Coroners will list immediate, intermediate, and underlying (proximate) cause of death. In that case the immediate cause of death would be say sepsis after surge

Coroners will list immediate, intermediate, and underlying (proximate) cause of death. In that case the immediate cause of death would be say sepsis after surgery, but the proximate cause of death is the cancer. If you are looking at cause-specific mortality I think you do include proximate causes even if it isn't the immediate cause. But like the other commenter said, I think this is factor is so small as to not be impactful.