positive equal to number in cell C) or less than 46 cells (Predicted negative equal to number in cell D)

PPV = P(Pred positive | a positive Biopsy) / [P(Pred positive | a positive Biopsy) + (Pred positive | a negative Biopsy)] = A / (A+C) = P(True positive (positive Biopsy) | a Pred positive (46 or more cells))

Sensitivity = P(Pred positive | a positive Biopsy) / [P(Pred positive | a positive Biopsy) + P(Pred negative | a positive Biopsy)] = A / (A+B) = P(Pred positive (46 or more cells) | True positive (positive Biopsy))

Reference

Gigerenzer G (2003) Reckoning with Risk: Learning to Live with Uncertainty. Penguin.