Permission granted by The New England Journal of Medicine, Hunger, S.P. and Mulligan, C.G., Acute Lymphoblastic Leukemia in Children, Volume No.373, Page No. 1542, Copyright © (2015) Massachusetts Medical Society. Reprinted with permission from Massachusetts Medical Society.
I have always been awed by the beauty of Science, of Mathematics, of Physics, and yes, even of Statistics.
In a former blogpost I wrote of a philosopher whom I admired growing up, “Life is Fleeting and Yet Rich”, who wrote my favorite quotation, which, among many other things, applauded the richness of life if you ‘open your eyes to its beauty,’ if you study the world in which you find yourself.
In that sense, equations of physics, Maxwell’s equations of Electromagnetism, Einstein’s of General Relativity, Schrodinger’s Wave Equation of Quantum Mechanics…all have their inherent beauty, much of that beauty revolving about the elegant simplicity and symmetry.
Sometimes the mathematics gets messy, and only a graph will do, as appears above. This is still an important part of Statistics, to display information succinctly.
Graphs such as this can be a critical part of statistical analysis, by depicting in a relatively easy view the benefits of certain decisions. The one above is an update of a previous, similar construct, which convinced me one evening, over forty years ago, to pursue the masochistic discipline of Oncology. The New England Journal of Medicine kindly allowed me to reprint this graph above, simple perhaps, as a single portrait, but overwhelmingly moving as a representation of discipline, integrity, compassion and human endeavour.
I was a young medical student, having changed horses in mid-stream, from the harsh physical black and white reality of Physics and Applied Mathematics, to the soft, fuzzy, subjective realm of Medicine. Precise measurements, strict physical controls, and strong theoretical underpinnings were the grist for the mill in the former. Personal opinion, anecdotal evidence, and group consensus was the fuel for the latter. At times, it was hard for me to make the switch, and I disdained medicine, as a science, because of its lack of mathematical discipline. That was then, or as it had been. What I didn’t know was that it was changing, even as I entered.
The revolution in Physics at the turn of the twentieth century solidified the discipline as a science of precision, of exact answers … even in the context of that probability imbedded in the new quantum mechanics. Even with such famous scientists as Einstein claiming that the Lord does not play dice.
By contrast, the development of the mathematics of survival analysis, of probability distributions used to transform randomness into a shape that could be analyzed and compared, was much younger, was just beginning (even though guided by statistical mechanics and thermodynamics of the century before).
Measuring disease progression, symptom control, even death and dying, proved to be a lot more fuzzy in its precision than measuring weights and times and distances, or even forces and energies. The fuzziness cried out for clarity, and rigidly logical scientists despaired of finding answers they could interpret.
The graph above is beauty in the extreme. These are survival curves of young children with Acute Lymphoblastic Leukemia, spanning almost five decades of systematic research, showing the gradual and unrelenting improvement in survival from a disease that was once a universal killer. And a heartbreaking one at that, a killer of lives of children who did not deserve such a tragedy; a killer of hopes of parents whose biological bonds and instincts, whose basic human love, tortured them in that process of death.
What impressed me so much was the discipline demonstrated by those researchers. Each line of the graph represents several studies and enormous work, which changed only a few therapeutic choices at a time. These incredible people resisted the dreadful temptation to try to ‘hit a home run,’ to knock it out of the park, by doing everything at once … all too often to be destined, had they done so, to having nothing at the end.
One drug at a time, one sequence at a time, slowly and surely, accepting the therapy which was better, discarding the treatment that was worse.
What pressure to cut corners is greater than the peril of an infant and the tears of a mother?
“If one drug is good, surely two drugs are better. If once a week is good, surely once a day is better.” No–they said. One step at a time. They must know which drug works and which ones don’t. They must know which sequence works and which doesn’t. Slow and steady.
Statistics helped them resolve what outcomes were just bad luck, and what results were real: the clever transformation of data which allows confidence in comparing those results to random chance. There is beauty in those equations which brings order to random processes, which converts complicated measurement into probability distributions that can be compared with randomness.
That beauty of form is not easy to see, in those equations. I studied them hard once, immersed myself in them once, and intermittently many times since, but it is hard to keep that understanding. Nevertheless, I know that it is there, and echoes of those equations are reflected in graphs like the one above. Indeed, that beauty of those equations is directly transformed into the beauty of this graph.
That figure, the first figure in Hunger and Mulligan’s article, is a striking and convincing demonstration of the improvement in medicine in this one small and important area. Each time period of two to five years, starting in 1968, shows progressive increase in overall survival. Thousands of patients, thousands of researchers, thousands of man-years of effort.
And incredible discipline.
For that young resident in Internal Medicine who had left his risky but precise home of Theoretical Physics to enter a somewhat comfortable but fuzzy science, as medicine had been up to 1970, the wonder of being able to do both, to treat sometimes messy human beings and their messy illnesses, and to do so with a precision just starting to emulate the physical sciences, well … that was enchanting. I was captivated, permanently.
I was fortunate, too, for it proved to be the age of change for medicine, a change reflected in the words now common to the discipline, “evidence based.” Nobody denies statistics anymore. Nobody gets away without it in medicine anymore. And all learn the beauty of those equations, whether viewed in the mathematics that hovers in the background, or painted by the figures and graphs such as the one above.
There is still a gap between the fuzziness of medicine and the rigidity of mathematics. It was somewhat later in my career that I realized that the Art of Medicine is in bridging that gap.