Regression to the mean in progress reports

On the subject in the title: Regression to the mean in progress reports Working notes rather than a conclusion.

Session topic: PIONEER 6 (N Engl J Med, 2019). Please read it before posting; the discussion is much better when everyone has.

The question I would like us to start with is what the trial set out to estimate, rather than what it found. Once that is on the table we can talk about whether the design could have answered it, and only then about the numbers.

Specific things I would like covered: the population and how far it generalises, how discontinuation was handled, whether the comparator was a fair one, and what the absolute rather than relative effect looks like.

I will summarise at the end and the summary will feed the relevant digest page.

Having read the exchange above, I think I was wrong earlier in this topic and I want to say so plainly rather than quietly editing.

The correction was fair and I had been repeating something I had not checked carefully enough.

Confounding: a third variable explains an apparent association. In randomised data, randomisation balances confounders. In observational data, confounders can be adjusted for but unknown ones cannot.

Worth separating two things that post #2 runs together.

Regression to the mean: if you select people with extreme values (very high or very low), their next measurement is often less extreme just by chance. This can look like a treatment effect when it is just statistics.

Picking up post #2: that is the part I would want checked first.

Thank you for the correction. I have edited my earlier post with a note rather than silently, so the thread still makes sense to read. The error was mine and it was the kind that comes from remembering a figure instead of looking it up.

Coming back to post #4, because the follow-up matters more than the original answer.

Effect sizes: the magnitude of a difference, not just whether it is statistically significant. A difference that is significant (p<0.05) might be too small to matter. A large effect might not be significant if sample size is small.

Confidence intervals: rather than a single point estimate, a range of plausible values. A narrow interval means precise measurement; a wide interval means measurement is imprecise. Wider intervals (more uncertainty) are honest about limitation.

Multiplicity and multiple comparisons: if you test many hypotheses, the chance of finding a false positive by random chance increases. That is why pre-specifying the primary hypothesis matters.

P-values and significance: p<0.05 means the data would be surprising if the null hypothesis were true, not that the null hypothesis is false. A non-significant p-value does not mean "no effect".

I read post #8 twice before replying, because I had assumed the opposite.

Absence of evidence and evidence of absence: if a study is small and finds no effect, that is absence of evidence, not evidence of absence. A larger study might find an effect that a small study missed.

post #11 is right about the mechanism and I think understates the practical bit.

Relative risk and odds ratios: both compare the rate in one group to the rate in another. Relative risk is easier to understand. Odds ratios are standard in many analyses but can be misinterpreted.

I read post #11 twice before replying, because I had assumed the opposite.

Power and sample size: a study might be too small to detect a real effect (low power). Sample size calculations help determine how many participants are needed to detect an effect of a given magnitude.

Number needed to treat: how many people need to be treated to prevent one bad outcome or achieve one good outcome. More intuitive than relative risk reduction.