Division of Biostatistics, National Jewish Medical and Research Center, and Departments of Preventive Medicine and Biometrics and of Physiology and Biophysics, University of Colorado Health Sciences Center, Denver, Colorado
ABSTRACT
This essay examines the historical significance of two APS classic papers that are freely available online: De Léan A, Munson PJ, and Rodbard D. Simultaneous analysis of families of sigmoidal curves: application to bioassay, radioligand assay, and physiological dose-response curves. Am J Physiol Endocrinol Metab Gastrointest Physiol 235: E97E102, 1978 (http://ajplegacy.physiology.org/cgi/reprint/235/2/E97). Merriam GR and Wachter KW.Algorithms for the study of episodic hormone secretion. Am J Physiol Endocrinol Metab 243: E310E318, 1982 (http://ajplegacy.physiology.org/cgi/reprint/243/4/E310).
There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning,... and where a Mathematical Reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.John Arbuthnot (1692)
THESE CLASSIC PAPERS, written by De Léan (Fig. 1), Munson, and Rodbard (3) (Fig. 2) and by Merriam and Wachter (4), are the Candles investigators now use to shed light on dose-response curves and peaks in hormone pulsations. The illumination provided by these two papers speaks for itself: authors have cited the papers nearly 4,000 times, researchers continue to request the software on which the papers were based, and commercial analytical packages incorporate descendants of the original algorithms.
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In 1966, Rodbard joined the National Institutes of Health (NIH) as a clinical associate in the Endocrinology Branch of the National Cancer Institute where Griff Ross and Mortimer Lipsett encouraged him to pursue mathematical and statistical aspects of bioassays, radioimmunoassays, ligand-binding systems, and other response curves, including sigmoidal dose-response curves. He did. 2
At some point, it dawned on Rodbard that it would be quite useful to analyze not just one response curve but a family of response curves. Why? Because he would be able to answer questions like are the curves identical, or do the curves have the same slope? At first, Rodbard used a generalized, nonlinear, least-squares, curve-fitting program written by Gary Knott to analyze a family of response curves. He recognized, however, that Knott's program would be impracticalperhaps impossiblefor most researchers to use. It was about at this point that De Léan and Munson met up with Rodbard.
De Léan graduated from Université Laval (Quebec, Canada) with an MD (1972) and then a PhD (1976). It was when he began writing his dissertation in endocrinology that De Léan came to appreciate fully the mathematical aspects of biology. This appreciation was likely self-fulfilling: De Léan had loved mathematics for years. As a teenager, he pored over textbooks of matrix algebra, vectorial algebra, and topology. It was later that De Léan learnedlargely on his owncomputer programming languages like APL, PL/1, Fortran, and Basic. With this unique combination of skills, De Léan joined Rodbard's laboratory in 1976 by virtue of a fellowship from the Medical Research Council of Canada.
In 1970, Munson graduated from St. Olaf College (Northfield, MN) after studying mathematics and chemistry. He earned an MA in mathematical logic from the University of Wisconsin-Madison in 1971 and stayed to pursue a PhD in pure mathematics. During his third year of the program, Munson became intrigued with applications of mathematical theory to biological systems, a field known then as biomathematics. It was at this point that Munson realized he was ready to abandon pure mathematics for a more practical field. As it turned out, he was able to do just that: his wife Martha, a demographer, was hired by the National Center for Health Statistics (Washington, DC), and Munson found work analyzing epidemiological studies at the National Cancer Institute. In 1976, when a position in Rodbard's laboratory opened up, Munson pounced. He was thrilled at the chance to do experimental research, and he thought he might learn more biomathematics. Perhaps most of all, he was excited that a mathematician might be able to tell biologists something about biological systems that they could not figure out for themselves. The confluence of De Léan, Munson, and Rodbard was complete.
