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

Aug 8, 2022
Starting now! I’ll be live tweeting this @DataSciJedi-sponsored session on Delivering Data Differently at #JSM2022. #JEDIatJSM
Our first speaker is @ajrgodfrey. He speaks from his experiences as a blind person. He emphasizes the importance of independence and dignity for the visually impaired. #JEDIatJSM
“A blind person must be able to collect, analyze, interpret, and manipulate scientific data in order to answer questions and communicate the knowledge gained from their results in a way that can be readily understood by their sighted peers.“ @ajrgodfrey #JEDIatJSM
Read 12 tweets
Jul 10, 2022
If a new SARS-CoV-2 variant is spreading 50% faster than an old one, does the new variant have a 50% higher R0? With each new variant more transmissible than the last, does that mean the latest variants have an R0 of 18? 😳

A short explainer…
A new variant may spread faster for a few main reasons (a non-exhaustive list):

- An increase in inherent transmissibility (e.g. higher viral load, better binding to cells)

- An increased ability to infect people with some baseline immunity (“immune evasion”)

Just because something has a 50% *growth advantage* in a population does not mean it is 50% more *transmissible.* Some (or most) of that growth advantage may come from immune evasion. 3/5
Read 5 tweets
Jun 10, 2022
I enjoyed participating in yesterday's #EEID2022 panel on scientific communication - what has worked, what hasn't, and what I've learned. For these types of panels, I have made a conscious decision to be very honest, including the good and the bad experiences. 1/
Yesterday, that included me telling the audience how much I angsted over questions like "Is it safe to do X? Our viewers want to know!" Or pressure to stay up to date on everything, or say yes to all requests. Worry that I'm saying the wrong thing or don't belong. 2/
Admitting vulnerability is a trait I admire in others because it takes bravery and normalizes common challenges. IMO, it's a similar bravery to scientific communication in the first place. Public engagement involves putting yourself out there in a way that can be intimidating. 3/
Read 4 tweets
Jun 6, 2022
Tracking down primary sources for the estimated 85% effectiveness of smallpox vaccines against #monkeypox is harder than I thought.

From what I can gather, ACAM2000 effectiveness was estimated from observational data of outbreaks in Africa. (Which studies are these?) ...
And then the JYNNEOS vaccine is cited as having "up to 85% effectiveness."

Per CDC "The effectiveness of JYNNEOS against monkeypox was concluded from a clinical study on the immunogenicity of JYNNEOS and efficacy data from animal studies." ...
I interpret this as non-inferiority data comparing JYNNEOS and ACAM2000 immune responses (hence the "up to" phrasing). (e.g. nejm.org/doi/10.1056/NE…)

Ultimately, I'm curious about the quality of the original 85% estimates.
Read 5 tweets
Apr 13, 2022
Recently I learned the term “hidden curriculum,” and it felt like an aha moment. A very short story about one of my hidden curriculum moments. 1/7
I interviewed for biostats PhD programs during my senior year of college. I really wasn’t sure what to expect at my interviews. I remember being so thrilled to be flown anywhere. I showed up enthusiastic and ready to learn about the field. 2/7
During a one-on-one interview, I asked a (white, male, very senior) faculty member to tell me about his research. I thought this to be a perfectly reasonable question. I really didn’t know much about what biostatisticians did, the range of projects they worked on. 3/7
Read 10 tweets
Jan 21, 2022
The end of the pandemic? Let's talk about modeling assumptions and future uncertainty. Are the IHME projections discussed in this @TheLancet comment assuming ~90% of Omicron infections are asymptomatic and thus likely to be missed? 1/5
The Omicron waves have certainly been large and many infections have been missed, but the evidence that the asymptomatic fraction is *so high* is thin. A model with this assumption would seem to attribute the rapid turnaround in a wave entirely to running out of susceptibles. 2/5
But in reality, there can be many factors that cause a turnaround. A build up of immunity is maybe the largest one, but also temporary protective changes in behavior. (I also think about our complex network structures, and whether a wave has fully percolated through.) 3/5
Read 5 tweets

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