Life

Colorectal Cancer and Meat-Eaters

In 2015, the World Health Organisation (WHO) added processed meat to group 1 carcinogens (carcinogenic to humans). It was based on a report published in October 2015 by the International Agency for Research on Cancer (IARC). The list contains, among others, tobacco, gamma rays, benzene, and asbestos!

IARC report scanned through scientific literature and concluded that there was evidence that processed meat could cause cancer in humans. The experts concluded that each 50-gram portion of processed meat eaten daily increases the risk of colorectal cancer by 18%.

Lost in Statistics?

As usual, the media went overboard with the news, some of them to the extent:

“BACON, HAM, SAUSAGES HAVE SAME CANCER RISK AS CIGARETTES: WHO REPORT” (First Post)”

Is it true that processed meat is as dangerous as smoking cigarettes? Are all items on the list have the same risk? Does 18% cancer risk mean 1 in 6 of the meat-eaters die of colorectal cancer?

Absolute and Relative Risks

The above was a classic case of people misinterpreting relative and absolute risks. 18% in the present case represented a relative risk – an increase of risk compared to the risk of getting colorectal cancer among non-processed meat-eaters. To understand relative risk, you first need to know the base or the absolute risk on which it was calculated. And if it is a low base, expect a high percentage for every unit change, like the GDP growth rates of smaller developing economies vs big, well-developed ones.

So, what is the absolute risk or the proportion of patients in the population? As per the American Cancer Society, the lifetime risk of developing colorectal cancer is about 1 in 23 (4.3%) for men and 1 in 25 (4.0%) for women. For simplicity, let’s take 5%; 18% of 5% is 0.009% or about 1 in 100. The bottom line is:

5 in 100 people can get colorectal cancer in the US, and if all of them start eating 50 g of processed meat every day, the risk increases to an additional person!

This also answers the remaining doubt on the group 1 list: Not all carcinogens in the WHO list have the same risk.

IARC Report on Processed Meat

Known Carcinogens: Cancer.org

Carcinogenicity of Processed Meat: The Lancet Oncology

How common is colorectal cancer: cancer.org

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Rational Thinking and Prisoner’s dilemma

The prisoner’s dilemma is a much-discussed subject in game theory. Police arrested two individuals for their involvement in some criminal activities and put them in prison. They have adequate evidence to frame charges and hand them two years of imprisonment but not for a maximum of ten years.

Police approach a prisoner and make an offer in return to testify against the other person. If she betrays the other and the other person remains silent, she can go free. If she keeps quiet and the other person gives evidence against her, she gets the maximum punishment of 10 years. If they both remain silent, the existing term of two years continues. If they both testify against each other, they both get five years.

Imagine A is a rational decision-maker, and she assumes that a similar offer may also have gone to prisoner B. She starts from the point of view of the other person before deciding on her own. Person B has two options: remain silent or betray person A. If B remains silent, A can remain silent (2 years) or cross B (0 years). Betray B is currently the better of the two. If B testifies, A can remain silent (10 years) or betray B (5 years). Betray B is the better one here again. In other words, A has no option but to give evidence against B.

Cooperation vs Competition

Decision-making such as this starts with knowing the potential strategies of the other. Once sorted out, the player will opt for the option that protects her, irrespective of the other’s choice. 

A rational decision may not be the decision that gives the maximum payoff. In the present story, cooperation might appear as that option, where each serves two years in jail. But it was not a cooperative game, where both the parties trust each other and form a joint strategy – to remain silent. Therefore, it is not the optimal option in cases where the players compete against each other.

Cold War and Nuclear Build-Up

The Nuclear build-up between the USSR and the USA during the Cold War period is an example of a prisoner’s dilemma in real life. From the viewpoint of the USA or the USSR, the rational (strategic) option was to pile up more nuclear warheads instead of reducing them, although one has every right to argue that the latter could have been the better choice for humankind.

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Cancer Happens

This one is going to disappoint some of you. What causes cancer? The answer is – life. Cancer happens; well, most of the time!

Primary reasons for cancer in humans are classified into three categories: environmental (E), hereditary (H), and mistakes during DNA replications (R).

Researchers at Johns Hopkins University evaluated cancer incidence in 69 countries and found correlations between cancer risks and these factors. Before going into details, please see the picture that I copied from Tomasetti’s paper (Tomasetti et al., Science. 2017 March 24; 355(6331): 1330–1334. doi:10.1126/science.aaf9011.).

