Wasn't planning on blogging today but the news cycle won't leave me alone :)

CDC Director Dr. Redfield made a bit of a stir yesterday when he told Congress - and I paraphrase - that **masks may offer individuals greater protection than vaccines**.

This is a very thoughtful statement which rewards some further comments.

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The way medicine is practiced, we are often misled to over-estimate the impact of drugs and vaccines. When the doctor says take pill X to treat condition Y, we think if we take pill X, condition Y will be cured. In reality, for most conditions and meds, if we take pill X, there is a chance C that pill X will cure condition Y. C is not 100 percent, and is usually way below 100 percent.

Flu vaccines are said to be 50 percent effective or less. What does that mean? Perhaps, that half the people who've gotten flu shots will be protected while the other half will still catch the flu. This isn't how experts use the word "effectiveness" but let me stay with this intuitive definition for now. (I'll turn to the technical definition in the last part of the post.)

This situation reminds me of the famous put-down of TV advertising: half the budget is wasted but we don't know which half.

The trouble of course is that if you halve the TV spending, you will still waste half the money while also losing half the benefit. Same with the vaccines. If only half the people get vaccinated, a quarter of the people will be protected.

**The FDA has announced that a SARS-Cov-2 vaccine with 50% effectiveness is acceptable**. Staying with the intuitive definition, this means getting the vaccine shot is like buying a lottery ticket with a 50 percent chance of winning. This is not news though. Taking any pill X or undergoing any surgery has always been a lottery with C percent chance of winning. The value of C depends on the treatment.

One of the reasons why some vaccinated people will still catch the flu is biological variation. Different people respond to the vaccine differently.

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What about wearing a mask? The mask works as a physical barrier and its function is not affected by anything biological. The same mask worn properly confers the same degree of protection on anyone. Any decent mask blocks some fraction of virus from entering one's respiratory system. Imagine an infectious person coughing directly at me. The mask reduces the amount of viral projectile even if it is not eradicated.

In other words, wearing a mask has a high C. Even though I am a skeptic of many things, mask wearing is not one of them.

Whether the vaccine will work for me or you depends on biology. I have no control over that. Either my body responds to the vaccine or it doesn't. The mask, on the other hand, works on everyone who wears one. That's what the CDC Director is saying, and he's right.

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Now that I've gotten your attention, let's switch to a proper interpretation of **vaccine effectiveness**. We have a coronavirus vaccine that demonstrates 50% effectiveness in a clinical trial. One possible scenario is it reduces the infection rate from 1% to 0.5%. (For reference, in the Moderna trial, they assume the baseline infection rate with no vaccine is 0.75% over a six-month period.) That's a 50% drop, and statistically significant.

For every 1000 patients receiving the vaccine shot, five patients will benefit from it as they would have caught Covid-19 without the vaccine. Another five will get sick despite being vaccinated. So C is 5/1000 = 0.5 percent for the vaccine. Getting vaccinated is like buying a lottery ticket with 5 percent chance of winning.

In medical jardon, we say the **number needed to treat** is 1000/5 = 200. For one person to benefit from vaccination, we must administer 200 vaccine shots. Similar to TV advertising, we can't know who would benefit ahead of time. Statistics tell us that on average, one out of 200 will.

Notice that C isn't 50 percent but only 0.5 percent. It can't be 50 percent because most people won't catch Covid-19 even without the vaccine. For every 1000 people vaccinated, 995 of them won't get sick. Of those 995, 990 would have stayed healthy regardless of vaccination. The 50% effective vaccine really only benefits 0.5% of those who took the shot. (Note again that I'm using the assumption from the Moderna clinical trial design.)

But this is not the full story. The practical effectiveness of the vaccine depends also on what proportion of the population takes the shots. Let's pretend that half the population get vaccinated. Then the 0.5% benefit of vaccination is halved. The infection rate in the population is reduced from 1% to 0.75% since the infection rate for the unvaccinated will remain at 1%.

**Herd immunity** now complicates this picture. If enough people get the vaccine, typically 60% or higher, the amount of virus circulating in the population is suppressed enough that the infection rate for the unvaccinated will dip below 1% so collective action creates a positive externality.

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