A thread for fellow statistical analysis plan nerds (warning: math ahead).

From Pfizer's protocol, vaccine efficacy will be estimated by the incidence rate ratio. A tutorial on how this corresponds to their planned beta-binomial analysis. 1/6
Even though vaccine efficacy is estimated by the incidence rate ratio VE=1-IRR=1-(m1/T1)/(m0/T0), the underlying test is an exact test for a single binomial proportion. The proportion in question is what fraction of total endpoints are in the vaccine arm p=(m1/(m1+m0)). 2/6
Under 1:1 randomization, we have roughly equal follow-up time across both arms (T1=T0). If our null hypothesis was VE=0, we would expect p=50%, with the same number of events across arms. This null can be expressed as a function of the follow-up time p=T1/(T1+T0). 3/6
In fact, we are interested in a different null hypothesis of VE<=0.30, to rule out a lower bound of 30% efficacy. So we can calculate, if VE=0.30, what proportion of events are expected in the vaccine arm? It is a bit lower - 41% - since the vaccine has some effect. 4/6
Under a frequentist paradigm, we can compare p_hat = m1/(m1+m0) to the null hypothesis value p using an exact test for a one-sample binomial proportion. This is equivalent to a test of IRR=1 because the test itself is built using the total follow-up T1, T0. 5/6
Pfizer is using a Bayesian analysis, hence the beta-binomial model with beta as the conjugate prior. They will assess the posterior probability P[VE>0.30|data]. Natural next question then is... what prior have they selected? Hope this thread was helpful! 6/END

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More from @nataliexdean

23 Jul
We know vaccines reduce your risk of infection, but they aren't *perfect.* Then what fraction of transmission in the population is from the vaccinated? How might this change with new variants?

In the thread below, I share a mental model with worked examples. 1/11
First, some definitions. We are familiar with vaccine efficacy (VE) against disease. This was estimated from trials. But many studies have helped us estimate VE against all infection (aka VE_S). For mRNA vaccines against early strains, this has hovered around 80-90%. 2/11
Even if infected, are vaccine breakthroughs less likely to transmit? Due to lower viral load, shorter illness, location of replication (nose, lungs). This is VE against infectiousness (aka VE_I). A recent preprint estimated 50% (w/ high uncertainty). 3/11
Read 12 tweets
10 Jul
The discussion about COVID vaccine boosters is really many sub-discussions at once. The lack of a transparent decision framework makes it feel more confusing.

A thread below to start to break out the points…
Question 1) Are boosters safe and effective? This includes boosters of the original strain and based on new variants. This is addressed by new trials of these new combinations, including immune response data.
2) Do booster doses improve vaccine effectiveness? This depends upon seeing a loss of effectiveness, either from waning over time or against new variants. This can be detected in observational studies and inferred from immune response data.
Read 7 tweets
14 Jun
The return of vaccine Monday, but maybe one of the last placebo-controlled trial results. In their large US/Mexico trial, Novavax confirms the excellent result seen in an earlier UK trial. This includes efficacy against the circulating alpha (UK) variant.
The two dose protein subunit vaccine can be stored at refrigerated temperatures and is cheaper to produce. The company will apply for an EUA in the third quarter of 2021, as they need more time to validate the manufacturing process.
It’s unclear what the market in the US will look like in late 2020, but there is enormous global need. Efficacy against variants not widely circulating during the trial is also unclear. A Phase 2b trial in South Africa showed some drop, but with a wide confidence interval.
Read 4 tweets
7 Jun
A text from a colleague: "Ok how on earth has Twitter decided that we know VE against variants?" 🤔

Twitter does love certainty! But better to think about VE against variants in terms of likely ranges rather than precise estimates. So how do make these assessments? A thread.
Sometimes we have randomized clinical trial data, like J&J Ensemble trial in South Africa and South America. But often we are assembling data from disparate (and imperfect) sources...
Source 1: Data from immunoassays. We can look at neutralizing antibodies against different vaccines and assume this roughly correlates with VE. But we are still characterizing these relationships, and these assays do not capture cell-mediated immunity.
Read 10 tweets
3 Jun
I hope people are aware of the enormous added value of HIV clinical trial networks. Groups who have been working on vaccine & treatment trials for decades leapt into action to work on COVID. OWS vaccine trials directly benefitted from the expertise of these groups. A big success!
There's a lot we can learn from this experience about:
- Leveraging existing networks
- Coordination between companies and researchers to standardize protocols across trials
- Using a centralized DSMB for oversight
- Pooling data, as planned for immune correlates analysis
A recent pub with more info:
"A single 11-member DSMB monitors all government-funded trials to ensure coordinated oversight, promote harmonized designs, and allow shared insights related to safety across trials."
@SteveJoffe et al.
Read 4 tweets
27 May
How will we know if we need COVID vaccine boosters?
If we observe that:
(1) Vaccine protection wanes over time.
(2) New immune escape variants emerge, resulting in a vaccine-strain mismatch.
These are distinct reasons. We can imagine how we would distinguish these in the data.
(1) Immunity wanes over time.
We would see that:
- Breakthrough cases occur most frequently in people who were vaccinated longest ago.
- These breakthrough cases include all types of strains.
(2) New immune escape variants emerge.
We would see that:
- Breakthrough cases are similarly common in people vaccinated recently and vaccinated longest ago.
- Breakthrough cases are disproportionately of the new variant type.
Read 4 tweets

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