RESUMO
Algorithmic scoring methods are widely used in the finance industry for several decades in order to prevent risk and to automate and optimize decisions. Regulatory requirements as given by the Basel Committee on Banking Supervision (BCBS) or the EU data protection regulations have led to an increasing interest and research activity on understanding black box machine learning models by means of explainable machine learning. Even though this is a step into a right direction, such methods are not able to guarantee for a fair scoring as machine learning models are not necessarily unbiased and may discriminate with respect to certain subpopulations such as a particular race, gender, or sexual orientation-even if the variable itself is not used for modeling. This is also true for white box methods like logistic regression. In this study, a framework is presented that allows analyzing and developing models with regard to fairness. The proposed methodology is based on techniques of causal inference and some of the methods can be linked to methods from explainable machine learning. A definition of counterfactual fairness is given together with an algorithm that results in a fair scoring model. The concepts are illustrated by means of a transparent simulation and a popular real-world example, the German Credit data using traditional scorecard models based on logistic regression and weight of evidence variable pre-transform. In contrast to previous studies in the field for our study, a corrected version of the data is presented and used. With the help of the simulation, the trade-off between fairness and predictive accuracy is analyzed. The results indicate that it is possible to remove unfairness without a strong performance decrease unless the correlation of the discriminative attributes on the other predictor variables in the model is not too strong. In addition, the challenge in explaining the resulting scoring model and the associated fairness implications to users is discussed.
RESUMO
Objective: To develop and validate a prognostic model for in-hospital mortality after four days based on age, fever at admission and five haematological parameters routinely measured in hospitalized Covid-19 patients during the first four days after admission. Methods: Haematological parameters measured during the first 4 days after admission were subjected to a linear mixed model to obtain patient-specific intercepts and slopes for each parameter. A prediction model was built using logistic regression with variable selection and shrinkage factor estimation supported by bootstrapping. Model development was based on 481 survivors and 97 non-survivors, hospitalized before the occurrence of mutations. Internal validation was done by 10-fold cross-validation. The model was temporally-externally validated in 299 survivors and 42 non-survivors hospitalized when the Alpha variant (B.1.1.7) was prevalent. Results: The final model included age, fever on admission as well as the slope or intercept of lactate dehydrogenase, platelet count, C-reactive protein, and creatinine. Tenfold cross validation resulted in a mean area under the receiver operating characteristic curve (AUROC) of 0.92, a mean calibration slope of 1.0023 and a Brier score of 0.076. At temporal-external validation, application of the previously developed model showed an AUROC of 0.88, a calibration slope of 0.95 and a Brier score of 0.073. Regarding the relative importance of the variables, the (apparent) variation in mortality explained by the six variables deduced from the haematological parameters measured during the first four days is higher (explained variation 0.295) than that of age (0.210). Conclusions: The presented model requires only variables routinely acquired in hospitals, which allows immediate and wide-spread use as a decision support for earlier discharge of low-risk patients to reduce the burden on the health care system. Clinical Trial Registration: Austrian Coronavirus Adaptive Clinical Trial (ACOVACT); ClinicalTrials.gov, identifier NCT04351724.