Mlodinow

In my social media feed a couple of weeks ago, someone posted an image of a television news piece (from Detroit’s CW50) and a short paragraph under the headline “Former Detroit TV Anchor Dies One Day After Taking COVID Vaccine.” There was no actual link to a site, and the headline, image and paragraph seemed to not have been put together by the original source of the news. But the suggestion was clear: the COVID vaccine could be the cause of death. The paragraph referred to Karen Hudson-Samuels, a Detroit news producer and anchor who, indeed, seems to have died a day after taking the vaccine. Some articles on the internet quoted her husband as saying the immediate cause may have been a stroke with no clear relation to the vaccine (e.g. Nour Rahal 2021).

An off the cuff calculation would show that, given the number of people in the US who die every day and the number or COVID vaccinations taking place every day, particularly for the population over 65 (Karen Hudson-Samuels was 68), chances are that there will be people dying the day after taking a COVID vaccine, for completely unrelated reasons. For example, as of Feb 27 there were approximately 12 million 65-74 year olds with at least 1 dose of the vaccine (CDC 2021). If there are at least 31 million 65-74 year olds in the country (there were more in 2019 according to the Census Bureau, USCB 2020) and if there were 75 days of vaccination between December 14 (day of first year of vaccination in the US) and February 27, the chances of a 65-74 year old receiving the first dose of the vaccine on any given day during that period was approximately 0.5% (12 million divided by 75 days out of 31 million). The likelihood actually gets greater towards the end of the period, when Karen Hudson-Samuels received it, because the number of 65-74 year olds who have not yet received their first dose decreases (the pool left to receive the dose keep getting smaller), assuming vaccination continues at the same pace. According to the CDC, the mortality rate of 65-74 year olds in the US in 2019 was approximately 1.7% (Kochanek et al, 220). Divided by 365 days, that means approximately 0.0047% of 65-74 year olds died on any given day for causes unrelated to COVID (COVID was not present at the time). If the same holds true in 2021, the likelihood that a 64-75 year old died the day after receiving the first doses of the COVID vaccine is 0.5% (chance of receiving a vaccine on any given day) x 0.0047% (chance of dying of an unrelated cause on any given day). That equals 0.000024%, or approximately 1 in 4 million. That seems like a very low chance. But if there are over 30 million 65-74 year olds in the US, that likely happened in over 7 cases between December 14 and February 27. And there were likely 7 more who died the same day of the vaccine, and 7 more two days after and so on.

The numbers above may be a bit off and the calculations assume receiving a COVID vaccine and dying of a non-related cause are independent events. This may not be the case if, for example, someone with a life threatening underlying health condition would be more likely to get a vaccine. In this case the chances of observing someone dying the day after receiving a vaccine would be even larger. On the other hand, if the fact that someone is visibly about to die makes them less likely to receive a vaccine, the chances would be smaller. But the general point should remain valid, even if the actual numbers are a bit different under varying circumstances: chances are there are several cases like that of Karen Hudson-Samuels that can be explained by pure chance, with no relationship to the COVID vaccine at all. Yet, all you need is 1 case to make the news and to persuade some people that the vaccine is likely the cause.

The post seems a clear example of the point that Leonard Mlodinow is making in the book I am currently reading, The Drunkard’s Walk: How Randomness Rules Our Lives (Mlodinow 2009). In this book he argues that random processes are all around us and play an important role in daily events. Yet, we seem to be ill equipped to recognize them and we often don’t. I am about half way through the book and so far have found most interesting his account of the development of statistical concepts and understanding over time. It is also a very pleasant read. I’ll be referring to this book again in future posts.

References

CDC (Centers for Disease Control and Prevention). 2021.  Demographic Characteristics of People Receiving COVID-19 Vaccinations in the United States. Available: https://covid.cdc.gov/covid-data-tracker/#vaccination-demographic. Accessed: 02/28/2021

Kochanek, Kenneth D., M.A., Jiaquan Xu, M.D., and Elizabeth Arias, Ph.D. 2020. Mortality in the United States, 2019. National Center for Health Statistics (NCHS) Data Brief 395, December. CDC (Centers for Disease Control and Prevention). Available: https://www.cdc.gov/nchs/data/databriefs/db395-H.pdf. Accessed: 02/28/2021

Mlodinow, Leonard. 2009. The Drunkard’s Walk. How Randomness Rules Our Lives. New York: Vintage Books. A Division of Random House.

Nour Rahal. 2021. Karen Hudson-Samuels remembered as Black TV news pioneer and Detroit history promoter. Detroit Free Press, 02/20/2021. Available: https://www.freep.com/story/news/obituary/2021/02/20/karen-hudson-samuels-black-tv-news-pioneer/6784796002/ . Accessed: 02/28/2021.

USCB (United States Census Bureau). 2020. Annual Estimates of the Resident Population by Single Year of Age and Sex for the United States: April 1, 2010 to July 1, 2019 (NC-EST2019-AGESEX-RES). Available: https://www.census.gov/data/tables/time-series/demo/popest/2010s-national-detail.html. Accessed: 02/28/2021