First, a primer on what I meant by the replication factor, R. Approximately three mutations occur every time a stem cell divides. Most of these are inconsequential to us, but occasionally, they cause trouble. What is so special about stem cells? Stem cells are the body’s prime cells that give birth to cells with specialized functions – the blood cells, brain cells, heart muscle cells or bone cells.

Leading environmental factors known to cause cancer in humans include UV from sunlight, tobacco, soot, asbestos, carcinogenic chemicals, and ionising radiation.

Randomness, Again

These results also partly explain the observed stochastic nature of the disease. Remember, “my granny had cancer without smoking, and my uncle still smoking healthy”, all that stuff! Now you know the reasons for the deadly outcome are many – some you know already, some don’t, and perhaps never will.

Not an Either Or

Results from the study also point to the human tendency to rush to wrong conclusions, similar to a deductive fallacy. Environmental reasons are responsible for some cancer types, but it does not mean all cancers are due to Environment. To be precise, two in three are not! Does it mean you ignore environmental factors, smoke, eat tobacco, and give up sunscreen? Quite the opposite. One must continue avoiding exposure to carcinogens as they are the levers to manage those individual probabilities that are within your control, which eventually leads to a reduction in the combined chances of getting the disease (remember the AND rule of probability?). You thus avoided the disease, at least for a while!

The last takeaway of the study, which showed Pearson’s linear correlation of 0.804 between total stem cell divisions and lifetime cancer risk, leads to an unwanted prize for achieving higher life expectancies – the more you live, the more your chance of dying of cancer!

Science. 2015 January 2; 347(6217): PubMed Link

Science. 2017 March 24; 355(6331): PubMed Link

Stem Cells: Mayo Clinic

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Appreciating Stochastic Processes

We all understand deterministic processes, where the outcome of an action is definite and predictable. You touch a hotplate, and it hurts, possibly a blister by the next day! Press the pedal, and the car goes faster. Certainty is nice and visible, a cause and an effect; decision-making is easy. Personal stories reinforce our appreciation for deterministic processes. The brain is wired for determinism.

artificial intelligence, brain, think-3382521.jpg

On the other hand, stochastic processes are not straightforward and require deliberate training to understand. Doctors say smoking causes cancer, yet we don’t see all smokers dying of cancer. To make matters worse, some non-smokers suffer lung cancer!

When Reasons are Many, Output is a Chance

It is the randomness of input that governs stochastic processes. The output becomes a set of probabilities. Be it weather predictions or movements in the stock market. Climate scientists use the best of their physics and thermodynamics to forecast the weather using the available data on wind speed, temperature, humidity, and pressure. Even small uncertainties in those variables can result in large ranges in predictions. Some of them may be random, others we never understand.

Extreme cases are the black swan events. Here, an event has a tiny chance of occurring but creates unimaginable consequences. Is anything better than the COVID-19 pandemic and its impact on the global economy?

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Survivors of Russian Roulette

This post is inspired by the famous book Fooled by Randomness by Nassim Nicholas Taleb.

Imagine a person who wants to play Russian Roulette. It is a game in which the referee (or the executioner?) takes a revolver containing one bullet in one of its six chambers, spins the cylinder, points to the head and pulls the trigger. If you survive, you get a prize – 4 million dollars.

Alive at Age 50

As seen in my previous posts, one can determine the person’s survival chance is 5 in 6 (83%) in one game. This person decides to play this game once a year, starting at age 25. What is the probability that she will become a 100-million-dollar net-worth individual (NWI) by 50? Use the Bernoulli trial that we had discussed in the previous post, and we get a survival chance of about 1% after 25 games [25C25 (5/6)25(1/6)0]. The odds to earn 100 million this way are, indeed, small; no two opinions but to acknowledge her exceptional luck!

Let me complicate the plot: imagine 1000 individuals started playing this game in different parts of the world (different venues, referees, different TV sponsors!). There is a definite possibility of about ten winners (give or take a few) after the 25th season of this deadly game.

A Superhero is Born

Suddenly, these superstars are on the covers of Fortune, in popular TV shows, and parents of young children start pressuring their kids to learn this game. Spiritual gurus proclaim their remarkable moral habits; TV anchors interview their grandmothers; data analysts flood YouTube, fitting their BMI to eating habits to academics with their achievements. Ladies and gentlemen, I am presenting you this evening: the superhero of all fallacies, the Survivorship Bias. It is a selection bias in which reasoning is made by considering only the survivors’ data and not those that have already ceased to exist.

