Healthcare & Clinical Calculations
Fagan’s Nomogram Calculator: Likelihood Ratios & Post-Test Probability
Replace straight-edge paper Fagan nomograms with exact Bayesian odds updates—converting Pre-Test Probability, Sensitivity, and Specificity into LR+, LR-, Positive Post-Test Probability (%), and Negative Post-Test Probability (%).
Compute exact Bayesian Fagan-nomogram updates without drawing ruler lines!
T. J. Fagan’s 1975 New England Journal of Medicine graphical nomogram taught generations of physicians evidence-based diagnostic reasoning by turning Bayes’ Theorem into a three-step odds chain: (1) Pre_Odds = Pre_Prob / (1 - Pre_Prob), (2) Post_Odds = Pre_Odds * LR, and (3) Post_Prob = Post_Odds / (1 + Post_Odds)! Here Positive Likelihood Ratio is LR+ = Sensitivity / (1 - Specificity) and Negative Likelihood Ratio is LR- = (1 - Sensitivity) / Specificity.
Look at how powerfully pre-test clinical probability shapes the exact same lab or imaging test (Sensitivity = 0.90, Specificity = 0.85 -> LR+ = 6.00, LR- = 0.1176): in an intermediate-risk patient with Pre-Test Probability = 25% (Pre_Odds = 1:3), a positive test raises disease probability to 66.67% while a negative test slashes it to just 3.77%; in a high-suspicion patient (Pre-Test = 60%), that exact same positive test drives Post-Test Probability to 90.00%!
| Clinical Pre-Test Probability (Sens = 0.90, Spec = 0.85) | LR+ = 6.00 Post-Test Prob (+) | LR- = 0.118 Post-Test Prob (-) | Diagnostic Interpretation |
|---|---|---|---|
| Intermediate Pre-Test (0.25 = 25%) | 66.67% | 3.77% (Strong Rule-Out) | Negative Test Excludes Disease |
| High Clinical Suspicion (0.60 = 60%) | 90.00% (Strong Rule-In) | 15.00% (Residual Risk!) | Negative Test Alone Insufficient |
| Boundary Probability (0 or 1) | Odds Singularity Guard | "Invalid Probability / Sens-Spec" | Requires Open Interval (0, 1) |
Positive Post-Test Probability (%) via LR+ = Sensitivity / (1 - Specificity)
Updates Pre_Odds = B2 / (1 - B2) by LR+ = B3 / (1 - B4) and converts back to percentage.
=IF(OR(B2 <= 0, B2 >= 1, B3 <= 0, B3 >= 1, B4 <= 0, B4 >= 1), "Invalid Probability / Sens-Spec", ROUND(100 * (((B2 / (1 - B2)) * (B3 / (1 - B4))) / (1 + ((B2 / (1 - B2)) * (B3 / (1 - B4))))), 2))Negative Post-Test Probability (%) via LR- = (1 - Sensitivity) / Specificity
Updates Pre_Odds by LR- = (1 - B3) / B4 to quantify residual post-negative disease probability.
=IF(OR(B2 <= 0, B2 >= 1, B3 <= 0, B3 >= 1, B4 <= 0, B4 >= 1), "Invalid Probability / Sens-Spec", ROUND(100 * (((B2 / (1 - B2)) * ((1 - B3) / B4)) / (1 + ((B2 / (1 - B2)) * ((1 - B3) / B4)))), 2))Try the example
Use the original values or change them to test your understanding.