Why Mr. Jones Got Surgery Even If He Didn't: Intention-to-Treat Analysis

Andrew J. Vickers, PhD


August 17, 2009

Let's say you were doing a study to see whether surgery was effective for patients with severe heart disease. The typical approach would be to randomize patients to surgery or control and then see what proportion in each group were alive a year later. The problem is that surgery takes some time to set up, and it's quite possible for a patient to die before you've even worked out which surgeon has a free slot.

Results of typical study might be something like this:

The obvious question is what to do with the 10 who died before their scheduled surgery date. One line of thought would be as follows:

  • The 10 individuals who died early never had surgery

  • It's silly to count these patients in the surgery group

  • It isn't really 30 of 100 in the surgery group who died -- it's 20 out of 90 (22%)

  • 22% is a lot lower than the 40% who died in the control group (P = .012), so surgery clearly makes a difference.

The problem with this argument is that patients in the control group who die are included in the analysis even if they died shortly after randomization. This is none other than our marathon runner cheating by starting her stopwatch only after she had started running (see "How to Win the Marathon: A Common Statistical Error Can Help"): We are starting the clock at a different time for the control group (immediately after randomization) and the surgery group (only once they have had surgery). Statisticians say that the fairest analysis is intention-to-treat: It doesn't matter what actually happens, it's what was intended that counts. In an intention-to-treat analysis, you compare the 40% death rate in controls with 30% in the surgery group, on the grounds that there were 100 patients randomized to surgery in the first place, and 30 of them died. In this particular case, you get a nonsignificant difference that is smaller than the per-protocol analysis described in the bullet points. "Per-protocol" analysis is described as such because it only includes patients who were treated as allocated.

Intention-to-treat makes sense because we can't control what actually happens -- we can only control our intentions. A beach trip is a simple example. Let's say that I am sitting at home with my family, and we are wondering whether to go to the beach. Part of the issue is that we sometimes make a huge effort to get out of the house -- round up towels and swimming stuff, put on sunscreen, make snacks -- and then load the car but never get to the beach because traffic gets very bad or because it starts raining. Imagine that we had a data set where we worked out what we'd done and rated each day.

What happened? How was the day?
Stayed at home Good
Went to beach Good
Tried to go to beach; sat in traffic for an hour; starting raining so we turned around and went home Bad
Stayed at home Bad
Went to beach Good

On days where we got to the beach, we had a good day 100% of the time, compared with 33% of days when we didn't get to the beach. But our decision isn't whether to go the beach, it's to try to get to the beach. To inform our decision: "Should we try to go to the beach?" we really have to count the days where we tried and failed to get to the beach as a beach day: This gives 67% of days where we tried to go to the beach being good ones compared with 50% of days when we didn't try to go to the beach.

So you count a day as a "beach day" even if you didn't get to the beach, and a patient, say, Mr. Jones, as having received surgery even if he didn't. This sounds all a bit paradoxical, until you realize that the alternative is not much different from the marathon runner only starting her stopwatch halfway through the race. Which is to say, intention-to-treat may not be perfect, but it is far better than intention-to-cheat.


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