Cost-Sensitive Threshold Explorer

Price a missed malignancy against an unnecessary operation and read the decision threshold straight off the cost ratio.

  • decision theory
  • threshold
  • cost
  • ROC

ROC — Out-of-fold (train)

00.10.20.30.40.50.60.70.80.9100.20.40.60.811 − specificitySensitivity

Total expected cost vs. threshold

C_FP/(C_FP+C_FN) = 0.33empirical min00.10.20.30.40.50.60.70.80.910200400600800100012001400Decision thresholdTotal cost (arbitrary units)

Confusion matrix at the cost-optimal threshold

Pred +Pred −
True +1365
True −76183

Operating metrics

MetricValue
Threshold0.333
Sensitivity0.965
Specificity0.707
PPV0.642
NPV0.973
Total cost430
Cost if everyone treated1295
Cost if nobody treated1410
The threshold is a value judgement, not a statistic
With C_FP = 5 and C_FN = 10, the cost-minimizing cut-point is C_FP/(C_FP+C_FN) = 0.333. Nothing about the model changes when you move the slider — only the price you attach to the two kinds of mistake. Note also how the external cohort, with lower discrimination and lower prevalence, pays a higher total cost at the same threshold.