correlation causation – Pertinent Observations

Pregnancy, childbirth, correlation, causation and small samples

When you’re pregnant, or just given birth, people think it’s pertinent to give you unsolicited advice. Most of this advice is couches in the garb ob “traditional wisdom” and as you might expect, the older the advisor the higher the likelihood of them proffering such advice.

The interesting thing about this advice is the use of fear. “If you don’t do this you’ll forever remain fat”, some will say. Others will forbid you from eating some thing else because it can “chill the body”.

If you politely listen to such advice the advice will stop. But if you make a counter argument, these “elders” (for the lack of a better word) make what I call the long-term argument. “Now you might think this might all be fine, but don’t tell me I didn’t advice you when you get osteoporosis at the age of 50”, they say.

While most of this advice is well intentioned, the problem with most such advice is that it’s based on evidence from fairly small samples, and are prone to the error of mistaking correlation for causation.

While it is true that it was fairly common to have dozens of children even two generations ago in india, the problem is that most of the advisors would have seen only a small number of babies based on which they form their theories – even with a dozen it’s not large enough to confirm the theory to any decent level of statistical significance.

The other problem is that we haven’t had the culture of scientific temperament and reasoning for long enough in india for people to trust scientific methods and results – people a generation or two older are highly likely to dismiss results that don’t confirm their priors.

And add to this confirmation bias – where cases of people violating “traditional wisdom” and then having some kind of problem are more likely to be noticed rather than those that had issues despite following “traditional wisdom” and you can imagine the level of non-science that can creep into so-called conventional wisdom.
We’re at a hospital that explicitly tries to reverse these pre existing biases (I’m told that at a lactation class yesterday they firmly reinforced why traditional ways of holding babies while breastfeeding are incorrect) and that, in the face of “elders”‘ advice, can lead to potential conflict.

On the one hand we have scientific evidence given by people who you aren’t likely to encounter too many more times in life. On the other you have unscientific “traditional” wisdom that comes with all kinds of logical inconsistencies given by people you encounter on a daily basis.

Given this (im)balance, is there a surprise at all that scientific evidence gets abandoned in favour of adoption and propagation of all the logical inconsistencies?

PS: recently I was cleaning out some old shelves and found a copy of this book called “science, non science and the paranormal”. The book belonged to my father, and it makes me realise now that he was a so-called “rationalist”.

At every opportunity he would encourage me to question things, and not take them at face value. And ever so often he’d say “you are a science student. So how can you accept this without questioning”. This would annoy some of my other relatives to no end (since they would end up having to answer lots of questions by me) but this might also explain why I’m less trusting of “traditional wisdom” than others of my generation.

Half life of pain

Last evening, the obstetrician came over to check on the wife, following the afternoon’s Caesarean section operation. Upon being asked how she was, the wife replied that she’s feeling good, except that she was still in a lot of pain. “In how many days can I expect this pain to subside?”, she asked.

The doctor replied that it was a really hard question to answer, since there was no definite time frame. “All I can tell you is that the pain will go down gradually, so it’s hard to say whether it lasts 5 days or 10 days. Think of this – if you hurt your foot and there’s a blood clot, isn’t the recovery gradual? It’s the same in this case”.

While she was saying this, I was reminded of exponential decay, and started wondering whether post-operative pain (irrespective of the kind of surgery) follows exponential decay, decreasing by a certain percentage each day; and when someone says pain “disappears” after a certain number of days, it means that pain goes below a particular threshold in that time period – and this particular threshold can vary from person to person.

So in that sense, rather than simply telling my wife that the pain will “decrease gradually”, the obstetrician could have been more helpful by saying “the pain will decrease gradually, and will reduce to half in about N days”, and then based on the value of N, my wife could determine, based on her threshold, when her pain would “go”.

Nevertheless, the doctor’s logic (that pain never “disappears discretely”) had me impressed, and I’ve mentioned before on this blog about how I get really impressed with doctors who are logically aware.

Oh, and I must mention that the same obstetrician who operated on my wife yesterday impressed me with her logical reasoning a week ago. My then unborn daughter wasn’t moving too well that day, because of which we were in hospital. My wife was given steroidal injections, and the baby started moving an hour later.

So when we mentioned to the obstetrician that “after you gave the steroids the baby started moving”, she curtly replied “the baby moving has nothing to do with the steroidal injections. The baby moves because the baby moves. It is just a coincidence that it happened after I gave the steroids”.

Doctors and correlation-causation

One of the common cribs about the medical profession is that most doctors don’t have enough grounding in mathematics and statistics (subjects they typically don’t study beyond high school). Given the role of mathematics and statistics in medicine, in terms of gathering evidence, medical testing, etc. the lack of mathematical or statistical knowledge can have serious consequences in terms of interpretation of techniques and symptoms and all that.

