Diagnostic test continuous variables

A new diagnostic test is compared to a gold standard, demonstrating poor sensitivity, worse specificity, PPV, and NPV.

Let us assume I know other data about the gold standard positive and negative cases (continuous variables such as patient age, temperature)

What tests can be used to interpret the differences in the new test and the gold standard? Should I compare these variables (age, temp) of TP vs FP? Or must I compare all of TP vs FP vs FN vs TN?