Exponential Growth, Selection Bias and Some Cold Stats: Don't Underestimate COVID19

A forwarded message on our coronavirus-obsessed family group read something like this: “There has been an international overreaction to Coronavirus, entirely in synch (sic) with the polarised world this virus was born into.” The text message attempts to demonstrate this so-called overreaction, by stating that only 5 percent of COVID19 cases actually need hospitalisation; fatality rates in warmer countries have been lower (eh?); and that the flu kills more people every year.

The message just triggered me, and I sent a long reply on how we are not overreacting - on what 5 percent needing hospitalisation translates into for an entirely unprepared healthcare system, and because I’ve just started Neil Degrasse Tyson’s masterclass on scientific thinking, I threw in the phrase “selection bias” a few times.

“We need to be freaked out while protecting the most vulnerable - the poor. We need the government to tell us how they are going to do that. What's their public health strategy that a) gives this the urgency it demands? And b) protects the livelihoods of the most vulnerable while doing so,” I typed out.

I then said that only scientific, medical and public health experts should write on coronaviruses - and although I’m none of the above, I’m triggered and have a lot of quarantine-imposed time on my hands.

There were many statements in today’s ill-timed forward that I’ve heard repeated not just by friends and family, but on television debates and in the op-ed pages of our favourite newspapers.

The message read: “In warmer countries, for some reason that is still not clear, the fatality rate is considerably lower than other places so far, and the overall fatality rate of about 4.5%.” It then attempted to quantify this statement. “Brazil: 2.7%; Malaysia: 1.2%; Thailand: 0.4%; Saudi Arabia: 0.3%; India: 2.3%.”

Hmm - there are a lot of other warm weather countries in the world. It’s still summer in Australia, and COVID19 has had no trouble spreading or killing people there. There are also cold weather countries where numbers remain low. Ever heard of Russia? Anyway, I don’t need to really get into a weather report - because the message debunked its own hypothesis without intending to do so.

“The two outliers are Indonesia and Philippines with 8.4% and 6.7% but experts have stated these figures have emerged due to very low testing in that part of the world; more testing would lower the fatality rates considerably,” it said. But then also added - “Low testing is a big problem in India as well.”

Okay - so if we know that low testing might be the problem in ALL of these countries (and others), how can we rely on this data to make a sweeping statement about warm-weather being less conducive to the spread of the virus? By the way, this is a classic example of selection bias.

Selection bias is a type of cognitive bias, as is confirmation bias - the tendency to interpret information as confirmation of one's existing beliefs or theories. Horoscopes are a classic example of this - but that’s deviating from the pandemic at hand.

Thinking we are special, when we are not, is classic selection bias. And as far as COVID19 is concerned, the ‘we’ is a collective Indian ‘we’ - where our warm weather and good immunity (because you know, Indians live with so many other diseases, so have a hardened immune system), are listed as reasons to explain why the virus hasn’t yet spread.

These arguments are made despite scientists repeatedly saying that there is no evidence to suggest that the virus will wane as temperatures rise. And we choose to focus on our historic exposure to disease rather than the widespread malnourishment and poverty that will - on the contrary - make us more susceptible to disease if the virus were to spread.

We are selecting facts that suit our hypothesis, and leaving out those which do not. This is the exact definition of selection bias. We are not special - the virus will follow the same rules of science and mathematics as it does in the rest of the world, and the key rule here is that of exponential growth.

Let me quote from the whatsapp message again. “Even with limited testing, the average number of new Indian cases is in the region of 100-120 a day; it has been like that for a week. Which means there is absolutely no evidence of exponential community spread till date in India. And that has so far been the case in all of the warm weather countries.”

Every country that now has cases in the thousands and tens of thousands, went through a period of a few hundred cases a day. That’s how exponential growth works. Let me explain.

I’ll give you a choice between two scenarios.

I’ll offer you Rs. 1 lakh every day for 30 days, or Rs. 2 on the first day, to double in value the next day for 30 days.

Which would you choose? I asked this question on my family whatsapp group. Everyone replied choosing the former - heck, you get Rs. 30 lakhs for just sitting quarantined at home. Not too shabby. My brother, though, said - “Rs. 1 lakh per day but I guess the 2 rupees will give more in the end!”

Bingo. Those two rupees, if doubled every day, over the next 30 days will give you - Rs. 1073741824. That’s 107+ crores.

Don’t believe me? Just google 2 raised to the power 30.

This is the law of exponential growth - and it’s actually quite hard for our brain to process how such a small number - those two rupees on the first day - can become such a huge number so quickly.

And that’s exactly the law underpinning the spread of COVID19. That one case doubles very quickly - and before you know it, that one infected person becomes 107 crore infected people. This is because this virus is incredibly infectious. Currently, the R0 for the virus that causes the COVID-19 is estimated at about 2.2, meaning a single infected person will infect about 2.2 others, on average.

This entire social distancing exercise (by the way, I agree with Kancha Ilaiah - we should call it “disease distancing”) is to reduce the rate of exponential growth, thereby reducing the rate of infection and “flattening the curve.”

Those 100 cases a day, dear whatsapp forward, will very quickly become 200 a day, and then 400 a day, and then 800 a day … and so on, as they have in every country in the world that failed to respond early on.

The whole effort to reduce the rate of exponential growth - we can also just rephrase it as reducing the rate of spread - is to not overwhelm our already inadequate healthcare infrastructure.

Again, I’ll quote from the forward.

“The following is the approximate outcome for infected people:
95% infected people need 2 weeks to recover with no medicine, from home.
5% need hospitalisation.
2% need ICU.
1% need ventilator.
So, the vast majority of infected people can just recover by staying at home, with no medicine.”

True - but our entire focus is on the 5 percent who need hospitalisation, the 2 percent who need an ICU, and the 1 percent who need a ventilator.

India is a country of 1.3 billion people, with only 70,000 to 100,000 hospital beds. That’s the number of seriously critical cases the country can handle at any one given time. We’re trying to make sure that the 5 percentage figure being thrown around is always less than 70,000. So that sick people who need hospitalisation, do not have to be turned away.

This is almost certainly too ambitious a goal, and given that there is no known cure or vaccine - it’s inevitable that the virus will outpace our efforts to social distance and curtail its spread. 70,000 beds is just too small a number for such a large population dealing with a novel virus.

By one estimate, the virus could infect 20-60 percent of Indians within a year, of which 4-8 million will be serious cases needing hospitalisation. Just let that figure of 70,000 hospital beds sit with you for a minute. And then think about the number of ventilators we have available - there are some 8000 ventilators in the public sector in the entire country.

Still think we are overreacting?

Let’s be clear: India is still in the early stages of exponential growth. We can slow it to some degree, through lockdowns and curfews and social (disease?) distancing - but those are not definitely not enough. In fact, it will be equally catastrophic to prolong a complete lockdown - leaving people without access to means of livelihood. 

What we need is a public health strategy that doesn’t underplay the urgency and seriousness of the crisis, but at the same time, doesn’t deny the poor and immuno-compromised their livelihood and access to basic resources. We need the government to start talking about and implementing a plan for more hospital beds, doctors and nurses, masks and ventilators. We need to test more. We need a clear and phased public health strategy that puts the poor and marginalised at its centre (this goes beyond small handouts) - and I can’t figure out why no one is talking about that.