Doctors and Blackjack

The other night I saw a newly-released movie involving an MIT student who tried to earn enough money for medical school by counting cards in Las Vegas games of Blackjack. (I refuse to mention the movie by name as a penalty for its superfluous use of slow-motion clips of stacks of chips being pushed around the table and cards being turned over one-by-one. The show seemed more like an ad for Las Vegas than anything.) I have no idea how to play Blackjack, but apparently there are a variety of systems (all known as "card counting") in which the player and/or his cohorts can keep track of the high and low cards being played from a deck, and therefore whether or not the remainder of cards in the deck are high or low. At one point in the movie, the rebel-cool Math Teacher (who apparently uses his classtime to talk about math history and throw around talk about basic calculus concepts his class should have learned about in high school) chastises our hero for giving into his emotions and actually gambling and relying on emotion rather than "sticking with the system", which had been proven to work.

It struck me that a somewhat tenuous analogy could be made between Blackjack and our modern healthcare systems. Both can involve ridiculous amounts of money, have people becoming very wealthy or losing the shirts off their backs, are often influenced by superstition, and on a case-by-case basis purely random factors can make all the difference. Now, taking care of very sick patients is actually a complicated process. The number of uncertainties that exists within as complicated of a system as the human body dwarf the number of uncertainties in a deck of cards. What information we can extract about what is actually going on with someone is obtained with more difficulty than flipping a card over. And once enough data points are obtained and we can conclude with some reasonable degree of probability what is going on, there are often numerous treatment points that each have their own nuances and uncertainty at to which is really the most effective and how to maximize that effectiveness. Now, as human beings our minds are comfortable with a few degrees of uncertainty, but when overwhelmed with a large number of variables, we cannot juggle them all simultaneously. In order to integrate the information available to us and act in the face of uncertainty, we have to have some kind of model that pulls it all together. If no existing model seems to adequately explain what we see, we may rely on reflex or some other basis for our actions (questioning the existing models is the job of research, and not something you do on call in the ER at night). We certainly can't just stand there. The patient is asking "What are you going to do, doc?"--the dealer is waiting for your bet. The way I see it, there are 3 ways to :

1. Mechanistic. In medical school, we learn a lot about normal human physiology and the mechanisms of disease. So perhaps we can try to make decisions by looking at the human body as a complex machine. Unfortunately, our understanding of it and the total effects of therapies we use (drugs or radiation or an invasice procedure) are limited, though much less so than even a decade ago. But even when this model is as informed as possible by current medical science, it frequently fails. It usually takes a series of well-controlled clinical trials to correct our intuition on certain matters. (E.g., who would have thought hormone replacement therapy causes cardiovascular events? Doesn't it lower cholesterol? What? Heparin is not

2. Pattern recognition. What have you seen before? What was that triad of symptoms I read about in my textbook? How have you seen other people treat this? How have you treated this in the past.

3. Emotion. A lot of times doctors order tests just so "they don't miss anything", covering themselves from an emotional and legal liability point of view. Or, in the case of an actively dying patient, pushing intervention after intervention, test after test while postponing a discussion with family members about goals of care.

So I guess the message of this post isn't anything new. Evidence-based medicine is the mantra of a new generation of physicians, and yes, most would agree, we should do more of it. However, I think that in order to solve the current healthcare crisis (which is due to an unsustainable rise in cost that enlarges the uninsured portion of our population), we'll have to approach medicine from a systems engineering point of view. Our various models for integrating data are inevitably error-prone, and the complexity of modern medicine calls for systematic checks on a doctors' judgment and actions. No doctor wants more of his personalized patient approach dictated by a cold algorithm or a heavy hand from a third party, but given that healthcare is a resource that will increasingly need to be rationed in some way or another as new technologies and treatments are advanced with marginal benefits in outcomes, we need to learn the wisdom of "stick with [a] system". Stricter institutional definitions of the indications for expensive testing and treatment, greater physician accountability for performance and efficiency, and serious discussions of which marginally beneficial treatments/technologies should be exempted from coverage by insurance/Medicare/Medicaid and therefore allowing for expanded basic coverage are such possibilities. As long as we as a society (including myself) are of the mind that the delivery of medical care should not be dictated solely by the blind but efficient hand of a completely free market, the healthcare industry needs to learn to discipline itself to a system of evidence-based and cost-effective care. Otherwise, we'll lose our money and get beat up by a bunch of goons in the back room of a casino.

Nerd hour

So the last few days have given me the chance to ponder how I'll be managing my money in the future, seeing how I'll be joining the working class in a few months (with sizeable education loans to boot). The question I had was that given a certain amount of extra money every month, how do I optimally distribute it among different investment opportunities and loan obligations with varying interest rates (my first two years of medical school loans were fortunately consolidated at very low rates). To those for whom this answer is obvious, please humor me a bit.

In the most simple scenario, the quantity you want to look at is your net change in wealth over a billing cycle or whatever they call the period over which interest accrues. It can be shown that for billing cycle i, your net wealth during the next cycle is:

W(i+1) = P1(i)* R1 + P2(i)*R2 + P3(i) *R3 + ... + PN(i)*RN + constant(i)

where P and R represent, respectively, payments and (1+r) for different investments or loan balances, with r being the interest rates. If you want, you can vary P from cycle to cycle (that's why I wrote P(i)). The constant takes into account the balances in these different investments and loans and has components growing exponentially as a function of i (increasing for the investments, and decreasing for the loans). What is interesting about this is that as long as your loan payments are at least enough to make sure that the constant factor is not increasing (this can be done by paying off at least the interest on those loans every cycle), then you can be guaranteed to maximize your growth of wealth from cycle to cycle as long as you can maximize the first few terms. Of note, those terms are identical in form to each other regardless of whether they represent interest rates on investments or loans.

The consequence of all this is that if you have a fixed amount of money, you're always better from cycle to cycle to throw it all behind the highest interest rate. This is because the gradient of W(i+1) as a function of payments always points predominantly in the direction of the higher interest rate. When the payments are all contstrained by a limited amount of money, that always leads to setting to the max the one associated with the higher interest rate (again, you need to still pay off accumulating interest on debts). Even if you propagate the process out a thousand times and try to find what would lead to the most wealth at W(1000), optimizing your payments at each cycle along the way would lead to the same conclusion. That may seem like a no-brainer, but I just wanted to check it for myself.