Let’s suppose you have an exquisitely accurate test. Hey it even meets the gold standard: it’s 99% specific and 99% sensitive. Tests don’t get much better than this. Recall that being 99% specific means you are only going to get one false positive when you test 100 people who do not have the disease and being 99% sensitive means when you test 100 people who have the disease it reports that 99 of them have it with only one false negative. (Always keep in mind: a specific test has very few false positives, a sensitive test has very few false negatives.) <\/p>\n\n\n\n

So you get tested and your doctor says: Well, I’m sorry to report you tested positive for this disease. The treatment has many side effects but since you tested positive with this very accurate test, I think we have no choice but to go ahead with the treatments.”<\/p>\n\n\n\n

Do you go ahead? Does this oh so accurate test have such good predictive power that you should start a series of treatments that have many many side effects or do you get a second opinion and more tests before starting the treatments?<\/em><\/p>\n\n\n\n

The answer to this question depends on calculating the odds of you having the disease correctly. Yes it means someone actually doing the mathematics and you and your doctor not jumping to conclusions until you see the result of the calculation. (And as you will see it’s really just arithmetic, no higher math needed!). But to give you the key idea:<\/p>\n\n\n\n

The odds of you having the disease depend not only on how good the test is but also on how prevalent the disease is given your symptoms.<\/em><\/p>\n\n\n\n

This is probably the single most important fact you need to know about testing for a disease!<\/p>\n\n\n\n

Still, it’s natural when you get tested for a disease to ask your doctor: Hey I got a positive test, what are the odds I really have the disease?” This is called the positive predictive value <\/em>of the test. Similarly, you could ask: “Hey I tested negative, what are the odds the test screwed up and I have the disease”. This is called the negative predictive value<\/em>. But I can’t stress enough these are among the most difficult things to understand about testing because the correct answer always require somebody doing some arithmetic using additional information that is outside the test itself. <\/p>\n\n\n\n

Why? Because yes it can’t be repeated enough: predicative value doesn’t only depend on the sensitivity and specificity of the test, it also depends on the prevalence of the disease given your symptoms<\/em>. In particular if you have the positive result because of routine testing and you have no symptoms, you really really want to do (or have someone do) the calculation for you!<\/p>\n\n\n\n

Let me reiterate it once more a different way: a positive test for a rare disease may still mean the odds are very much against you having the disease. This is why it is sometimes called the paradox of the false positive. And I also can’t stress enough, surveys show doctors get this wrong a lot<\/em>. <\/p>\n\n\n\n

Of course, as you might expect, there is a number that measures these odds: it is called the false discovery rate<\/em>. You really really care about the false discovery rate! (And, by the way, the same interaction between the prevalence of the disease and the accuracy of the test that determines the false discovery rate also comes up when using antibody testing to determine who had the disease. It’s why the CDC issued their warning about antibody testing yesterday.)<\/p>\n\n\n\n

But since this blog entry is already fairly long, I will explain the (elementary) math behind all these concepts as well as explain what is going on with the CDC’s warning\/calculation, in my next blog!<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Let’s suppose you have an exquisitely accurate test. Hey it even meets the gold standard: it’s 99% specific and 99% sensitive. Tests don’t get much better than this. Recall that being 99% specific means you are only going to get one false positive when you test 100 people who do not have the disease and … Continue reading “Testing 4: I tested positive, do I really have the disease?”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-226","post","type-post","status-publish","format-standard","hentry","category-the-pandemic"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/posts\/226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/comments?post=226"}],"version-history":[{"count":20,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/posts\/226\/revisions"}],"predecessor-version":[{"id":255,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/posts\/226\/revisions\/255"}],"wp:attachment":[{"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/media?parent=226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/categories?post=226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/garycornell.com\/wp-json\/wp\/v2\/tags?post=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}