Survivorship bias exists everywhere, far more than what you think. The superstars of the stock market were Taleb’s favourite example. Consistent longer-term performances of fund managers have been the subject of many studies. More often than not, they were no better than Roulette gamers. Then comes the band of ultra-rich business leaders – risk-takers, college dropouts, lonely, full of grand ideas …

Another example is our obsession with the past. You must have heard about extraordinary claims of how prosperous, healthy and long-living our ancestors used to be when living ‘close to nature’ – all these when the average life expectancy was just in the 20s! Of course, the author who wrote the stories included only those who survived their adolescence AND showed some amazing ‘acts of valour’. Try calculating the joint probability of the following: chance of surviving adolescence x having some remarkable skills x being found by the author x getting the king’s approval to include in the book.

Dice Probability Calculator

Human Life Expectancy PNAS

Mistakes due to Survivorship Bias: BBC

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Monty Hall: You Got Goat

The Monty Hall problem has confused the heck out of people. It is a probability puzzle loosely based on an American game show, Let’s Make a Deal, once hosted by Monty Hall. The problem statement is as follows:

You are in a game show, and the host shows three closed doors behind which there are three objects – one car and two goats. Your task is to guess the correct door and win the car. Once you make the pick, the host opens one of the other two doors and shows you a goat. She now hands in a chance to switch your original choice. Will you stick with your original door or switch to the remaining unopened door?

The correct answer is: you better switch the door, but let’s work out how I arrived at this.

Method 1: Bayes’ Theorem

The equation of life! The equation is pasted below:

Turn that to fit our problem, the chance that my door is correct, provided the host showed me the goat, P(MyDoor|ShowGoat) =

P(ShowGoat|MyDoor) x P(MyDoor) / [ P(ShowGoat|MyDoor) x P(MyDoor) + P(ShowGoat|OtherDoor) x P(OtherDoor)]

P(ShowGoat|MyDoor) = chance of the host showing a goat in that door if my choice is right = 0.5 (or 50% chance to pick one of the remaining doors as both have goats)

P(MyDoor) = prior chance of my door having a car = 0.33 (or 1 in 3, at the beginning of the game, it’s anyone’s pick)

P(ShowGoat|OtherDoor) = 1, (100%, the host has only this option as the other door has the car)

P(OtherDoor) = 0.33 (original chance of the other door having a car)

P(ShowGoat|MyDoor) = (0.5 x 0.33) / [ (0.5 x 0.33) + (1 x 0.33)] = 0.33 (1 in 3 chance)

Now, evaluate the chances that the other door has the car once the host showed me a ‘goat door’. P(OtherDoor|ShowGoat) =

P(ShowGoat|OtherDoor) x P(OtherDoor) / [ P(ShowGoat|OtherDoor) x P(OtherDoor) + P(ShowGoat|MyDoor) x P(MyDoor)]

P(ShowGoat|OtherDoor) = chance of the host showing goat in that room if the other room has a car = 1 (or 100%, she has no other option)

P(OtherDoor) = prior chance of the other room having a car = 0.33 (or 1 in 3 at the beginning of the game)

P(ShowGoat|MyDoor) = 0.5. If my door has the car, the host had a 50% chance of opening that door

P(MyDoor) = 0.33 (my original chance of choosing one door)

P(OtherDoor|ShowGoat) = (1 x 0.33) / [ (1 x 0.33) + (0.5 x 0.33)] = 0.667 (2 in 3 chances)

So, switching doors has double the chance of winning than sticking to the original choice.

Method 2: Argument

In the beginning, you have a 1 in 3 chance of picking a door that has the car. That automatically means a 2 in 3 (67%) chance to find the car outside your door. Initially, that 67% was hiding behind two doors, but the host has helped you narrow that chance by removing one. It’s so simple!

Method 3: Perform Experiments

Still not convinced? Then, you do the actual experiment. There are two ways to experiment: 1) Build three doors, perform hundreds of trials with a partner, and find the average. 2) Perform a Monte Carlo simulation and run the trial a few thousand times. Trust me, I have done the latter using R programming, and the code is here:

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Carbon Inequality

In an ideal world, our activities should result in about 2 tonnes of CO2 emissions per person per year, but in reality, it is 70 tonnes for the top 1% and less than 1 for the bottom 50%

The new Oxfam report starkly reminds us of the global disparity in consumption-based CO2 emissions and how the Paris Effect may impact the low-income 50%. The report presents a collection of data and future realisations, but I will not go through all of them.

