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Thinking Outside the Box

Blog entry posted by anciendaze, Mar 15, 2014.

Many years ago there was a strange joke going around among aeronautical engineers: "What's bigger than an ox, has square corners, and flies?" After the victims spent a while trying to make sense of this they were told the answer was "a flying ox box." This fit all the stated requirements while failing to satisfy any lingering desire to make sense. A similar dissatisfaction strikes me when confronted with numerical answers to questions about health provided by modern medicine.

Recent experience in attempting to interpret laboratory panels for friends with different medical problems brought this to mind. The convenient intervals always marked on the report form a bounding box which is said to contain all reports from patients indicating health, with those outside the box presumed to be demonstrably ill. The idea that this bounding box in some number of dimensions should have square corners is tantamount to saying there is no interaction at all between the various measures of health. This is implausible on the face of it, but saves a lot of thinking.

A second problem is that these numbers are generally taken to apply to anyone. Thus a 20-year-old with new measurements normal for a 70-year-old is presumed to be just fine, even if previous measurements were different. (This happens regularly to ME/CFS patients experiencing acute onset.) Using mean values plus some variance or standard deviation to define acceptable ranges, irrespective of individual characteristics, would be questionable on a number of grounds. What it does allow is for doctors claiming to be highly-trained experts to collect corresponding compensation for treating generic patients according to printed checklists (the paint-by-numbers approach). This is not to say there are no highly-trained, appropriately-experienced doctors who are exceptionally valuable. It only says that less competent professionals can claim rewards of expert judgment without exercising it. There is some reason to believe these professionals are present in large enough numbers to exert peer pressure on any who march to a different drum.

(My mother was always worried about how well her doctor might have done on specialized subjects in medical school. "Suppose he just scraped by in liver?" This choice struck me as peculiar because her liver was one organ which never gave her trouble.)

I have to admit to a strong prejudice against meaningless numbers, for personal reasons that are sound, but irrelevant here. When I have counted the digits in laboratory reports, I decided they would not only be enough to identify an individual human out of the entire human population of the Earth, but might possibly be enough to identify an individual of any possible sentient species in the entire galaxy, if individual characteristics were considered important. It seems pretty clear that these numbers were generated for some purpose unrelated to individuals. The ideal seems to be reducing the apparent impressive information content down to a single bit which says healthy/ill. There are still problems with this minimal interpretation.

Just how large an effect is likely to be hidden behind those numbers, even temporarily leaving the assumption of random variation unchallenged? I'll give an artificial example based on the idea the true "shape of health" defined by those numbers is a smooth shape like a circle or sphere in n dimensions. The advantage of this artificial problem is that the fraction of the box inside such a n-sphere can be precisely calculated. (It may be coincidence that I am writing this on 3/14/2014, otherwise known as "Pi day".)

In two dimensions the volume is really area and the ratio of areas is Pi/4 = 0.785... This makes the bounding box a crude but acceptable estimate. As the number of dimensions increases the ratio gets worse. By the time you reach 10 dimensions the ratio is (Pi^5)/(120*1024) = 0.00249... Most of the volume is in those damned square corners, the least plausible aspect of the bounding box model.

Do I believe the shape of health is an n-sphere? No, for most quasi-periodic processes the manifold on which the point describing current state moves is some generalization of a torus. There is good reason to believe things like heart rate and breathing are quasi-periodic. Does this favor the bounding box approach? No, the fraction of volume inside the surface of a torus within a bounding box is even smaller than in the case of an n-sphere.

Am I being too stringent in talking about 10 interacting dimensions? You decide. A standard metabolic panel has 15 distinct measures, which are all said to be related to metabolism. Those who have been through a wide range of laboratory tests can produce pages of reports. I won't even try to decide how many dimensions are involved, but don't see any reason to believe it is less than 10. (Perhaps readers can count the measures on their own reports, and come up with better estimates.)

This brings us to the point of asking if all those patients with measures outside the box are considered ill. There is always the distinct possibility the laboratory simply screwed up. Random testing of laboratories has not produced results which engender confidence. (You can also have very peculiar non-pathological circumstances at work in the patient. I recall a bachelor friend who couldn't find anything for breakfast except a can of sardines on the morning before he was admitted to a hospital. This produced albumin levels way out of bounds, and these led to pointed questions about his diet.)

Therefore, the practicing physician is likely to ignore an isolated value slightly out of bounds. If he/she pays attention, he/she will say "we're going to have to watch your X". "Watching readings", in the hope they will return to the bounding box is a common exercise in the practice of medicine. (You might say the bounding box is permeable, but only in one direction. Osmosis?) If repeated tests show readings way out of bounds, the patient will be referred to a specialist, who will demand more tests. This sequence of events will predictably take place in cases of progressive disease, where you can depend on the patient to die if nothing is done. What happens in chronic disease is much less predictable.

