MS-CPFI: A model-agnostic Counterfactual Perturbation Feature Importance algorithm for interpreting black-box Multi-State models

Multi-state processes (Webster, 2019) are commonly used to model the complex clinical evolution of diseases where patients progress through different states. In recent years, machine learning and deep learning algorithms have been proposed to improve the accuracy of these models' predictions (Wang et al., 2019). However, acceptability by patients and clinicians, as well as for regulatory compliance, require interpretability of these algorithms's predictions. Existing methods, such as the Permutation Feature Importance algorithm, have been adapted for interpreting predictions in black-box models for 2-state processes (corresponding to survival analysis). For generalizing these methods to multi-state models, we introduce a novel model-agnostic interpretability algorithm called Multi-State Counterfactual Perturbation Feature Importance (MS-CPFI) that computes feature importance scores for each transition of a general multi-state model, including survival, competing-risks, and illness-death models. MS-CPFI uses a new counterfactual perturbation method that allows interpreting feature effects while capturing the non-linear effects and potentially capturing time-dependent effects. Experimental results on simulations show that MS-CPFI increases model interpretability in the case of non-linear effects. Additionally, results on a real-world dataset for patients with breast cancer confirm that MSCPFI can detect clinically important features and provide information on the disease progression by displaying features that are protective factors versus features that are risk factors for each stage of the disease. Overall, MS-CPFI is a promising model-agnostic interpretability algorithm for multi-state models, which can improve the interpretability of machine learning and deep learning algorithms in healthcare.