In one of my previous posts, I commented about the present total CO2 emissions, around 47 billion tonnes in 2018 (Gt/yr). Oxfam report estimates the consumption-based emission to be about 35 Gt in 2015. The emission rate we need to target for 2030 is 18 GtCO2 to stay on course with the 1.5 oC target. Before we jump into the report details, take a stop for a quick recap of climate targets. 

The global mean temperature has now reached about 1 oC above the pre-industrial level; the world needs to keep its peak to about 1.5 oC to manage catastrophic climate change. In other words, the world can only emit a total of 420 – 580 Gt, as per the IPCC special report (SR 15), which is already three years old! So what remains with us to spend from today is less than 500 billion tonnes (carbon budget). There are different pathways to achieve the goal, and one of them is to cut the emissions by half by 2030 and net-zero emissions by 2050.

Back to the report: today’s total global consumption-based carbon emission is 35 GtCO2 – 17 from the top 10%, 15 from the middle 40% and a mere 3 from the bottom 50%! The per capita emissions are

21 tonnes per person for top 10%

5 tonnes per person for middle 40%

< 1 tonne per person for bottom 50%


Note that the top 10% is already trending at the total target of 2030 (18 GtCO2). The report estimates the expected reduction of the richest and the middle to be about 10%, which is much lower than the 90% and 57% required to reach parity (everyone shares the same per capita emissions).

The Paris Effect and its gaining traction in the developed world can lead to another moral failure of the equity principle. As we have seen in the distribution of COVID-19 vaccines, the morally agnostic twins, capitalism and technology, parented by populism and mistrust, will again fail to support the marginalised. Forcing emission cuts across the board will disproportionately impact the poor and widen the existing wealth and opportunity gaps. There must be additional climate finance, with a fair share from the top emitters, not just countries but also individuals beyond borders, to support the lower and middle-income groups to achieve the climate targets. Innovators, especially from the developing world, should also use this opportunity and focus more on inclusive low-carbon technologies.

IPCC Special Report

Oxfarm Report on Carbon Inequality

Paris Agreement

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The New Study Reveals That

WebMD ran an article in 2008 titled Eating Breakfast May Beat Teen Obesity. The article caused quite a stir in the public domain. The original study, published in Pediatrics, focused on the dietary and weight patterns of 2,216 teenagers over five years (1998-2003) from public schools in Minneapolis-St. Paul, Minnesota. 

Did the study conclude that breakfast is a medicine for teenagers to fight against obesity? At least the title and the opening remarks gave that impression. Before jumping to a conclusion, let us examine the various possibilities.

Cause or a Coincidence?

The first possibility is that it could be a complete coincidence that those who ate breakfast gained less weight. That is an easy remark that one can pass to any such study.

What Other Reasons?

Think about possibilities that can make someone skip breakfast. Maybe she wakes up late and has no time to breakfast before school. This could be because she sleeps long or goes to bed late. What about the eating habits of people who sleep late at night? The late sleepers may pack their meal with more or multiple sets of food.

What about some of them skipping breakfast because they were already obese (for any other reasons) and wished to cut some calories (cause and outcome reversed)?

How important are the study location, socioeconomic background, and education levels? As per the CDC, even in the US, obesity is lower among people with lower and higher income but higher in middle-income groups. What could be the outcome had the research been conducted in India, Australia, The Netherlands, or the Republic of Congo?

Or Just a Correlation?

Would the conclusions have differed if the researchers had examined their lunch, dinner, or snack habits? WebMD leaves some clues.

“A new study shows teenagers who eat breakfast regularly eat a healthier diet and are more physically active throughout their adolescence than those who skip breakfast”.

So it is not just eating breakfast, but a set of other things, or confounding factors, are also important. The first word to notice is regularly, which suggests certain habits. The second one is more physically active, and the third is a healthier diet, which may include more fibre and less fat. We know cutting excessive fat consumption and regular exercise leads to weight loss.

There are many possible explanations to explain this correlation other than a simplistic statement for weight loss. In statistics, these are confounding variables, which happen when a common cause gives out multiple results, leading to the confusion that one of the outcomes is caused by the other.

WebMD Article

Adult Obesity: CDC

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Gambling on a Roulette Wheel

It is critical to decide on the objective of visiting a casino – for fun or to make money. If it’s for fun, you can stop reading this post, go to a casino, and have fun. If it’s for making money, the rest of the post is for you.

