Priors in medecine

Context

Why is is so hard to agree on the efficiency of a cure for an ill patient ?

I would argue here that this is caused by disagrement on about each one perceives the patient condition.

First and foremost, a deviation

Let's take a slight deviation to some subsets of mathematics, called statistics and probability theory.

The statistics is the science dedicated to measure the prevalence of an event, and of its relations to other events, inside the universe of "past measurable events".

The probability theories explore how one can estimate the occurence of an event in the future. They work within a universe of "possible events".

Statistics and probabilities are often linked through a probability theory.

Frequentist or Bayesian

Two main probability theories are common, they both express probabilities between 0 ("not possible at all") and 1 ("fully certain"), but ascribe different meanings.

The frequentist theory poses that the only "possible events" are events whch were already measured in the past.

For instance, if a dice has rolled only 6s for eight rolls, there is only one possible outcome in the frequentist probability theory for a future roll, which is a 6, so the frequentist probability of rolling a 6 is 1.

On the other end, the bayesian probability is not interested directly in measure events, but on "natural causes". A 6 face dice perfectly balanced has "a natural probability of rolling a 6" of 1/6. This natural probability is called a prior.

Interesting enough, if the number of rolls is large, the probabilities in both models converge to the same value, called the expected value : the more rolls you observe, the more precise will be your prior, and the more precise your frequentist probability.

Convergence on large population, divergence at small scale

However, this only applies for a large number of measured past events, and not for each individual event. This fact is hopefully well known for all gamblers amongst you, and depending if you are more inclined towards the frequentist , after our eight rolls, you will bet big on the next roll being a 6, whereas if you are a bayesian player, you wouldn't bet much, and probably begin to suspect that the "fair" dice might be not so fair...

Back to medecine

So when one has to evaluate the relevance of a cure, they only get at best the probability measured in a statistically way. For the frequentist practitioner, this is the true probability, and should be used for decision. However the true probability would only be meaningful if we were talking about exactly the "same event" ; aggregating a cure given to different people into "a same cure" is probably dubious at best, because every patient had different circumstances (general immunity health, gene expressions...). The frequentist approach is probably not the best approach for an MD.

On the other hand, for the bayesian practitioner, it is at best one element influencing their own estimation of the prior, the other elements being their perception of the prevalence of the disease in the general population, and their own biases based on when and how they have been taught medecine, and all the consensus slowly formed by experimenting. One can see that the bayesian approach might be here more relevant, as it somehow integrates the "causal factors" of a disease propagation. However, at the extreme, if a bayesian practitioner does not known about an emerging disease, which becomes heavily prevalent, then, they will be biased against curing it...