{"id":36936,"date":"2013-06-07T08:00:58","date_gmt":"2013-06-07T12:00:58","guid":{"rendered":"http:\/\/blogs.nejm.org\/cardioexchange\/?post_type=voices&p=36936"},"modified":"2013-06-07T07:42:40","modified_gmt":"2013-06-07T11:42:40","slug":"your-mortality-risk-is-11-827","status":"publish","type":"post","link":"https:\/\/blogs.nejm.org\/cardioexchange\/2013\/06\/07\/your-mortality-risk-is-11-827\/","title":{"rendered":"“Your Mortality Risk Is 11.827%”"},"content":{"rendered":"

An 85-year-old woman named Betty presents with a non\u2013ST-segment elevation myocardial infarction. Despite her advanced age, she is active, lives by herself, and continues to work as a volunteer in the hospital\u2019s gift shop. She has hypertension, well-controlled diabetes, and a serum creatinine level of 1.8 mg\/dL. She also has recurrent angina despite intensive medical therapy, so cardiac catheterization is performed. It reveals a high-grade stenosis of the left-main coronary artery, as well as complex multivessel disease. The Society of Thoracic Surgeons\u2019 online risk calculator<\/a> estimates Betty\u2019s mortality risk after urgent CABG to be 11.827%.<\/p>\n

What does that number mean? And how do you explain it to Betty so that she knows what to expect? Probability is a way to quantify uncertainty about the future. But what exactly does an event\u2019s numeric probability tell us?<\/p>\n

What Probability Means <\/b><\/p>\n

Mathematicians and philosophers have been arguing about the meaning of probability for about 300 years. They have settled on two distinct notions: a frequentist notion and a personal notion. The frequentist dogmatists, such as R.A. Fisher, say that probability is a count of events \u2014 how things turn out over the long run, like the number of adverse events documented in an observational study. The personal probability dogmatists, such as Bruno de Finetti, say that probability represents a degree of belief or conviction \u2014 a forward-looking way to predict single events, like the chance that it will rain tomorrow or that Betty will make it through a risky operation.<\/p>\n

As physicians, we use both notions of probability, even though we don\u2019t give them much thought. We can look back at a database to find the frequency of survival in patients just like Betty. And we can switch to a personal notion of probability to talk with Betty about her chances. Tell Betty she has an 11.827% risk for mortality, and she may laugh at the false precision and the illusion of certainty. She might say, \u201cWhat do you mean, doc? For me, it\u2019s either 0% or 100%.\u201d We might respond, “If I had 10 patients like you, 9 would survive surgery.” What we mean, of course, is that we are about 90% sure that Betty will make it through the operation. But that\u2019s a tough idea to grasp when you\u2019re the one going under the knife.<\/p>\n

Probability\u2019s Many Faces<\/b><\/p>\n

Probability comes in various forms: simple, compound, conditional, complementary, and cumulative. And there are \u201codds\u201d \u2014 namely, a probability divided by its complementary probability. If there is a 75% probability of rain tomorrow, the odds of rain are 0.75 divided by 0.25, or 3 to 1. Odds are a handy format, because prior odds can be multiplied by other numbers such as likelihood ratios or Bayes factors, to give posterior odds. Using odds, we can calculate probability estimates in our heads or with a calculator. For example, if we think a patient has a 50% prior probability of coronary artery disease, the odds of CAD would be 0.5\/0.5, or 1. If an imaging stress test is positive, we multiply the prior odds (1) by the positive likelihood ratio for an imaging stress test (6); that yields a posterior odds value of 6. Converting odds back to probability (p=odds\/odds+1) gives us a posterior probability of CAD of 86%.<\/p>\n

We often use subjective quantifiers to express probability and make intuitive judgments. We throw around terms such as \u201cunlikely,\u201d \u201cpossible,\u201d \u201cprobable,\u201d and \u201calmost certain\u201d to express probability. Psychologists tell us that we frequently make mistakes when we subjectively estimate probability. We could turn the whole thing over to computers, but most patients don\u2019t want cold calculations. So it seems important to calibrate our intuition from time to time using hard numbers. But first we have to wrap our minds around the meaning of probability.<\/p>\n

We speak about probability all the time in medicine, yet we rarely stop to reflect on it. Philosophers such as Ian Hacking have written extensively about the meaning of probability. I have a chapter on it in my iBook, The Science of the Art of Medicine<\/i> (free and available for download through the iBookstore<\/a>). In my book, I discuss the history of probability ideas, how probability is viewed and calculated, and the various mistakes we sometimes make when we try to estimate probability.<\/p>\n

What is your concept of probability, and how do you use it in clinical practice? How can we refine our notions of probability to improve medical decision making? <\/b>I invite you start the conversation with me and other CardioExchange members right here.<\/p>\n","protected":false},"excerpt":{"rendered":"

John Brush reflects on what clinicians understand about the concept of probability and how to explain it to patients.<\/p>\n","protected":false},"author":379,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[949,1835],"class_list":["post-36936","post","type-post","status-publish","format-standard","hentry","category-general","tag-decision-making","tag-probability"],"_links":{"self":[{"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/posts\/36936","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/users\/379"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/comments?post=36936"}],"version-history":[{"count":0,"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/posts\/36936\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/media?parent=36936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/categories?post=36936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.nejm.org\/cardioexchange\/wp-json\/wp\/v2\/tags?post=36936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}