Pauker & Kassirer's threshold model turns "should I test?" into three probability zones. The treatment threshold is the probability at which treating and not treating have equal expected utility:
P* = H / (H + B)
B = net benefit of treating a diseased patient
H = net harm of treating a healthy patient
A test with sensitivity Se and specificity Sp shifts probability via its likelihood ratios:
LR+ = Se / (1 − Sp) LR− = (1 − Se) / Sp
posttest odds = pretest odds × LR
odds = P / (1 − P) P = odds / (1 + odds)
The test is only worth ordering if its result could plausibly flip the decision. That defines two more thresholds, both derived from P* and the likelihood ratios:
P_test = odds(P*)/LR+ → below this, even a POSITIVE result can't reach P* — don't test, don't treat
P_tx = odds(P*)/LR− → above this, even a NEGATIVE result can't drop below P* — don't test, treat empirically
- P below P_test — disease too unlikely to act on; skip both test and treatment.
- P between P_test and P_tx — the test's result can genuinely change management; order it.
- P above P_tx — disease likely enough that testing can't change the plan; treat empirically.
The bottom-left panel plots the test itself as a point on a sensitivity/specificity square: dragging it up-right (higher Se, higher Sp, further from the diagonal chance line) narrows the "order the test" zone because a stronger test needs less room to flip the decision. The bottom-right panel is the same three probabilities as vertical bars, so you can compare pretest, post-positive and post-negative probability at a glance.
Real-world relevance: this exact framework is taught in clinical decision analysis to decide when imaging, biopsy or lab work-up is worth the cost, delay and risk versus acting directly on clinical probability.