I’d like to investigate from published data if two different diagnostic evaluations have similar performance regarding survival. Usually the studies I’d like to pool report the binary outcome percentage and the hazard ratio of the two groups. As an example:

-diagnostic evaluation 1, group with high risk has an HR of 2.3 compared to group with low risk

-diagnostic evaluation 2, group with high risk has an HR of 2.0 compared to group with low risk

All the studies evaluate the same patients with both the two diagnostic methods.

I was thinking of calculating a ratio with 95%CI between the Hazard ratios and seeing if this would include or not 1. Would this be a formally correct approach?