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naraburns  nihil supernum  1yr ago (text post)   3549 thread views

Friday Fun Thread for December 16, 2022

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In Merck's recent press release for the results of their phase 2 melanoma trial, they said this:

Adjuvant treatment with mRNA-4157/V940 in combination with KEYTRUDA reduced the risk of recurrence or death by 44% (HR=0.56 [95% CI, 0.31-1.08]; one-sided p value=0.0266) compared with KEYTRUDA alone.

Does that confidence interval look wrong to anyone else? It should be geometrically symmetrical around the point estimate, right?

  • 0.56/0.31 = 1.81

  • 1.08/0.56 = 1.93

Even making the most accommodating assumptions about rounding, I can't make the math work out:

0.5649 / 0.3050 * 0.5649 = 1.046

Also, 1.08 is weirdly far from 1 given that the one-tailed p value is only 0.0266. I would expect it to be just barely greater than 1.

Depends on the distribution. For normal or t-distributions, sure, but not for asymmetric ones.

Assuming "HR" means "hazard ratio", it seems likely to be some sort of logistic regression, bounded on the left but not the right. This is not my area of expertise, but I'd expect that to lead to much larger distances on the right tail.

Edit: just saw your comment about other studies. There goes my theory. It might still explain why a 0.025 p wouldn't correspond to 1.0? Either way, I'd really like to see their published numbers now.

This is not my area of expertise, but I'd expect that to lead to much larger distances on the right tail.

It does, but I accounted for that. The right tail is longer than expected even when accounting for the fact that it's logistic. Either there's something I'm not understanding about how this works, or someone screwed up somewhere.

Apparently, asymmetric confidence intervals are perfectly possible. See here and here.

Re the confidence interval, as I understand it, a p-value is an estimate of how likely it is that an effect is real, and a CI tells us the size of the effect. See here. So, a p-value can be low even if the CI is wide.

Edit: See also here ("The CI gives an indication of the precision of the sample mean as an estimate of the "true" population mean. A wide CI can be caused by small samples or by a large variance within a sample. . . . The p-value is the chance of getting the reported study result (or one even more extreme) when the null hypothesis is actually true.").

It's not a question of how wide the confidence interval is, but of how much of the interval is greater than 1. For a 95% confidence interval, a one-tailed p of 0.025 should correspond to a CI with an upper (or lower) bound of 1.0. Since the p value is only slightly greater than 0.025, I would expect the upper bound of the CI to be closer to 1.

I checked confidence intervals of hazard ratios for several other published studies and found that the CIs were consistently geometrically symmetrical (i.e. upper/point = point/lower) around the point estimate, but now that I think about it, they all had large samples. I'll have to look into why small sample can result in asymmetric confidence intervals.

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