A razor is a rule of thumb that is helpful, although it isn't always correct. In medicine we're familiar with Occam's razor (the rule of parsimony).
The cutoff razor states: if a continuous variable is dichotomized using a cutoff, then values near the cutoff provide little information.
A simple illustration of the cutoff razor is in how we interpret D-dimer values in the diagnosis of pulmonary embolism. D-dimer is a continuous variable, as shown below. Higher values are more suggestive of PE than lower values:
Due largely to laziness, we dichotomize the D-dimer value using a single cutoff value. Of course, this is an artificial dichotomy. When we create this artificial dichotomy, we lose a lot of information:
The cutoff razor reminds us that D-dimer values close to the cutoff (e.g., 480 ug/mL or 520 ug/ml) actually lack significant diagnostic value. These values are straddling an artificial demarcation – so they are in fact stranded in between the bulk of negative values (<< 500 ug/mL) and the bulk of positive values (>>500 ug/mL). They don't truly lie in a positive or negative region: they're in no-man's land.
Medicine is full of continuous values which have been dichotomized using cutoff values. A few that pop to mind include the following:
- Temperature 38.4 is a fever, but 38.2 is normal.
- ST elevation >1 mm is a STEMI, but 0.9 mm is not.
- Lactate of 4.1 is shock, but lactate of 3.8 isn't.
- QRS duration of 122 ms is left bundle branch block, QRS duration of 118 ms isn't.
- PaO2/FiO2 of 290 is ARDS, but a value of 320 isn't ARDS.
- P-value of 0.04 is significant, P-value of 0.06 isn't.
If you dig into the literature surrounding these cutoff values, you'll generally find that they are arbitrary. However, even if the cutoff value was meticulously selected based on all available evidence, that still doesn't help – values close to the cutoff remain ambiguous. The cutoff razor merely provides a cognitive heuristic to help us recognize these arbitrary cutoffs, allowing us to avoid being fooled by misleading data generated near the cutoff.
The cutoff razor will come as no surprise to any seasoned diagnostician, or anyone with an understanding of statistics. Nonetheless, it may be useful to name this concept, to promote communication about our diagnostic reasoning.
Photo by Erik Mclean on Unsplash
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