Time-to-event analysis in nested case-control designs

I would like to ask for ideas on nested case-control study analysis for time-to-event analysis in the presence of competing risks. For example, a database with 500 cancer patients with thrombosis (cases), and 500 cancer patients without thrombosis (controls). Thromboses occur months after diagnosis, data are censored, and death represents a competing event. The design is nested since the true incidence of thrombosis is around 7-10%. If competing risk models (e.g., FG model) are applied, I do not know how the subhazards should be interpreted. Or how the hazard ratio would be interpreted if I fit a cause-specific Cox model.