For readings only a little out of bounds the most likely result is the above watching and hoping they improve. In the case of particularly confusing organ systems, like the immune system, doctors may well ignore three different out-of-bounds readings, provided they are not too extreme. Seen from the vantage point of patients, these experiences demonstrate that it is probably just as well doctors generally don't try to interpret the numbers on those reports themselves. (Such realistic assessment of the effectiveness of current medical practice could be an unexamined cause of major depressive disorders.)

Now, back to the assumption the variation from mean values is random variation. If this were true it would predict that changes over time would be random walks around the mean value, and this leads to a way to test the hypothesis. If you have a time series of measurements, you mark each time interval with something like +1 or -4 to indicate the change of the measure in that interval. If the time behavior is a random walk, randomly permuting these intervals will not make any significant change in the results. You can't make something already random any more random by mixing things up. Quick tests with variations in heartbeat will show the hypothesis is wrong. There is a definite deterministic component to variation in heartbeat intervals. This is far from an isolated example, though it is especially important.

This brings us into the range of theories of dynamics. In a fully deterministic system with measures of both state and rates of change, like position and momentum in mechanics, the future time behavior can be predicted completely. Think this only applies to fully deterministic systems? Even in cases where there is an unmistakable random variation, the volume of phase space in which future activity will take place is predictable, even if the location within that volume is not. There are actually powerful theorems about this used in classical statistical mechanics. Even in the case of quantum mechanics, where fundamental uncertainty is unavoidable, advanced methods using phase space are common. None of the arguments I've heard convince me dynamical systems theory does not apply to medicine. In cardiology I can even point to some notable successes like implanted defibrillators.

One problem with current medical tests is that they do not get both values of a conjugate pair of variables like position and momentum. They may have a static value like an ion concentration, but not a clue about the rate of change. They may also have a rate, like heart rate, for which there is neither a corresponding static value nor any data on the way it is currently changing. It is pretty clear the measures were deliberately chosen in a way that would eliminate evidence of dynamic changes, because these were hard to interpret. This has the effect of collapsing the phase space down into a configuration space with only half the number of dimensions. For comparison, consider the effect of collapsing an image of a three-dimensional object into two dimensions. This may or may not be possible to interpret, with only one dimension missing. Diagrams of four-dimensional objects projected onto two-dimensions are conundrums for mathematicians, and these still fall short of the confusion created by typical medical measurements. Interpreting the resulting report begins to resemble picking numbers for a lottery.

There was a case in the not-too-distant past where a transplant recipient was found to be infected with rabies. When I mentioned this to one doctor I was told this was so unbelievably improbable it was not surprising it took months to identify the problem and warn other recipients of organs from the same donor. This patient was being carefully monitored, and subjected to repeated laboratory tests during the months before the problem was identified. With such objective data you should not be falling back on guesses based on a priori probabilities. If objective measurements and expert interpretation were not able to quickly identify one of the most lethal diseases known what does this say about those measurements and opinions in less obvious situations?

All this leads to serious questions about the value and interpretation of routine tests which make up a substantial part of the healthcare budget. Perhaps there will come a future time when all these tests will be scrapped as a cost-saving measure, with all patient diagnosis and care beginning in the emergency department.
anciendaze

About the Author

As the name suggests, I am old and dazed. The avatar illustrates my rule of thumb: "Hang on! This ride isn't over."
  1. anciendaze
    In response to one objection to that rabies case as an example, what would have made sense was for early tests to show evidence of infection, and most likely some kind of virus. Evidence the virus was attacking nerves should then narrow the possibilities, with common viruses quickly being ruled out. A delay of weeks to identify a very unexpected problem would be reasonable. In practice, this wasn't the way things worked at all. I'm less concerned with assigning blame for the particular lapse than asking what kind of common laboratory panels and ordinary diagnostic skills would allow such a lapse to slip by without involving gross negligence.

    I'm afraid those numbers on reports serve much the same purpose as earlier explanations of illness: "an excess of yellow bile" (cholera), "an excess of black bile" (melancholia), "bad air" (malaria), "the influence of malign winter stars" (influenza) or "the King's Evil" (scrofula). Pasteur's innovation, "you have some kind of virus", was also easier to pronounce than the previously popular "phthisis" = wasting or "tissick", (though it would never compete with "phthisis florida" = "galloping consumption" for weighty impact on death certificates.)