* Choice A: X% chance of aggressive cancer, which worsens as it is left untreated.
* Choice B: X% chance of finding and treating aggressive cancer. Y% chance of false positive leading to significant side effects.
If Y is zero, then the choice to do further testing is obvious. If Y is large, then it depends on how large the side effects are, and what the chance of running into them is. You have risk in either case, and you will never reduce risk to zero. The question is how much risk you have, and what cost there is to mitigate that risk.
* Choice B: X% chance of finding and treating aggressive cancer. Y% chance of false positive leading to significant side effects.
If Y is zero, then the choice to do further testing is obvious. If Y is large, then it depends on how large the side effects are, and what the chance of running into them is. You have risk in either case, and you will never reduce risk to zero. The question is how much risk you have, and what cost there is to mitigate that risk.