"Specificity is a measure for the true negative rate, that is: given that the test result returns negative, how likely are you to be truly cancer-free?"
This is a common mistake - you've actually given the definition of a different measure here, "negative predictive value" (NPV). Specificity is different: given that you don't have the disease, how often do you get a negative result.
In other words:
Specificity = P( negative test result | no disease )
"Eleven cancer types including ovary, pancreas and colon cancer have an excellent specificity above 80%. Notably, Galleri also achieved a high specificity for lung cancer (74.8%), particularly impactful as this is the leading cause of death amongst all cancers. On the other end of the scale, Galleri performs poorly for some cancers, notably prostate and breast cancer, which both have large sample sizes."
In this paragraph, where you wrote "specificity", I think you meant "sensitivity".
Nice piece! Two nits:
"Specificity is a measure for the true negative rate, that is: given that the test result returns negative, how likely are you to be truly cancer-free?"
This is a common mistake - you've actually given the definition of a different measure here, "negative predictive value" (NPV). Specificity is different: given that you don't have the disease, how often do you get a negative result.
In other words:
Specificity = P( negative test result | no disease )
NPV = P( no disease | negative test result )
https://online.stat.psu.edu/stat507/lesson/10/10.3
"Eleven cancer types including ovary, pancreas and colon cancer have an excellent specificity above 80%. Notably, Galleri also achieved a high specificity for lung cancer (74.8%), particularly impactful as this is the leading cause of death amongst all cancers. On the other end of the scale, Galleri performs poorly for some cancers, notably prostate and breast cancer, which both have large sample sizes."
In this paragraph, where you wrote "specificity", I think you meant "sensitivity".