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From the statnews article - "The Moderna vaccine reduced the risk of Covid-19 infection by 94.5%. There were 95 cases of infection among patients who received placebo in the company’s 30,000-patient study. There were only five infections in patients who developed Covid-19 after receiving Moderna’s vaccine, mRNA-1273."

I wondered what the 94.5% reduction in risk means. Assuming 95/15000 is the risk with placebo and 5/15000 is the risk with vaccine, then (95 - 5)/95 = .947. Does this sound right?

asahi
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    Here is a blog post about the analogous question of how the 90% came about for the BioNTech/Pfizer vaccine: http://skranz.github.io//r/2020/11/11/CovidVaccineBayesian.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+skranz_R+%28Economics+and+R+%28R+Posts%29%29 – Christoph Hanck Nov 16 '20 at 13:30
  • FWIW, I show in a related posting how to obtain the estimate and CI using emmeans(). https://stats.stackexchange.com/questions/495843/how-to-calculate-95-ci-of-vaccine-with-90-efficacy – Russ Lenth Dec 01 '20 at 03:57

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The usual measure for vaccine efficacy ($VE$) is $1 - rr$ where $rr$ is relative risk. Relative risk is the ratio of disease incidence in vaccine protected people to those who are unvaccinated. That is the number you computed:

\begin{align} VE &= 1- rr \\ &= 1-I_{vac}/I_{unvac} \\ &= 1- \frac{5}{15000}/\frac{95}{15000} \\ &\approx .947 \end{align}

So why the discrepancy between that number and the reported 94.5% effectiveness? An NIH News Release about the Moderna vaccine says the trial had "more than 30000 participants". If the actual total was not 30000 but some slightly different number (maybe fewer in the end due to exclusion criteria) then that could account for the difference between the reported 94.5% and the above calculation of 94.7% effectiveness.

abstrusiosity
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  • Shouldn't it be though 90/15000. They said 90 from placebo group and 5 from vaccine group and a total of 95. And this comes out 0.944444 which is getting pretty close to 94.5% – Meir Maor Nov 19 '20 at 06:41
  • Actually they probably do some cox regression and take into account timing of the diagnosis and get even more accurate results, – Meir Maor Nov 19 '20 at 07:07
  • Good point. A proper analysis would account for censoring due to the limited observation period. – abstrusiosity Nov 19 '20 at 12:56
  • @Meir Maor You are correct about the use of Cox regression. “Primary analysis: VE will be estimated with 1 – HR (mRNA-1273 vs placebo) using a Cox proportional hazard regression model with treatment group as a fixed effect and adjust for stratification factor based on the PP Set, with cases counted starting 14 days after the second dose of IP.” "PP" stands for "Per Protocol." Page 89 of COVE protocol. https://www.modernatx.com/cove-study – Diana Petitti Nov 20 '20 at 21:22