The cow of doubt — Parshat Vaera

In 1930s Britain and United States, mortality rates showed a sudden increase in deaths from lung cancer. In 1947, the British Medical Research Council asked two epidemiologists, Richard Doll and Austin Bradford Hill, to investigate the cause. There were several ideas floated by scientists to explain the increase. Doll wrote that:

Much of the increase… could be attributed to improved diagnosis… The cause of any real part of the increase… might be found in atmospheric pollution, because of the urban-rural gradient in mortality and an inverse correlation with the recorded hours of sunshine in large towns… Sir Ernest Kennaway, however, thought that this was an unsatisfactory explanation… Tobacco, he suggested, was a more likely cause, particularly when smoked in the form of cigarettes.

Doll and Hill carried out a large-scale statistical experiment to determine whether the rise in lung cancer deaths were attributable to more pollution, caused perhaps by exhaust fumes from the increasing number of cars on the road, by smoking cigarettes, or perhaps did not even exist and was merely a function of improved diagnosis.

The pair began by interviewing more than 700 patients in 20 London hospitals who had lung cancer and a similar number of patients of the same ages, gender and hospital who did not have cancer. In 1950 they published their findings. They had discovered that the main difference between those with lung cancer and those without was the number of cigarettes they smoked.

They published their paper in the British Medical Journal and concluded with the following:

The figures obtained are admittedly speculative, but suggest that, above the age of 45, the risk of developing the disease increases in simple proportion with the amount smoked, and that it may be approximately 50 times as great among those who smoke 25 or more cigarettes a day as among non-smokers.

Even before the paper was published, in 1949, Doll saw that the evidence was so compelling that he gave up smoking, after a 19-year habit.

In 1950, four other independent studies from the US and two from Germany also showed a link between smoking a lung cancer rates.

Wanting to prove his hypothesis beyond a doubt, in 1951, Doll and Hill continued with a more in-depth study of smoking habits and a possible link to lung cancer. They sent out questionnaires to over 40,000 doctors around the country. The pair decided that British doctors would make a perfect research group, because they were likely to fill out the questionnaires accurately, would probably have access to the best medical treatment and would be easy to keep track of through the UK’s registry of physicians. At that time, 87% of doctors were heavy smokers.

Doll and Hill analyzed the answers and looked at 879 deaths and found a strong correlation between increased mortality from lung cancer or coronary thrombosis and the number of cigarettes the doctors smoked.

This was one of the most rigorous statistical studies ever conducted at that time and the evidence seemed very strong.

However, the findings remained controversial and there were several famous statisticians who came out publicly against Doll and Hill’s results.

Ronald Fisher. (CC BY-SA, Madhura.u/ Wikimedia Commons)

Ronald Fisher, who was extremely influential in creating the foundation for modern statistics, stressed that correlation does not imply causation. In a paper entitled, “Cigarettes, Cancer and Statistics” Fisher argued that Doll and Hill’s trials were not completely random and had designed the experiment to find the conclusion they were looking for. He then cast doubt on all their conclusions, asking enough questions to potentially undermine their entire study.

Fisher pointed to discrepancies between cigarette smokers and pipe smokers. He suggested that perhaps it was the cigarette paper that caused cancer rather than the tobacco. Perhaps it was because the tobacco was burned at a higher temperature in cigarettes than in pipes. Or perhaps it was related not to the tobacco at all but to the amount they inhaled. He even went so far as to suggest:

Is it possible, then, that lung cancer – that is to say, the pre-cancerous condition which must exist and is known to exist for years in those who are going to show overt lung cancer – is one of the causes of smoking cigarettes? I don’t think it can be excluded. I don’t think we know enough to say that it is such a cause.

He posited that the inflammation of the lungs caused by cancer may be soothed by cigarette smoke. This would explain the correlation between smoking and cancer, but the causation would be reversed entirely. If so, wrote Fisher, “To take the poor chap’s cigarettes away from him would be rather like taking away his white stick from a blind man. It would make an already unhappy person a little more unhappy than he need be.”

In a 1958 paper published in Nature, Fisher suggested that the same genetic factors that made someone predisposed to develop lung cancer may also be the genes that cause them the desire to smoke.

Nobody denied that Fisher was a genius, an expert in the field of statistics. Yet it turned out that his argument in favor of smoking was entirely false. Was he biased because he was himself a smoker? Or did the fact that he was funded by the tobacco industry influence his conclusions?

