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We developed an inherently interpretable multilevel Bayesian framework for representing variation in regression coefficients that mimics the piecewise linearity of ReLU-activated deep neural networks. We used the framework to formulate a survival model for using medical claims to predict hospital readmission and death that focuses on discharge placement, adjusting for confounding in estimating causal local average treatment effects. We trained the model on a 5% sample of Medicare beneficiaries from 2008 and 2011, based on their 2009--2011 inpatient episodes, and then tested the model on 2012 episodes. The model scored an AUROC of approximately 0.76 on predicting all-cause readmissions -- defined using official Centers for Medicare and Medicaid Services (CMS) methodology -- or death within 30-days of discharge, being competitive against XGBoost and a Bayesian deep neural network, demonstrating that one need-not sacrifice interpretability for accuracy. Crucially, as a regression model, we provide what blackboxes cannot -- the exact gold-standard global interpretation of the model, identifying relative risk factors and quantifying the effect of discharge placement. We also show that the posthoc explainer SHAP fails to provide accurate explanations.