title: Regression coefficient-based scoring system should be used to assign weights to the risk index.
abstract: 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.
  
  
  
  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).
  
  
  
  Regression coefficient-based models (Beta, Beta10/integer, Beta/Schneeweiss, Beta/Sullivan) had lower AIC and higher R2compared 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).
  
  
  
  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.
authors.affiliation: Department of Surgery, University of Texas Medical Branch, 300 University Blvd, Galveston, TX 77555, USA.
authors.forename: Hemalkumar B
authors.initials: HB
authors.lastname: Mehta
authors.affiliation: Department of Pharmacoepidemiology, Merck, 351 N Sumneytown Pike, North Wales, PA 19454, USA. Electronic address: vinay_mehta@merck.com.
authors.forename: Vinay
authors.initials: V
authors.lastname: Mehta
authors.affiliation: CERobs Consulting LLC, PO Box 16041, Chapel Hill, NC 27516, USA.
authors.forename: Cynthia J
authors.initials: CJ
authors.lastname: Girman
authors.affiliation: Department of Surgery, University of Texas Medical Branch, 300 University Blvd, Galveston, TX 77555, USA.
authors.forename: Deepak
authors.initials: D
authors.lastname: Adhikari
authors.affiliation: Department of Pharmaceutical Health Outcomes and Policy, College of Pharmacy, University of Houston, 1441 Moursund Street, Houston, TX 77030, USA.
authors.forename: Michael L
authors.initials: ML
authors.lastname: Johnson
mesh_terms: D000368:Aged; D015331:Cohort Studies; D015897:Comorbidity; D015340:Epidemiologic Research Design; D005260:Female; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D016017:Odds Ratio; D016016:Proportional Hazards Models; D012189:Retrospective Studies; D012306:Risk
keywords: Charlson comorbidity score; Regression coefficient; Risk index; Risk ratio; Scoring algorithm; Scoring system