The BIRADS score for breast cancer mammography is made of several categories that stand for different ranges of estimated probabilities for underdiagnosed breast-cancer:
First off, 2% risk is an odds of 2:98 or 1:49, not 1:45. Second, it is not necessarily the case that you can derive a rational cut-off in this way from a categorical variable. For instance, imagine that the risks from a score like BIRADS were 1%, 4%, 25%, 40% and 50% for 1 - 5 respectively. If a typical threshold was 10%, then the cut off would be score 3 or above because a score of 2 gives a risk below the threshold and a score of 3 gives a risk above the threshold. But you can’t reverse engineer this to say that because the cut-off is 3, then the threshold is 25%. The final point, and linked to the point above, is that you can’t assume no variation in thresholds because a categorical scale was used. For instance, if the range of reasonable thresholds was 5 - 20%, that makes score 3 the sensible cut-point because that entire range of thresholds is above the risk for score 2 and below the risk for score 3. The use of score 3 doesn’t mean no variation in threshold.
I don’t think that this is the case, unlike other scores BIRADS categories stands for ranges and the decision tends to be deterministic as far as I know.
Let’s say that under different setting:
Category 1: Estimated Probability - [0, 0.01), Decision: No-Treat
Category 2: Estimated Probability - [0.01, 0.04), Decision: No-Treat
Category 3: Estimated Probability - [0.04, 0.25), Decision: Treat
Category 4: Estimated Probability - [0.25, 0.40), Decision: Treat
Category 5: Estimated Probability - [0.40, 1], Decision: Treat
On that case, I can’t say that 0.04 is the only probability-threshold?
So far on the theoretical side, on the practical side the decision is not entirely binary: Category 3 on BI-RADS means followup mammography in 6 months (instead of 2 years).
On that case, I can’t say that 0.04 is the only probability-threshold?
No. the Thresholds could be anywhere from 4 - 25% or a range within those two numbers.
If risk for score of 2 is 4% and risk for score of 3 is 25%, it doesn’t matter if your risk threshold is 5%, 8%, 24%, 11% or whatever between 5-25%, a score of 2 is a risk that is too low and a risk from a score of 3 is sufficiently high.