The components of a user-friendly program that could analyze a family of response curves were soon woven together by De Léan, Munson, and Rodbard. De Léan adapted an iterative Marquardt-Levenberg algorithm from a Fortran subroutine written by Richard Shrager and modified by Henry Feldman. Munson developed SuperBasica synthetic programming languageand a compiler that translated the code into other programming languages. Because the program could estimate all parameters in all curves in some family of dose-response curves, De Léan, Munson, and Rodbard named it AllFit. Once their classic paper (3) was published, De Léan, Munson, and Rodbard distributed AllFit free of charge. It was not long before the statistical principles embodied in AllFit were incorporated in Ligand, an even more popular program that could analyze ligand-binding systems (2, 5).
Today, Andre De Léan is Professor of Pharmacology at the Université de Montréal. Peter Munson is Chief of the Mathematical and Statistical Computing Laboratory for the Center for Information Technology at the National Institutes of Health. David Rodbard is Managing Research Scientist and Managing Director at the American Institutes for Research.
Merriam (Fig. 5) and Wachter (Fig. 6) unbeknownst to themselveslay the cornerstone for their classic paper long before they even knew about peaks in hormone pulsations. Merriam, a freshman, and Wachter, a sophomore, met at Harvard College in the fall of 1965. By coincidence, each had been named a Presidential Scholar his last year of high school in New Jersey. After they graduated from Harvard, Merriam and Wachter roomed together at Trinity College (Cambridge, UK). Merriam studied physics and explored Russian language and literature; Wachter pursued statistics. The foundation for their classic paper was cemented on hiking and climbing sojourns in New England and Scotland.
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Because he had absorbed some of John Tukey's philosophies in exploratory data analysis during a stint at Bell Laboratories (Murray Hill, NJ), Wachter suggested an exploratory approach based on time-series techniques. Merriam and Wachter liked the idea of a formal statistical procedure that could identify peaks in hormone pulsations and that would approximate the visual identifications made by practicing endocrinologists.
Like many collaborators, Merriam and Wachter struggled to overcome the barrier of geographical separation. But they persevered. It must have helped that their collaboration provided an excuse to brainstorm on treks to peaks of the northern Appalachians, the Sierra Nevada, and the Interior Ranges of British Columbia. That the Appalachian Mountain Club and the Scottish Mountaineering Club had developed criteria to identify discrete mountain peaks within an extended ridge line provided Merriam and Wachter with even more inspiration.
Merriam and Wachter christened their program Pulsar because they enjoyed astronomy and because they thought it was a pithy name for a pulse-detection algorithm. The original code for Pulsar was written in Fortran and ran on the DEC-10 mainframe at NIH. With the explosion of computing capabilities in the 1980s, several groups adapted Pulsar to run on different platforms. One branch of the Medical Research Council in Scotland bundled Pulsar with related programs and called the package Munro, a fitting name if ever there was one.3
Today, George Merriam is Professor of Medicine at the University of Washington and Deputy Associate Chief of Staff for Research in the Veterans Affairs Puget Sound Health Care System. Kenneth Wachter is Professor of Statistics and Professor and Chair of the Department of Demography at the University of California at Berkeley. Nearly 40 years after they met at Harvard, Merriam and Wachter remain friends.
These classic papers written by De Léan, Munson, and Rodbard (3) and by Merriam and Wachter (4) embody the happy marriage of statistics to science. It goes without saying that the union of these two disciplines is productive: science flourishes with statistics. For the people involved, the union of these two disciplines is rewarding and sometimes just plain fun. May the continued impact of these classic papers inspire more scientists to collaborate with statisticians!
ACKNOWLEDGMENTS
I thank Andre De Léan, Peter Munson, David Rodbard, George Merriam, and Ken Wachter for sharing some of their personal histories and memories of these classic papers.
FOOTNOTES
Address for reprint requests and other correspondence: D. Curran-Everett, Division of Biostatistics, M222, National Jewish Medical and Research Center, 1400 Jackson St., Denver, CO 80206 (e-mail: EverettD{at}njc.org)
1 A sigmoidal dose-response curve can be written
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3 In 1891, Sir Hugh Munro compiled the first list of Scottish mountains 3,000 ft. and higher. The compilation continues as Munro's Tables. Today, each 3,000-ft peak is known as a Munro, and someone who climbs them all becomes a hallowed Munroist.
REFERENCES
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