### Abstract

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 R^{2}, and net reclassification improvement (NRI). Results: Regression coefficient-based models (Beta, Beta10/integer, Beta/Schneeweiss, Beta/Sullivan) had lower AIC and higher R^{2} 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.

Original language | English (US) |
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Journal | Journal of Clinical Epidemiology |

DOIs | |

State | Accepted/In press - 2016 |

### Keywords

- Charlson comorbidity score
- Regression coefficient
- Risk index
- Risk ratio
- Scoring algorithm
- Scoring system

### ASJC Scopus subject areas

- Epidemiology

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## Cite this

*Journal of Clinical Epidemiology*. https://doi.org/10.1016/j.jclinepi.2016.03.031