# Does BI-RADS imply agreed preference regarding treatment harm?

Hi all.

The BIRADS score for breast cancer mammography is made of several categories that stand for different ranges of estimated probabilities for underdiagnosed breast-cancer:

BI-RADS 1, 2, 3: p(malignancy) < 0.02 → No Biopsy
BI-RADS 4, 5: p(malignancy) > 0.02 → Biopsy

If I understand correctly this implies that the exchange rate between TP and FP is 1:49 -

U(TP) = 49*U(FP)

Therefore i should create a decision “curve” (more like a point) with only one probability threshold: 0.02.

Is that so? @VickersBiostats

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.

1 Like

Silly mistake

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).

1 Like

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.

How come?
Estimated Probability of 0.04-0.25 leads to treatment

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.

I get that, but on the BI-RADS score each category stands for ranges of estimated probabilities.

Therefore each estimated probability leads to a specific binary decision.

On your example we cannot derive binary decision if we derive estimated probability of 0.09 or any other estimated probability in (0.04, 0.25).

In my example each estimated probability leads to a binary decision.

That’s why I think we can get the preference unit from BI-RADS.

On your example we might get ranges of units of preferences.

A score cannot possible stand for a range of probabilities.

1 Like