The 30-day unplanned hospital readmission rate has been used in provider profiling for evaluating hospital-facility care coordination, medical cost-effectiveness, and patient quality of life. Current profiling analyses use logistic regression to model readmission as a binary outcome, and the presence of competing risks (e.g., death) is not explicitly considered. Overlooking competing risks leads to an underestimation of the true readmission rate and invalid profiling analysis. To address these drawbacks, we propose a discrete competing risk model of readmission within a cause-specific hazards framework. Hazards of the event processes are sequentially formulated to exempt the nuisance competing risk hazard from a full specification. To foster model fitting with high-dimensional parameters and facility-effect inference with patient-level clustering, we also develop a Blockwise Inversion Newton algorithm with scalability and memory efficiency, and a stabilized robust score test suitable even for facilities with extreme outcomes. Evidence from simulations and application demonstrates the superior performance of our proposed methods over existing analyses.