It's really easy to demonstrate with some basic math too. All of the numbers below are pulled from memory from a textbook example: Imagine you have a test with

It's really easy to demonstrate with some basic math too. All of the numbers below are pulled from memory from a textbook example: Imagine you have a test with a 1% false positive rate when screening for a disease that has a prevalence of 1 in 1,000 and the invasive operation to confirm the diagnosis has a 10% chance of serious (potentially life altering) complications like internal infection or an embolism. If you test 10,000 people, you'll identify 10 true cases (assuming 0% false negative rate) and 100 false cases. Meanwhile testing those 110 people will result in 11 patients suffering serious complications. Once you include the complicated math of quality-adjusted life years, it's almost never worth it. In reality the numbers are a lot worse - there is a long tail of diseases with 2-10% false positive rate tests and 1 in 10,000 incidence or worse, with 20% of patients experience QALY effecting complications from false positives. On top of that there are a lot of interventions that require invasive procedures with low rates of success.