Parapsychologists are constantly protesting that they are playing by all the standard scientific rules, and yet their results are being ignored - that they are unfairly being held to higher standards than everyone else. I'm willing to believe that. It just means that the standard statistical methods of science are so weak and flawed as to permit a field of study to sustain itself in the complete absence of any subject matter.
— Eliezer Yudkowsky, Frequentist Statistics are Frequently Subjective
Imagine if, way back at the start of the scientific enterprise, someone had said, "What we really need is a control group for science - people who will behave exactly like scientists, doing experiments, publishing journals, and so on, but whose field of study is completely empty: one in which the null hypothesis is always true.
"That way, we'll be able to gauge the effect of publication bias, experimental error, misuse of statistics, data fraud, and so on, which will help us understand how serious such problems are in the real scientific literature."
Isn't that a great idea?
By an accident of historical chance, we actually have exactly such a control group, namely parapsychologists: people who study extra-sensory perception, telepathy, precognition, and so on.
It matters to your case. I refuse to believe that writing a patient's name on this list rather than that list has a direct causal influence upon their state in 2 years. The influence can only proceed via their actual treatment.
The decision facing you is whether to have surgery early or not. That is the thing whose effect on the outcome you want to know. To the extent that in the study this differs from the initial assignment, the study is diminished; therefore it should matter to the people conducting the study also.
I see from the paper that 23% of those assigned to Watchful Waiting nevertheless had surgery within 2 years, and 17% of those assigned to surgery did not have surgery in 2 years. (Some others died of unrelated causes or left the study early.)
I'll leave it to a dan-grade statistician to judge how to obtain the best conclusion from these data.
But the question is whether it's safe to advise people to wait, knowing that they can have surgery later if needed.
Anyway my main question was whether I'd done the stats right.