Pierre Dybman (dybmapi) wrote,
Pierre Dybman
dybmapi

Statistics and probability, how useful and deceptive they can be for your health

One of the first thing you can find, after you've been diagnosed with a certain type of cancer, is the survival rate at 5 years for your specific type of cancer at your specific stage (0 to IV).

If you find out that the survival rate at 5 years in your case is 69%, what does it mean for you, right now? Surprisingly, not very much...

Of course, it's reassuring to find out that the average survival rate in your specific case is 69%, compared to another type of cancer at the same stage that would have fo instance only 26%. Overall, this means that there are therapies in your case that have demonstrated, over the years, a much better success rate than in the second case.

The sheer number of cancer cases, painstakingly reported in all developed countries, has allowed to build a very reliable statistical image per type of cancer, and per stage for each of them, at the moment of the diagnostic.
You can find more detailed explanation about the statistics, how they're collected and what variables are collected and/or calculated here: http://www.cancerresearchuk.org/health-professional/cancer-statistics/cancer-stats-explained/statistics-terminology-explained


This allows to provide this type of final data, the overall survival rate at five years, after which in most cases you should be off the hook, that is in complete remission. Of course this figure changes over time, better treatments leading to a better survival rate. Which means, if you can hold off for a few more years before you get cancer, you'll be better off; But you're always have better chances with finding a very early cancer (stage 0 or I) now, than finding out you have stage III or IV in a few years, irrespective of the improvements in medicine!


While this survival rate may vary a bit depending ont he country you're in, and the quality of the health care system provided, it gives a good rule of the thumb idea of your chances.
Or does it, really?

This is where we need to move from statistics to probabilities. And this is where Gaussian curves come into play:



As you can see, any statistical series can be broken down as a bell curve, which is defined by its standard deviation or 𝛔

This defines the range of statistical events on which is based the probability of a future event. For instance, there are 68% of chances to be close to the median, that is between one standard deviation below and one standard deviation above the median. In our case, the median is the survival rate at 5 years. but that also means that you have a 50% chance of having a higher chance of survival, and also, unfortunately, a 50% risk of having a lower chance of survival. If the deviation is small, you have two-thirds chances to be very close to the median, but you can also see that, at two standard deviations from he median, you have about 2,5% chances to be much better-off than most people, and symmetrically 2,5 % risks of being much worse than most people in the same case.

And this is where science ends, and you, your body, your fighting spirit and you specific environment conditions come into play.

The only real information that this data gives you, is that, should you be able to live a hundred times (or more), you would in 68 cases survive around 5 years without trouble, but also, in the best 2 or 3 cases, you will live a very long time without any more cancer trouble. But also in 2 or 3 of those lives, you're not going to do very well. And so on.
But you only have one life, it's here and now, and we're not studying newtonian physics, where gravity or the speed of light is a constant, and you can repeat an experiment 100 times and get the same result each time!

The thing gets more complicated yet, as you can have a statistical phenomenon with a similar median, but with different deviations, such as in the following diagram, where you an see that, the bigger the deviation, the higher the population, and risk, of being below the median.



In social sciences, and in medicine, while mostly everybody's main vital functions are the same, there are more or less significant variances, your body is going to react better or worse to the agression of a tumour, your body is going to react better than expected, or worse, to the standard treatment that, statistically, produces the best overall result for thousands and hundreds of thousands of people.

But you got only this one shot at it, so you better make it right, right now!

This is why some people get much better results than expected (on average), and this is where all the non medical aspects of your life come into play: your overall health before the diagnostic (don't fall ill on a frail body), your personality (glass half-full, half-empty or optimistic/pessimistic), your social environment (happy couple, caring friends, supportive work environment), your financial situation (work and salary, medical coverage, need or not to advance the significant sums involved...).

All this is going to give you a boost, or be a ballast, that will substantially improve your odds, and may allow you to move into the right part of the Gauss curve, where your success rate is going to be much better.


So, buckle up, because "when the going gets tough, the tough get going"!
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