By Joseph Mazur
Statistics can show evidence, but it cannot prove that one thing causes another. Hidden variables can tell us a great deal about truth if they can be exposed. Coincidences mistakenly used as causes unintentionally contribute to vaccine hesitancy. For those hesitant under the rains of false information that hesitate to be vaccinated, there is worry about the new variant, delta, coming around the world this fall.
A powder extracted from the bark of a willow tree has been known since the fifteenth century b.c. to be a medication that eases headaches and relieves fevers. In 1899, when the German pharmaceutical company Bayer started producing the extract in pill form, we got to know it as aspirin. Statistics demonstrate its strong efficacy. Billions of users for more than a century were relieved of pains and fevers. Still, after so many centuries of use, nobody knew why it worked. Then, fifty years ago, the British pharmacologist John Robert Vane showed that aspirin suppressed the production of certain molecular compounds that regulate the contraction and relaxation of muscle tissue. Finally and decisively, we had a cause.
Science often has statistical indicators for reasons long before having the direct links between causes and effects. Humans tend to make connections where there are none; they manage to ignore correlations that are too complex to predict. We see coincidences as events mysteriously fated by some deeply significant design. That might be true, and it might not be. But whenever we genuinely have a reason for something, it almost always turns out that there is no single explanation.
When two variables appear to have a statistical connection, either by chance or through hidden variables, a mistaken belief in a false linkage is encouraged. One example among many is pediculosis (louse infestation). In New Hebrides (now called Vanuatu), a South Pacific archipelago in the South Pacific, the elders believed that body lice infestation was an indication of good health. For centuries the elders noticed that healthy natives had head lice while sick ones did not. Almost everyone on the islands had lice most of the time. But a fever causes lice to die. Since sick islanders with fevers had no head lice, the elders assumed that pediculosis was a sign of health. The confusion was over the fact that unhealthy people were the ones who got fevers and were lice-free.
Events in nature depend on so many variables that spotting what causes what is almost always eluding. A simple event, such as the flip of a coin, depends on countless undetectable happenings in a mildly chaotic world of accidentally colliding atoms. Immeasurable vibrations of air currents, minute tremors of the wrist, and even pulses determine the landing position. What does that tell us about the far more complex performances of cancer cells? Discovering the cause of cancer is not the same as having a pretty good guess of what is suspect. Some scientists attributed the increase in lung cancer in industrialized countries following WWII to occupational factors and new industrial products. Asphalt was a suspect once because of the proliferation of road building in America and Europe.
We know that cigarette smoking has some causal association with lung cancer and cardiovascular diseases; yet, still, even today, we do not know any actual cause. Cigarette smoking is one of perhaps many other contributory causes. How do we know? There was a coincidental spike in cancer among American women during WWII, when they suddenly entered the workforce by the millions and started smoking for the first time. If we were wrong in accusing cigarette smoking as a factor, we would not have seen the dramatic decrease in lung cancer and cardiovascular disease over the last five decades when the smoking population in the United States dropped by 57 percent. Many studies over the past sixty years have shown statistical correlations between smoking and lung cancer. Smoking is a huge factor. Many natural relations that are not explainable through laws or observation may be linkable by statistical measurements. But, statistical data will not yield a cause. They find suspects, not the cause. Statistics is all about probabilities. A cause is a reason.
It is not unusual for false beliefs to arise from coincidences of hazy data correlations when the truth lies in the hidden variables. Often there are confounding circumstances that make us think that a statistical correlation implies a cause. But knowing a cause does not come directly from statistical data; often, it comes from logical thinking. A could appear to cause B by causing C that happens to cause B.
Unfortunately, the results of too many health studies generate speculations about causes and prevention that end up too quickly in the popular media. Health officials once claimed that to diminish our chances of heart disease, we should take vitamins C and E and beta-carotene as antioxidants. To prevent colon cancer, we should be eating more fiber. We were once told to have a low-roughage diet, and then a few decades later, to eat plenty of roughage. Just because a clinical study involving tens of thousands of subjects in trial and control trial confirms a hypothesis, it does not mean that one event causes another. All it can do is provide a possibility of being correct. Often At best, it only gives circumstantial evidence that one event causes another. Without knowing the cause for sure, we know very little about how to make specific recommendations. Indeed, if the conclusion is incorrect, the recommendations might do more harm than good. Such is the case with Covid-19 vaccines.
Let’s take the example of the Pfizer/BioNTech’s Covid-19 vaccine. There are 226 recorded cases of myocarditis (inflammation of the heart muscles) or pericarditis (inflammation of the pericardium) among 159 million fully vaccinated people in the United States. They are cases that mainly affect young men between the ages of 16 and 30. With those numbers, the risk factors of being vaccinated against a deadly coronavirus are extremely small. Yet one influential news outlet wrote on its website, “CDC advisors reported that myocarditis cases following vaccination in the 16-to-24 age group were higher than expected.” A commentary authored by Dr. Sean O’Leary in the journal Pediatrics concluded, “there are some concerns … that might suggest a causal relationship between the vaccine and myocarditis.”
All of that might be true since the expected number is less than 100 in that age group. However, one factor to be noted about the increase in myocarditis cases is that doctors are carefully watchful of odd side effects since they are required to report them. A second factor is living rearrangements of our pandemic years. They have altered the physical and mental health of many people in that age group. Eating, exercise, and sleep patterns have become misaligned with the circadian rhythms of body clocks. And there is a third factor: Because of haphazardly floating talk about side effects coming from news outlets and social media, we have become far more watchful for anything that makes us feel different immediately after receiving a Covid-19 vaccination.
