Dynamic survival analysis via a landmarking-gradient boosting approach and its application to kidney transplant data

In some survival studies, longitudinal biomarkers, along with baseline covariates, play crucial roles in predicting patient survival. Dynamic prediction models that incorporate updated longitudinal marker information offer updated survival predictions for patients. In this study, we employ a combination of the nonparametric gradient boosting machine learning algorithm and the landmark approach, which not only facilitates dynamic prediction but also circumvents the limitations of classical methods.

We conducted two simulation studies under different scenarios to compare three dynamic prediction models: the joint model, the Cox landmarking model, and the Landmarking Gradient Boosting Model (LGBM). We compared the three dynamic survival prediction methods using AUC (Area Under the Curve) and Brier score metrics. Using the LGBM, we performed dynamic prediction at various landmark times on a real kidney transplant dataset in the presence of two longitudinal markers.

Simulation studies demonstrated that when there was a simple linear relationship between longitudinal markers and the survival process, the joint model outperformed both Cox landmarking and LGBM in terms of higher AUC (better discrimination) and lower Brier score (better overall performance) indices. Conversely, in scenarios characterized by complex and nonlinear relationships between longitudinal markers and the survival process, the LGBM outperformed the two classical methods, under conditions involving larger sample sizes (n = 1000, 1500 vs. n = 300, 650), higher censoring rates (90% vs. 30%, 50%), and later landmark times (3.5, 5, 6.5 vs. 0.5, 2). The application of LGBM to real kidney transplant data revealed that at early landmark time points, factors such as blood urea nitrogen (BUN) (variable importance [VIMP] = 0.34), age (VIMP = 0.26), creatinine (VIMP = 0.24), hypertension (VIMP = 0.10), and gender (VIMP = 0.06) were associated with the risk of kidney transplant failure. At subsequent landmark time points, creatinine, BUN, and age emerged as the most important factors associated with kidney allograft failure.

Our findings demonstrate that in situations where the relationships between variables are complex and the proportional hazards assumption does not hold, the LGBM method performs better than Cox landmarking and joint modeling for dynamic survival prediction in cases with large sample sizes, high censoring rates, and later landmark times.

Not applicable.