Absence of evidence and evidence of absence

Absence of evidence and evidence of absence Writing it up because I had to work it out twice and would rather nobody else did.

Session topic: SURMOUNT-OSA (N Engl J Med, 2024). 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.

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

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.

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.

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.

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 disagree with the reply above, and I think the disagreement is substantive rather than terminological.

The distinction being drawn does not survive when you look at the published data for this specific question. I would be glad to be shown wrong on this, because the version I am arguing against is more convenient.

Coming back to post #5, because the follow-up matters more than the original answer.

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.

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 #5 runs together.

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.

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".

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.

On post #8 — agreed on the reasoning, with one qualification.

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.

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.

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.