Competing Risk Modeling with Bivariate Varying Coefficients to Understand the Dynamic Impact of COVID-19

The coronavirus disease 2019 (COVID-19) pandemic has exerted a profound impact on patients with end-stage renal disease relying on kidney dialysis to sustain their lives. A preliminary analysis of dialysis patient postdischarge hospital readmissions and deaths in 2020 revealed that the COVID-19 effect has varied significantly with postdischarge time and time since the pandemic onset. However, the complex dynamics cannot be characterized by existing varying coefficient models. To address this issue, we propose a bivariate varying coefficient model for competing risks, where tensor-product B-splines are used to estimate the surface of the COVID-19 effect. An efficient proximal Newton algorithm is developed to facilitate the fitting of the new model to the massive data for Medicare beneficiaries on dialysis. Difference-based anisotropic penalization is introduced to mitigate model overfitting and effect wiggliness; a cross-validation method is derived to determine optimal tuning parameters. Hypothesis testing procedures are designed to examine whether the COVID-19 effect varies significantly with postdischarge time and the time since the pandemic onset, either jointly or separately. Applications to Medicare dialysis patients demonstrate the real-world performance of the proposed methods. Simulation experiments are conducted to evaluate the estimation accuracy, Type I error rate, statistical power, and model selection procedures. Supplementary materials for this article are available online.