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

Objective Some previously developed risk scores contained a mathematical error in their construction: risk ratios were added to derive weights to construct a summary risk score. This study demonstrates the mathematical error and derived different versions of the Charlson comorbidity score (CCS) using regression coefficient–based and risk ratio–based scoring systems to further demonstrate the effects of incorrect weighting on performance in predicting mortality. Study Design and Setting This retrospective cohort study included elderly people from the Clinical Practice Research Datalink. Cox proportional hazards regression models were constructed for time to 1-year mortality. Weights were assigned to 17 comorbidities using regression coefficient–based and risk ratio–based scoring systems. Different versions of CCS were compared using Akaike information criteria (AIC), McFadden's adjusted R², and net reclassification improvement (NRI). Results Regression coefficient–based models (Beta, Beta10/integer, Beta/Schneeweiss, Beta/Sullivan) had lower AIC and higher R² compared to risk ratio–based models (HR/Charlson, HR/Johnson). Regression coefficient–based CCS reclassified more number of people into the correct strata (NRI range, 9.02–10.04) compared to risk ratio–based CCS (NRI range, 8.14–8.22). Conclusion Previously developed risk scores contained an error in their construction adding ratios instead of multiplying them. Furthermore, as demonstrated here, adding ratios fail to even work adequately from a practical standpoint. CCS derived using regression coefficients performed slightly better than in fitting the data compared to risk ratio–based scoring systems. Researchers should use a regression coefficient–based scoring system to develop a risk index, which is theoretically correct.