The media has all sorts of strange takes on what we should believe from misinterpreted polling studies: pesticides in farmlands cause autism; power lines cause brain tumors; wasabi-root tea is a muscle relaxant; 9 out of 10 doctors agree that cereal for breakfast promotes good health; children with longer arms reason better than do those with shorter arms; and walking in a pine forest once a week decreases the stress hormone cortisol, blood pressure, and heart rate. Women should take estrogen to diminish their chance of heart attacks. Estrogen therapy increases the likelihood of heart attacks for women who already had heart disease. Estrogen therapy might protect women against osteoporosis and perhaps colorectal cancer, but it might also increase the risks of heart disease, stroke, blood clots, breast cancer, and dementia.
Many of these beliefs come from coincidental connections. Inevitably, some people who start estrogen therapy will soon have a stroke. Others will have blood clots. With millions of vaccinations a day, it should not be a surprise to find that some people experience epileptic seizures, allergies, type 1 diabetes, hepatitis C, even HIV. But were they caused by the vaccine, or, were they merely expected coincidences?
These coincidences insinuate causes contributing to vaccine hesitancy. The latest and most absurd reason for not getting vaccinated in the United States is the notion that the government is putting chips in vaccination serum to keep track of personal behavior. One should wonder how that is possible when the smallest microchip that can send a signal (as simple as, say, a person’s geometric coordinates) is larger than the size of a grain of rice (2 mm in diameter). How will such a piece of hardware pass through a needle of diameter 0.514 mm, the size of a horse’s hair? But let’s assume the concept has validity. The chip is in; now, how will it be used? It needs to be powered to send a signal. That means that a battery also must be inserted, perhaps at the second shot. A battery fitting through a vaccination needle?
New oppositions to vaccinations pop up every day through mistrust, rumors, and conspiracy theory media outlets. You will attract malaria-carrying mosquitos; it will make you gay, cause life-long skin rashes, and make you sterile. Who knows what the list will contain next week? Will it be blindness, weight loss, being allergic to sunshine? The underlying problem is that we will not be able to sink the current pandemic without dealing with the lack of confidence in our vaccines. To rebuild vaccines’ eroded trust, we need to build a stringent cohesion between news and media outlets and respected scientific laboratories and journals.
The United States is now in a heightened state of confidence, yet after 174 million people were fully vaccinated, the percentage of its population receiving at least one dose of vaccine against Covid-19 still stands just above fifty-six. The daily number of doses has come up against a stalwart blockade of vaccine holdouts, making herd immunity unlikely anytime soon. That does pose a problem for future outbreaks.
A belief that the Covid-19 vaccine was accepted under emergency approval by the FDA too soon is the most popular argument against vaccinations. That argument is by no means valid. Pharmaceutical companies have been working on the mRNA model of vaccines for almost two decades, starting with Severe Acute Respiratory Syndrome (SARS). The problem is the unbreakable strength of conformational bias. It was one thing to say that 30,000 volunteers were too small a group, quite another to say that 3.42 billion is not enough; that’s the number of people vaccinated to date worldwide.
Things are looking up for those of us who are vaccinated. However, in the last few weeks, the number of daily new cases has held steady at about 14,000, no longer shrinking. It seems the reason is that too many Americans are choosing not to vaccinate. Those who are not vaccinated should be worried about the new variant, delta, rapidly increasing in the United States. Yet almost a third of the world follows misleading vaccine information enabling more powerfully contagious, acutely symptomatic, and deathly variants to arrive in the fall. Vaccination hesitancy banks on the fantasy: I didn’t get Covid in all the time it’s been moving around the world, so I doubt I will get ever get it. Nothing could be riskier than banking on that notion. Covid-19 is death’s weapon of choice at this moment. Ask Dr. Robert Wachter of the University of California, San Francisco, the Holly Smith Distinguished Professor in Science and Medicine. He says, “If you’re fully vaxxed, I wouldn’t be too worried, especially if you’re in a highly vaxxed region. If you’re not vaccinated: I’d be afraid. Maybe even very afraid.”
Do! Because vaccines vastly reduce the number of Covid-19 cases, including those coming from any known variant. If you are fully vaccinated, the odds of dying from Covid-19 are minuscule. You might have had some symptoms with no direct connection to the symptoms you receive from a shot in the arm.
About the Author
Joseph Mazur, is Professor Emeritus of Mathematics at Marlboro College. He holds a Ph.D. in Mathematics from M.I.T. and is a recipient of fellowships from the Guggenheim, Bogliasco, and Rockefeller Foundations, among others. His work has appeared in Nature, The New York Times, The Guardian, The Wall Street Journal, Slate, Science, and many other publications. He is the author of Euclid in the Rainforest: Discovering Universal Truth in Mathematics; The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space; What’s Luck Got to Do with It? The History, Mathematics, and Psychology behind the Gambler’s Illusion; Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers; and Fluke: The Math and Myth of Coincidence. His latest book is The Clock Mirage: Our Myth of Measured Time.
-  Darrell Huff, How to Lie With Statistics (New York: Norton, 1993) 10.
-  Joseph Mazur, Fluke: The Math and Myth of Coincidences (New York: Basic Books, 2016) 127-28.
-  https://www.cnn.com/2021/06/09/health/myocarditis-covid-vaccination-link-clearer/index.html
-  Danielle Ofri, “Heidi Larson, Vaccine Anthropologist,” The New Yorker, June 12, 2021.
-  Heidi Ledford, “Six months of COVID vaccines: what 1.7 billion doses have taught scientists,” Nature 594, 164-167 (2021)