### 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) |
---|---|

Journal | Journal of Clinical Epidemiology |

DOIs | |

State | Accepted/In press - 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Epidemiology

### Cite this

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

**Regression coefficient-based scoring system should be used to assign weights to the risk index.** / Mehta, Hemalkumar; Mehta, Vinay; Girman, Cynthia J.; Adhikari, Deepak; Johnson, Michael L.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Regression coefficient-based scoring system should be used to assign weights to the risk index

AU - Mehta, Hemalkumar

AU - Mehta, Vinay

AU - Girman, Cynthia J.

AU - Adhikari, Deepak

AU - Johnson, Michael L.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Charlson comorbidity score

KW - Regression coefficient

KW - Risk index

KW - Risk ratio

KW - Scoring algorithm

KW - Scoring system

UR - http://www.scopus.com/inward/record.url?scp=84977492400&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977492400&partnerID=8YFLogxK

U2 - 10.1016/j.jclinepi.2016.03.031

DO - 10.1016/j.jclinepi.2016.03.031

M3 - Article

JO - Journal of Clinical Epidemiology

JF - Journal of Clinical Epidemiology

SN - 0895-4356

ER -