In the field of statistics we have this adage that goes that we should “treat the disease and not the symptom”. This is no less true in the medical profession – let’s say that you have a bacterial infection which causes a fever, a poor doctor would diagnose your fever by taking your temperature, assume that it is the fever thanks to which you are sick and give you medication to lower the fever without realising that there is a “third variable” that might be causing both – your fever and your sickness. Thus, your fever might come down and consequently your sickness but both would presently appear.

I’ve had chronic pain in my heels for a few months now. It’s especially severe whenever I put my feet on the ground from a raised position. Someone had told me that it occurs due to calcification near the Achilles Tendon, and I must take medication for that. Having pushed it for a few months now I finally went to see my uncle who is an orthopaedic yesterday (this is the same guy who told me about my Boxer’s Fist).

He promptly diagnosed me with Plantar Fasciitis, and wrote down some medication, and told me what I need to do in order to reduce the pain in my feet. After a short conversation on what else I need to do, and any precautions, and all such, I asked him about the calcification thingy – whether he had ruled out that calcification of the Achilles Tendon was causing this problem.

“I’m sure there will be some calcification”, he said, “and I’m not sending you for an X-ray because I have a very good idea of what it will show and it won’t add much value”. And then he proceeded to explain that calcification is a “result” of plantar fasciitis and not a cause of it. He didn’t use the terms “correlation” or “causation” but he explained that when you suffer from plantar fasciitis you end up with both calcification of your Achilles Tendon and also shooting pain in your heels, especially immediately after waking up. The two are thus related, he said, but neither causes the other, but there is a third factor (fasciitis) that causes both, and that is the one that he is treating me for!

I was doubly impressed with him – first for understanding “information theory” in terms of understanding that the X-ray wouldn’t add much information, and secondly for recognising that there was a third factor and that correlation should not be mistaken for causation. Or perhaps I had a particularly low prior for mathematical and statistical skills of doctors!

Postscript

He refused to charge me a fee, since I’m his nephew. While on my way out I was thinking about it and wondering on what circumstances I would waive my professional fees for my consulting. And I realised it would be hard to do so for anyone! It made me wonder what made my uncle waive his medical fees, while I’m extremely unlikely to do that.

I realised it has to do with the investment. He spent about five to ten minutes with me (perhaps a bit longer), but essentially his marginal cost of treating me was quite low. And this was a marginal cost that he was willing to sacrifice in return for the goodwill he gets for treating the extended family for free. Considering the size of my engagements, though, the marginal cost is usually high and is seldom justified by goodwill!

Moron Astrology

So this morning I was discussing my yesterday’s post on astrology and vector length with good friend and esteemed colleague Baada. Some interesting fundaes came out of it. Since Baada has given up blogging (and he’s newly married now so can’t expect him to blog) I’m presenting the stuff here.

So basically we believe that astrology started off as some kind of multinomial regression. Some of ancestors observed some people, and tried to predict their behaviour based on the position of their stars at the time of their birth. Maybe it started off as some arbit project. Maybe if blogs existed then, we could say that it started off as a funda session leading up to a blog post.

So a bunch of people a few millenia ago started off on this random project to predict behaviour based on position of stars at the time of people’s birth. They used a set of their friends as the calibration data, and used them to fix the parameters. Then they found a bunch of acquaintances who then became the test data. I’m sure that these guys managed to predict behaviour pretty well based on the stars – else the concept wouldn’t have caught on.

Actually it could have gone two ways – either it fit an extraordinary proportion of people in which case it would be successful; or it didn’t fit a large enough proportion of people in which case it would have died out. Our hunch is that there must have been several models of astrology, and that natural selection and success rates picked out one as the winner – none of the other models would have survived since they failed to predict as well on the initial data set.

So Indian astrology as we know it started off as a multinomial regression model and was the winner in a tournament of several such models, and has continued to flourish to this day. Some problem we find with the concept:

correlation-causation: what the initial multinomial regression found is that certain patterns in the position of stars at the time of one’s birth is heavily correlated with one’s behaviour. The mistake that the modelers and their patrons made was the common one of associating correlation with causation. They assumed that the position of stars at one’s birth CAUSED one’s behaviour. They probably didn’t do much of a rigorous analysis to test this out
re-calibration: another problem with the model is that it hasn’t been continuously recalibrated. We continue to use the same parameters as we did several millenia ago. Despite copious quantities of new data points being available, no one has bothered to re-calibrate the model. Times have changed and people have changed but the model hasn’t kept up with either. Now, I think the original information of the model has been lost so no one can recalibrate even if he/she chooses to

Coming back to my earlier post, one can also say that Western astrology is weaker than Indian astrology since the former uses a one-factor regression as against the multinomial regression used by the latter; hence the former is much weaker at predicting.