Without evidence of benefit, an intervention should not be presumed to be beneficial or safe.

- Rogue Medic

Why 90% vs. 62% for the Efficacy of the AstraZeneca Vaccine Candidate?


There was a press release from AstraZeneca at 7 AM today. It includes two different dosing methods with two dramatically different rates of efficacy. One group received half a dose, followed by a month later by a full dose. The other group received a full dose, followed by a month later by another full dose.


One dosing regimen (n=2,741) showed vaccine efficacy of 90% when AZD1222 was given as a half dose, followed by a full dose at least one month apart, and another dosing regimen (n=8,895) showed 62% efficacy when given as two full doses at least one month apart. The combined analysis from both dosing regimens (n=11,636) resulted in an average efficacy of 70%. All results were statistically significant (p<=0.0001). More data will continue to accumulate and additional analysis will be conducted, refining the efficacy reading and establishing the duration of protection.


Usually, the result of the differences in dosing is to use the lowest effective dose, in order to minimize any side effects, which are usually dose related. A higher dose is expected to be more effective, but also to have more side effects.


The part people are having a hard time explaining is that the 90% efficacy is in the smaller dose group. This does not seem to make medical sense, but this is what people who understand statistics expect.




Daniel Kahneman explains this in his excellent book, Thinking, Fast and Slow. He uses the following example as an introduction:


A study of the incidence of kidney cancer in the 3,141 counties of the United States reveals a remarkable pattern. The counties in which the incidence of kidney cancer is lowest are mostly rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West. What do you make of this?


This is known informally as the Law of Small Numbers. Intuitively, we can come up with many different explanations about a healthy rural lifestyle, or something else. Kahneman follows that with the statistics on counties with the highest incidence of kidney cancer, which are also mostly rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West.


The important factor is not lifestyle, not politics, and not geography. The important factor is that these are all sparsely populated counties, which means that the number of cases of kidney cancer will be disproportionately affected by the addition/subtraction of a tiny number of cases.


The small sample size is the most likely explanation for the 90% efficacy in the half dose, then full dose group. When more cases of COVID-19 are diagnosed among those who have received the half dose, then the full dose, expect the estimate of benefit to drop closer to 70%. The 70% efficacy is also based on small numbers, but those numbers (including the 90% sample) are more than four times the size of the 90% sample. This is not certain. This is statistical probability. A reasonable person should feel comfortable in placing a wager on the results dropping to near 70%.


In other words, the news is worse than expected, although still good news. There is another vaccine candidate that, based on the preliminary numbers, meets the approval criteria of better than 50% efficacy.




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