Thread by @mlipsitch

New preprint on estimating and Interpreting vaccine efficacy trial results for infection and transmission | medRxiv. With ⁦@rebeccajk13⁩. Long discussion on applications to observational VE studies medrxiv.org/content/10.110…

tl;dr: Analyze separately cases ascertained for different reasons. Don't combine those found because symptomatic with those found by screening a cross section or by testing contacts.

In an RCT there are typically one of these (symptomatic cases, the primary endpoint in most COVID trials) or two (symptomatics and cross-sections). Symptomatics are incident cases and VE is properly measured by 1- incidence rate ratio. The VE measured is vs symptomatic infxn

This can be seen as 1-(1-VES)(1-VEP) where VES is reduction in chance of getting infected and VEP is reduction in chance of symptoms if infected. Has been called VESP.

(By the way this reasoning is essentially an application of the basic principles led out by @betzhallo @ilongini & Claudio Struchiner academic.oup.com/aje/article/14… and in their textbook springer.com/gp/book/978038…)

The second kind of data is cross-section -- take a bunch of people, swab them, and compare vaccinated to placebo (or unvax in obs context).1- the odds ratio (not risk ratio, though in practice almost the same for SARS-Cov-2 outside a major surge) measures VE vs viral positivity

That OR can be interpreted as the impact of vaccine on incidence combined with impact on duration of virus positivity -- at equilibrium recall prevalence odds = incidence x duration. This has an interpretation as a lower bound on the efficacy of the vaccine vs. transmission.

Lower bound because there could be a further effect on viral load among the positives. This reasoning too has roots in a great "classic paper" in this case by Rinta-Kokko et al. pubmed.ncbi.nlm.nih.gov/19490983/.

The key point is that this is a prevalence measure, the first is an incidence measure, each with a clear interpretation under reasonable assumptions. Combining them gives something with no clear interpretation, at least if you don't swab everyone in the trial.

Comparing a mix of sympt & asympto infections with different prob of detection gives a measure that is hard to interpret. "All infections" in observ studies especially hard this way -- that's why in nejm.org/doi/full/10.10… we were careful to talk of "documented" rather than all

Last, in observational studies (less often in trials) there may be contact tracing so you can measure positivity for virus in testing of contacts of cases to assess protection from the vaccine. Here you are conditioning on infection (unlike cross-section screening)

so the proper measure is risk ratio. This is a straightforward measure of VES. (thanks again @betzhallo et al @AmJEpi 1997). Best measured separate from the other kinds of ascertainment.

The modeling in the paper is not so much for estimation but to show that these measures get the "right" answer when done separately but something else when different kinds of cases are mixed together.

The Moderna estimate is just the straightforward application of the odds ratio measure to the cross-sectional data from the original trial at the time of 2nd swab.

Small point: modeling notes that the Moderna trial would have slightly underestimated the effect of the first dose (to be fair they make no such estimate, but do report the data) on infection because some would still be PCR+ on day 28 who were infected before dose 1 took effect.

Further reasons why the long-term effects could be larger: 1) 2 doses rather than 1. 2) may be an effect on viral load too on top of infection prevention or shortening.

Guess this thread is almost as long as the paper, but perhaps chattier.

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