Vaccine efficacy in blocking infection & transmission

(I think) We can now estimate the (minimum) reduction in transmission from the Moderna vaccine.

Thread

tl;dr Moderna vaccine blocks >90% (87-93%) of infections & 91% (89-94%) of transmission.

*Critiques welcome!

Background
By now, everyone knows there are 4 vaccines "approved for full use" (NY Times wording) in one or more countries: Pfizer, Moderna, Sputnik 5, Astrazeneca https://www.nytimes.com/interactive/2020/science/coronavirus-vaccine-tracker.html

These 4 have shown moderate (Astrazeneca) to very high efficacy in reducing "symptomatic" infections.
https://www.bbc.com/news/world-asia-china-55212787

Their efficacy in reducing severe disease is thought to be higher, but there is less data than for mild/moderate infections b/c severe infections are rarer. I wrote a detailed thread about this for Pfizer vaccine: https://twitter.com/DiseaseEcology/status/1336446195284070400

The big remaining Q is whether vaccines just reduce disease or also block infection or reduce transmission. I wrote a thread on this too.
https://twitter.com/DiseaseEcology/status/1339093180151603202
Smarter people than me ( @mlipsitch @nataliexdean) are also talking about this. https://science.sciencemag.org/content/370/6518/763/tab-pdf

It matters enormously, both in terms of if is safe for vaccinated people to hug ( @JuliaLMarcus https://www.theatlantic.com/ideas/archive/2021/01/giving-people-more-freedom-whole-point-vaccines/617829/), & for who we should allocate the vaccine to ( https://science.sciencemag.org/content/early/2021/02/01/science.abe6959).

Many people know that neither the Pfizer or Moderna trial included regular swabbing of participants, so it was difficult to quantify asymptomatic infections. In fact, the ~95% efficacy against symptomatic infections left a wide range of possibilities open.

Here's a graph illustrating possibilities. We know from meta-analysis @nicolamlow that 20% of infections are asymptomatic https://doi.org/10.1371/journal.pmed.1003346 (see 1.placebo group). If vaccine only reduced disease but not infections, we'd get option 2 - no reduction in total infection but...

a 95% reduction in symptomatic infections but a huge INCREASE in asymptomatic infections.
If vaccination reduced both symptomatic & asymptomatic infections 95% we get outcome 3. Finally, it's possible to get outcome b/w 2 & 3, shown as outcome 4.

What do the data indicate?
A *CRUCIAL* bit of data was shared from Moderna trial based on swabs taken on day of 2nd dose. These data showed a 61.5% reduction in infections on this day. But was this estimate of reduction in total infections or asymptomatic? https://twitter.com/DiseaseEcology/status/1339093206122655747

The difference is *crucial*. If reduction is in total infections, then it's better than outcome 2, but only 2/3 of the way towards outcome 3. If reduction is in asymptomatic infections then much better b/c w already know symptomatic infections are 95% lower.

I emailed authors of study (DOI: 10.1056/NEJMoa2035389) & Dr. El Sahly was kindly able to confirm that the swabs represent truly asymptomatic infections. This is fantastic because it indicates we have outcome 4 - reductions of 95% in symp. & 61.5% in asymp infections.

Finally, a very recent paper from @RoyKishony Israel suggested that infections following vaccination reduces viral load by ~2 Ct starting 12d after 1st dose ( https://doi.org/10.1101/2021.02.06.21251283)

Another recent set of papers showed that lower viral loads are strongly correlated with lower transmission
https://twitter.com/DiseaseEcology/status/1357117171369824258

Linking these last two datasets is a little tricky given diffs in Ct b/w labs & logistic relationship b/w Ct & transmission- I've done a back of the envelope version below. Also vaccine from Israel study is Pfizer, not Moderna. This only affects transmission efficacy calculation.

If we put this all together, I *think* we can estimate the (minimum) reduction in both infection & transmission from vaccinated individuals. *Minimum* b/c reduction in asymptomatic infections & viral load is based on data BEFORE 2nd dose. Efficacy should improve w/ 2nd dose.

Point estimate:
Infection efficacy: (IE)
0.8*0.95+0.2*0.385=88.3%
Transmission efficacy:
IE*0.93^2 (.93 per log, 2 logs) = 89.9%

Incorporating uncertainty from each component (except Ct-infectiousness correlation) w/ parametric boostrapping produces median reductions of 90% (87-93%) in infection & 91% (89-94%) of transmission
(Note: many CIs were not symmetrical so median !=mean/point estimates):

Note that infection reduction calcs are based on Moderna vaccine (no data on asymp infection for Pfizer). As noted above, trans reduction calcs use data from Pfizer, so a little bit of mixing & matching which is less than idea, but vaccines are very similar so prob not far off.

Have I made an error somewhere? If so, please let me know and I'll revise & update.
(or if it's a big error, I'll delete the whole thread).
@mlipsitch @nataliexdean @JoannaMasel @LucaFerrettiEvo

Add1:
I made a couple typos (that don't change calcs but confused people; apologies) in showing calcs of point estimates:
Reductions in infection should have been:
0.8*0.95+0.2*0.615=88.3%
Reduction in transmission
1-[(1-0.883)*0.93^2] = 89.9%

Add2: h/t @taaltree
Reduction in transmission due to lower viral loads from an individual person has more uncertainty than pop estimate calc above. This expands 95% CI quite a bit so reduction for individual is:
91% (84%-96%)

Add3: h/t @JamesGWood_UNSW
Data from 2nd swab is point prevalence estimate, not precise measure of all asymp infections. If duration of RNA shedding differs b/w vacc & unvacc, this alters ratio of prev vs # infect. Overall effect on reduction in infection is small if... (cont)

ratio of shedding durations is not huge (e.g. <2 or 1/2) b/c 95% efficacy for sympt inf is main effect & asymptomatic prev was (61.5%) lower. I thought I saw data on lower duration of shedding w/ vaccine but can't find it. @RoyKishony @segal_eran
Please link to it if you can.

Add4: @mlipsitch
Some of the PCR+ swabs @ 2nd dose will be detecting RNA from infections that occurred before vaccine has any efficacy. If we use 12d post-1st dose as cutoff, then if incidence ~constant, using @bennyborremans we can estimate this as...
https://elifesciences.org/articles/60122 

Frac of cases days 1:12 of 1:28=12/28
Prob of detecting RNA from these cases (simple linear interpol.): 0.255
Swabs + in vaccine group on day of dose 2= 15
12/28*0.255*15=1.64 swabs still being detected by residual RNA from cases detected on days 1-12

Add5:
Vaccine efficacy in reducing infection (incidence) can be calculated (w/ assumptions) using point prevalence P using eq from doi:10.1016/j.vaccine.2009.04.009 (h/t @mlipsitch)
But, 1-P_V & 1-P_C =~1, b/c
P_V=15/14,711
P_C=39/14,617
so correction (1-P_C)/(1-P_V)=0.998

Accounting for two revisions above increases efficacy estimates a tiny bit, but it's lost in rounding estimates to avoid over-precision:
Infection: 90% (86%-93%)
Transmission: 91% (82%-96%)
New boxplot w/ more draws to show full range of outcomes.