Stratified Cox models with time‐varying effects for national kidney transplant patients: A new blockwise steepest ascent method

Analyzing the national transplant database, which contains about 300,000 kidney transplant patients treated in over 290 transplant centers, may guide the disease management and inform the policy of kidney transplantation. Cox models stratified by centers provide a convenient means to account for the clustered data structure, while studying more than 160 predictors with effects that may vary over time. As fitting a time‐varying effect model with such a large sample size may defy any existing software, we propose a blockwise steepest ascent procedure by leveraging the block structure of parameters inherent from the basis expansions for each coefficient function. The algorithm iteratively updates the optimal blockwise search direction, along which the increment of the partial likelihood is maximized. The proposed method can be interpreted from the perspective of the minorization‐maximization algorithm and increases the partial likelihood until convergence. We further propose a Wald statistic to test whether the effects are indeed time varying. We evaluate the utility of the proposed method via simulations. Finally, we apply the method to analyze the national kidney transplant data and detect the time‐varying nature of the effects of various risk factors.