Additive vs. logistic risk models for cardiac surgery mortality

Abstract

Logistic regression is most often used to produce a cardiac operative risk model. But the logistic equation requires a computer to solve. Thus, simple additive models have been derived from logistic models by adding the odds ratios or modified coefficients. However, this simplification has no statistical justification, and the additive scores do not equal the original logistic probabilities. The EuroSCORE risk model is a very successful and widely used cardiac surgery risk model and it comes in both an additive and a full logistic version. We applied the EuroSCORE model to the 28,337 cardiac surgeries in the Providence Health System Cardiovascular Study Group database. The discrimination of the models was assessed by the c index. The comparison of the mortality predictions of the logistic and the additive model are mostly descriptive and graphical. Theoretical considerations would predict that the additive model greatly underestimates the risk for the higher risk patients, and clinical data confirm this fact. For the 23,463 (83%) cases with complete data, the predicted mortality was 8.3% by the logistic model and 5.4% by the additive model. The discrimination (c index) of the additive (0.794) and logistic (0.791) models was equally good. A modified additive score is proposed (the mean of the logistic predicted mortality for each original additive score) which could be provided as a look-up table along with the scoring sheet. The additive EuroSCORE gives excellent discrimination, as good as the logistic risk model, but it greatly underestimates the risk of high-risk patients, compared to the logistic. The logistic equation should be used to predicate the mortality when possible. If this is not feasible, a modified additive score could be employed at the bedside. But the logistic should always be used for comparison of providers and for research publications.