Regression coefficient-based scoring system should be used to assign weights to the risk index

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Previously developed risk scores contained a mathematical error, adding risk ratios instead of multiplying them.
• This error in weighting impacts the accuracy of summary risk scores.

Purpose of the Study:

• To demonstrate the mathematical error in risk score construction.
• To compare the performance of different versions of the Charlson Comorbidity Score (CCS) using regression coefficient-based and risk ratio-based scoring systems in predicting mortality.

Main Methods:

• Retrospective cohort study of elderly individuals from the Clinical Practice Research Datalink.
• Cox proportional hazards regression models were used to assess time to 1-year mortality.
• Comorbidity weights were derived using both regression coefficient-based and risk ratio-based systems, with performance compared using AIC, R², and NRI.

Main Results:

• Regression coefficient-based CCS models demonstrated superior performance with lower AIC and higher R² compared to risk ratio-based models.
• Regression coefficient-based CCS showed improved reclassification of individuals into correct risk strata (NRI 9.02-10.04) versus risk ratio-based CCS (NRI 8.14-8.22).

Conclusions:

• The mathematical error of adding ratios in prior risk score development is confirmed.
• Regression coefficient-based scoring systems provide a theoretically correct and practically superior method for developing risk indices like the CCS.