In cancer studies, patients often experience two different types of events: a non-terminal event such as recurrence or metastasis, and a terminal event such as cancer-specific death. Identifying pathways and networks of genes associated with one or both of these events is an important step in understanding disease development and targeting new biological processes for potential intervention. These correlated outcomes are commonly dealt with by modeling progression-free survival, where the event time is the minimum between the times of recurrence and death. However, identifying pathways only associated with progression-free survival may miss out on pathways that affect time to recurrence but not death, or vice versa. We propose a combined testing procedure for a pathway's association with both the cause-specific hazard of recurrence and the marginal hazard of death. The dependency between the two outcomes is accounted for through perturbation resampling to approximate the test's null distribution, without any further assumption on the nature of the dependency. Even complex non-linear relationships between pathways and disease progression or death can be uncovered thanks to a flexible kernel machine framework. The superior statistical power of our approach is demonstrated in numerical studies and in a gene expression study of breast cancer.