Modeling Probability-Based Injury Severity Scores in Logistic Regression Models: The Logit Transformation Should Be Used

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Abstract
The International Classification of Disease Injury Severity Score (ICISS) and the Trauma Registry Abbreviated Injury Scale Score (TRAIS) are trauma injury severity scores based on probabilities of survival. They are widely used in logistic regression models as raw probability scores to predict the logit of mortality. The aim of this study was to evaluate whether these severity indicators would offer a more accurate prediction of mortality if they were used with a logit transformation.Analyses were based on 25,111 patients from the trauma registries of the four Level I trauma centers in the province of Quebec, Canada, abstracted between 1998 and 2005. The ICISS and TRAIS were calculated using survival proportions from the National Trauma Data Bank. The performance of the ICISS and TRAIS in their widely used form, proportions varying from 0 to 1, was compared with a logit transformation of the scores in logistic regression models predicting in-hospital mortality. Calibration was assessed with the Hosmer-Lemeshow statistic.Neither the ICISS nor the TRAIS had a linear relation with the logit of mortality. A logit transformation of these scores led to a near-linear association and consequently improved model calibration. The Hosmer-Lemeshow statistic was 68 (35-192) and 69 (41-120) with the logit transformation compared with 272 (227-339) and 204 (166-266) with no transformation, for the ICISS and TRAIS, respectively.In logistic regression models predicting mortality, the ICISS and TRAIS should be used with a logit transformation. This study has direct implications for improving the validity of analyses requiring control for injury severity case mix.