An interpretable cluster-based logistic regression model, with application to the characterization of response to therapy in severe eosinophilic asthma

Asthma is a disease characterized by chronic airway hyperresponsiveness and inflammation, with signs of variable airflow limitation and impaired lung function leading to respiratory symptoms such as short- ness of breath, chest tightness and cough. Eosinophilic asthma is a distinct phenotype that affects more than half of patients diagnosed with severe asthma. It can be effectively treated with monoclonal antibodies target- ing specific immunological signaling pathways that fuel the inflammation underlying the disease, particularly Interleukin-5 (IL-5), a cytokine that plays a crucial role in asthma. In this study, we propose a data analysis pipeline aimed at identifying subphenotypes of severe eosinophilic asthma in relation to response to therapy at follow-up, which could have great potential for use in routine clinical practice. Once an optimal partition of patients into subphenotypes has been determined, the labels indicating the group to which each patient has been assigned are used in a novel way. For each input variable in a specialized logistic regression model, a clusterwise effect on response to therapy is determined by an appropriate interaction term between the input variable under consideration and the cluster label. We show that the clusterwise odds ratios can be meaning- fully interpreted conditional on the cluster label. In this way, we can define an effect measure for the response variable for each input variable in each of the groups identified by the clustering algorithm, which is not possi- ble in standard logistic regression because the effect of the reference class is aliased with the overall intercept. The interpretability of the model is enforced by promoting sparsity, a goal achieved by learning interactions in a hierarchical manner using a special group-Lasso technique. In addition, valid expressions are provided for computing odds ratios in the unusual parameterization used by the sparsity-promoting algorithm. We show how to apply the proposed data analysis pipeline to the problem of sub-phenotyping asthma patients also in terms of quality of response to therapy with monoclonal antibodies.