Gambling is a business whose objective is to make money – pay off the cost of operations and make some profit. Therefore, it is structured to keep the overall odds in its favour. Since it doesn’t care about the individuals in the process, gamblers have opportunities to have fun, get some money if lucky, etc.

Look at the math and business of the Roulette game:
There are multiple types of bets one can make, and one of them is red-black. You bet 1 dollar on a red; if you get a red, you make a dollar; if black, you lose your money.

Look at the above picture. There are 18 reds in a total of 38 numbers, and your chance to get a red is 18 in 38 (or 18/38). The chance you lose your 1 dollar is 20 in 38 (20/38).

Overall expected profit for you is equal to:
chances of your win x prize you win – chances of your loss x price you lose = (18/38)x(1) – (20/38)x(1) = – 0.0526.

About 5.3 cents per 1 dollar goes to the casino, which is their profit.

Now you change the betting type and say the first 12 for a dozen. In this bet, you will get 2 dollars for every dollar. Your chance of getting in the first 12 is 12/38; for not getting, it is 26/38. If you work out the math, you will get (12/38)x(2) – (26/38)x(1) = – 0.0526.

Take another type that is betting on a single number (straight up). The prize for a win is 35 dollars for every dollar. And the expected returns? (1/38)x(35) – (37/38)x(1). No marks for guessing: 5.3 cents per 1 dollar goes to the casino!

Does that tell you that you will never make money in gambling? You may make money sometimes, and that is where your purpose of visiting makes the difference. If your goal is to make money, you have a problem, as the game is designed for the casino to make money. Or the odds are stacked against you. It is okay if it is for pure fun, as any luck you may get becomes a bonus. It also means that the longer you play, the higher the chance of you losing money as you slowly regress to the mean. The same is true if you place multiple bets simultaneously; it accelerates your chances of reaching the mean, which is biased against you. Since the game never stops, the casino will manage to match their odds in the end.

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SLC24A5 and the Great Human Divide

SLC24A5 is a gene. The gene finds a special place in human cultural discourse because it produces a protein critical to the production of melanin – the great-divider pigment of human skin.

What is an SNIP?

A single nucleotide polymorphism, or SNP, is a variation at a single position in a DNA sequence among individuals. If it occurs in more than 1% of a population, they are an SNP group. If the SNP occurs in a gene (resulting in what is known as alleles), it can have some consequences – rs1426654 is one of them, as we shall see.

A Quick Tour to the Basics

Imagine that the GENOME is a book. There are 23 chapters called CHROMOSOMES. Each chapter contains several thousands of stories, called GENES. Each story is made up of paragraphs, called EXONS, which are interrupted by advertisements called INTRONS. Each paragraph is made up of words called CODONS. Each word is written in letters called BASES. The words are written on long chains of sugar and phosphate called DNA!

– Matt Ridley in “Genome”
gene tree, tree of life, evolution-1490270.jpg

Allele and Us

As we have seen earlier, a gene has more than one allele if an SNP occurs within a gene. Our SLC24A5 gene also has alleles: the original allele that still dominates in the African and East Asian population (and contains the amino acid alanine), and the variant allele dominates in the Europen population (and contains threonine).

Why Me?

Why do ‘the originals’ have an alanine version, and what does it do? To answer the first part of the question, you should know how nature works. It is not that the originals have alanine, but only the alanine-containing humans survived the test of time in that location. The alanine allele triggers pigment production and defends the lower layers of the dermis from cancer-causing ultraviolet light, giving a small but significant additional life expectancy for people carrying this natural sunscreen.

The case with the sun-starved European side is quite the opposite: to fight Vitamin D deficiency, they must capture as much light (UV) as possible, and the pigment melanin is a potentially fatal blocker!

Does This Change Our Attitudes?

Unlikely. The notion that human complexion is only skin deep may be necessary but never a sufficient argument for people to stop distinguishing others based on colour (racism). Irrational as we are, humans will always keep inventing newer tricks to match their fancies and exercise their territorial powers. But this can, at least, refute one such stupid argument, and I will say I did not waste my page!

[1] SNP Definition: Nature

[2] Human Skin Color Gene: Scientific American

[3] SLC24A5: Science

[4] The Light Skin Allele of SLC24A5: Plos

[5] Skin Color for Indian Population: The Hindu

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