Tim Harford, begins his book “How to Make the World Add Up” (named “The Data Detective” in the USA), with the Doll and Hill study showing that cigarette smoking causes cancer. He then mentions the most popular book ever written on statistics, 1954’s “How to Lie with Statistics” by Darrel Huff.

Huff was a journalist, not a statistician, but he managed to point out the many pitfalls of bad statistical analysis, and particularly focused on the fact that often statistics can show a link between two sets of data that are completely unconnected.

For example, in Copenhagen for about a dozen years after World War II, there was a strong correlation between the number of storks nesting in the city and the number of human babies born. Does this imply that storks really do deliver babies? Of course not. Even though both sets of data are valid, there is no correlation between them.

Today there is an entire website dedicated to such spurious correlations, including such gems as an apparent connection between people who wash their own cars and those who like hummus, people who type slower appear more likely to enjoy radishes – things like that.

Huff’s book sold over 1.5 million copies and became essential reading for all statisticians (and anyone who cared about discovering the truth about “lies, damn lies, and statistics”). Yet that doesn’t mean that all statistics are false.

On March 22, 1965, Huff testified before Congress about whether labels should be placed on cigarettes warning of the dangers of smoking. He argued that even though there was a correlation between smoking and lung disease, that did not imply that smoking caused lung disease.

In his testimony he pointed out “eight major warning signals” that the many rigorous studies, including those of Doll and Hill, could not be trusted.

One of the senators then asked him, “Do you honestly think there is as casual a relationship between statistics linking smoking with disease as there is about storks?” To which Huff replied, “The factors seem to me the same.”

We now all know how absolutely wrong Huff was. He was not a scientist, but he had become an expert on statistics. How could he not have spotted the difference between stork babies and smoking deaths?

Pointing out flaws in statistical analysis had made Huff a lot of money, so perhaps that blinded him to the fact that sometimes statistics were correct. Or perhaps his bias came from the fact that in 1965 The Tobacco Institute was funding him to write a book entitled, “How to Lie with Smoking Statistics.” (The book was never published, but most of the unpublished draft can be found online here).

The Richard Doll Building, Oxford. (Public Domain/ Wikimedia Commons)

Doll continued his research into the link between cigarette smoking and lung cancer. He continued sending questionnaires to the same doctors for half a century. He published the results of “The British Doctors Study” in 1957, 1966, 1971, 1978, 1991, and 2001. In 2004, he released his final 50-year findings. More than 30,000 doctors were involved in the study, and Doll had data from over 25,000 deaths.

Doll was an excellent statistician, and his research ultimately probably saved millions of lives. Had his research not been undermined by other experts funded by the tobacco industry, perhaps more people would have given up smoking much earlier and countless more lives could have been saved.

A plaque in the Richard Doll building in Oxford has the following quotation from the great man:

Death in old age is inevitable, but death before old age is not. In previous centuries 70 years used to be regarded as humanity’s allotted span of life, and only about one in five lived to such an age. Nowadays, however, for non-smokers in Western countries, the situation is reversed: only about one in five will die before 70, and the non-smoker death rates are still decreasing, offering the promise, at least in developed countries, of a world where death before 70 is uncommon. For this promise to be properly realised, ways must be found to limit the vast damage that is now being done by tobacco and to bring home, not only to the many millions of people in developed countries but also the far larger populations elsewhere, the extent to which those who continue to smoke are shortening their expectation of life by so doing.

The British Medical Journal referred to Doll as “The Man Who Stopped Smoking.”

However, even Doll was not immune to reaching mistaken conclusions, nor to receiving funding from interested parties.

In 2006, The Guardian reported that Doll had failed to disclose that he had been paid by chemical companies while investigating links between certain chemicals and cancer.

In the 1980s Doll testified that there was no evidence that Agent Orange caused cancer. At the time he was receiving $1,500 a day from Monsanto, the company that produced Agent Orange. He also found no link between certain plastics and most cancers, while receiving funding from the Chemical Manufacturers Association, Dow Chemicals and ICI.

The main tactic in the tobacco industry playbook was to sow doubt. A 1969 internal memo from R. J. Reynolds stated, “Doubt is our product since it is the best means of competing with the ‘body of fact’ that exists in the mind of the general public.”

There was no need to refute the science or even provide alternative explanations for the facts. All that was necessary for the tobacco industry to continue selling cigarettes for decades was to make people question the facts. Often, the questions themselves would be contradictory. For example, when fighting labels showing the dangers of cigarettes, the industry argued both that, “Since everyone knows cigarettes are harmful, there is no need for labels” and, “There is absolutely no scientific evidence that smoking is dangerous.”

