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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.

@article{mehta_regression_2016, title = {Regression coefficient-based scoring system should be used to assign weights to the risk index}, volume = {79}, issn = {1878-5921}, doi = {10.1016/j.jclinepi.2016.03.031}, 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.}, language = {eng}, journal = {Journal of Clinical Epidemiology}, author = {Mehta, Hemalkumar B. and Mehta, Vinay and Girman, Cynthia J. and Adhikari, Deepak and Johnson, Michael L.}, month = nov, year = {2016}, pmid = {27181564}, keywords = {Charlson comorbidity score, Regression coefficient, Risk ratio, Scoring algorithm, Scoring system, risk index}, pages = {22--28} }

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