Health & Fitness
Cox Survival 10-Year Cardiovascular Risk (Framingham / PCE Formula)
Evaluate 10-year ASCVD / Framingham Cox proportional-hazards event probability Risk_10yr = 1 - (S_0 ^ EXP(Individual_BetaX - CohortMean_BetaX)) and ACC/AHA risk-tier thresholds.
Understand the exact Cox survival math inside ACC/AHA & Framingham calculators!
How do Framingham General CVD (D'Agostino et al., Circulation 2008) and the ACC/AHA Pooled Cohort Equations (Goff et al., 2013) turn log-transformed Age, Total Cholesterol, HDL-C, Systolic BP, Smoking, and Diabetes into an exact 10-year event probability? Both models use Sir David Cox's Proportional Hazards Survival Equation!
Given Demographic Baseline 10-Year Event-Free Survival S_0 (e.g., S_0 = 0.9144), Cohort Mean Linear Predictor Mean_BetaX (e.g., 61.18), and the patient's Individual Linear Predictor Ind_BetaX = SUM(beta_i * ln(X_i)): the patient's Hazard Ratio relative to the cohort average is HR = EXP(Ind_BetaX - Mean_BetaX), Event-Free 10-Year Survival is S_0 ^ HR, and 10-Year ASCVD Risk = 1 - (S_0 ^ EXP(Ind_BetaX - Mean_BetaX))! ACC/AHA guidelines classify <5% Low, 5%–7.4% Borderline, 7.5%–19.9% Intermediate, and >=20% High Risk!
| Patient Profile (Cohort S_0 = 0.9144, Mean_BetaX = 61.18) | Ind_BetaX Score | Hazard Ratio EXP(dB) | 10-Yr Risk = 1 - S_0^HR |
|---|---|---|---|
| Cohort-Average Risk Profile | 61.18 (dB = 0.00) | HR = 1.000x | 1 - 0.9144 = 0.0856 (8.56% Interm.) |
| Elevated Multi-Factor Profile | 62.10 (dB = +0.92) | HR = 2.509x | 0.2011 (20.11% High Risk >=20%!) |
| Optimal Nonsmoker Profile | 59.50 (dB = -1.68) | HR = 0.186x | 0.0165 (1.65% Low Risk <5%) |
Cox Proportional-Hazards 10-Year Event Probability = 1 - S_0 ^ EXP(Ind - Mean)
Evaluates 1 - (B2 ^ EXP(B4 - B3)) from baseline 10-year survival S_0 (B2), cohort mean predictor (B3), and patient linear predictor (B4).
=IF(OR(B2 <= 0, B2 >= 1), "Baseline S0 Must Be in (0, 1)", ROUND(1 - (B2 ^ EXP(B4 - B3)), 4))ACC / AHA Primary-Prevention 10-Year ASCVD Risk Tier Classifier
Stratifies 10-year probability into Low (<5%), Borderline (5%–<7.5%), Intermediate (7.5%–<20%), or High (>=20%).
=LET(r, 1 - (B2 ^ EXP(B4 - B3)), IFS(r < 0.05, "Low Risk (<5%)", r < 0.075, "Borderline Risk (5-7.4%)", r < 0.20, "Intermediate Risk (7.5-19.9%)", TRUE, "High Risk (>=20%)"))Try the example
Use the original values or change them to test your understanding.