This playbook of creating doubt has been used to great effect by (among others) the oil industry to invalidate climate change research, soft drink companies trying to prevent labels on dangerous colors, flavors, or high levels of sugar and by the National Football League to downplay the risks of Chronic traumatic encephalopathy caused by concussions.

To conceal the truth, one doesn’t have to present an alternative truth or refute the facts. It is enough to merely allow for the possibility of doubt.

In this week’s Torah reading, Vaera, we find that doubt in the face of overwhelming evidence was enough to cause many Egyptian deaths.

We know that God hardened Pharaoh’s heart. But that does not explain the behavior of many of his people.

Before the plague of hail, Moses warned the nation to bring all their possessions inside. This was already the seventh plague. You would perhaps expect that the Egyptians would no longer doubt Moses. Yet we read in Exodus 9:18-21:

Behold at about this time tomorrow I will rain down very heavy hail, the like of which has never been before in Egypt from the day it was founded until today. And now, send and gather your cattle and everything you have in the field; all the people and animals that are in the field and not brought into the house – the hail will fall them, and they will die. All those who feared the word of God among Pharaoh’s servants hastened his servants and his cattle into the houses. But those who did not take the word of God to heart abandoned their slaves and their cattle in the field…

Verse 25 tells us what happened to the servants and animals of the skeptics:

And the hail destroyed in all the land of Egypt everything that was in the field, from person to animal.

Surely the evidence was overwhelming by this point. For years I have wondered how anyone could have left people and animals to die in the field despite an explicit warning from Moses and months’ worth of evidence that one plague would be followed by the next.

I think the answer may be due to doubt alluded to in an unusual phrase in the fifth plague.

God sent a plague that killed many of the Egyptians’ animals. Moses specified that “Nothing belonging to the Children of Israel shall die,” (Exodus 9:5).

Sure enough, “All the cattle of Egypt died, but of the cattle of the Children of Israel even one did not die. And Pharaoh sent and behold, none of the cattle of Israel had died, not even one. And Pharaoh hardened his heart and did not send the people,” (Exodus 9:6-7).

Malbim notes that the phrase “Not even one” appears also after the Egyptians were drowned at the Red Sea. Exodus 14:28 states, “There remained not even one.” Yet the Mechilta there interprets the phrase to mean that only one remained – Pharaoh himself. Malbim explains that similarly with the cattle of the Israelites, it means that exactly one cow did die.

Therefore, according to Malbim’s reading of the verse, the Egyptians could have justified their refusal to listen to Moses and bring their animals and servants in from the fields. Everyone would have heard of the one cow that did die in the earlier plague. There was just enough doubt to justify ignoring the warning.

I can just imagine one Egyptian discussing it with his friend:

I know Moses told us that anything left in the field would die, but can we really trust what he says? Last time, he said that none of the Israelite’s cows would die, but I heard from my friend that someone he knows checked and discovered that they were covering up an Israelite cow that did die. Maybe there were more cattle of the Israelites that died that they aren’t telling us about. How can we trust what Moses says? There is anecdotal evidence that he is wrong. Perhaps it is a conspiracy to get us to bring our things inside for some reason.

It was not only the Egyptians who doubted clear evidence. In a couple of weeks we will read the Torah portion of Beshalach. Days after the Israelites had seen the splitting of the Red Sea, eaten the manna that fell from heaven, and experienced untold miracles, they complained that there was no water to drink. Even though God instructed Moses to bring water from a rock, the people began to doubt everything they had been through. They asked, “Is God in our midst or not?” (Exodus 17:7).

Immediately afterwards, the Israelites were attacked by the tribe of Amalek. Even though this nation had also seen the miracles performed for the Israelites and had witnessed the plagues in Egypt, they had enough doubt about the invincibility of the Israelites that they decided to attack.

Even a tiny shred of doubt can undermine bookshelves full of scientific studies, and even the evidence of our own eyes.

I guess the past couple of years have shown me how convincing doubt can be. Our brains aren’t very good at dealing with large data samples or evidence that cannot be easily understood. We tend to trust things we hear from our friends and family more than things we are told by so-called experts. We are skeptical of anything that doesn’t fit neatly into our worldview. Often, there is no amount of evidence that can outweigh a single possible doubt.

This year, for the first time, I understand the Egyptian who saw that one cow survived and believed it contradicted Moses’s words. The thousands of living cows were meaningless because there was a tiny shred of doubt caused by the single dead cow.

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