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: E97–E102, 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: E310–E318, 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.
Why are these recent papers honored as classic papers? Because they transformed the estimation of sigmoidal dose-response curves1 (Fig. 3) and the identification of peaks in hormone pulsations (Fig. 4). Before the publication of these classic papers, most investigators used simple graphic tools and subjective visual techniques; these papers provided objective algorithms that returned reliable estimates and essential statistical results.
As you might expect, it was at different times that De Léan, Munson, and Rodbard embarked on the paths that led them to their classic paper. Rodbard was the trailblazer: in 1960, he graduated from the University of Buffalo, now the State University of New York at Buffalo, with an interdisciplinary major in mathematics and chemistry. In part, his penchant for mathematics and statistics was fanned by his father Simon, a cardiovascular physiologist, who involved him in data analysis, curve fitting, and mathematical modeling while David was in high school, college, and medical school.
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 impractical—perhaps impossible—for 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 learned—largely on his own—computer 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 SuperBasic—a synthetic programming language—and 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 themselves—lay 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.
It was when Merriam assumed an endocrine fellowship at the National Institute of Child Health and Human Development in 1978 that he began to consider how to standardize the identification of peaks in hormone pulsations. Merriam used the pivotal paper of Santen and Bardin (9) to define his objectives: he wanted to incorporate information about noise in the hormone assay, he wanted to incorporate information about the duration of a peak as well as its amplitude, and he wanted to allow for fluctuations in the baseline level of the hormone. Merriam was confident about his objectives, but he was unsure about how to accomplish them. So he called his friend Ken Wachter, who by then was at the University of California at Berkeley.
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!
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.
↵1 A sigmoidal dose-response curve can be written where Y is the response of interest, X is the actual dose of some agent, a is the response at X = 0, d is the response at X = ∞, c is the ED50, and b is a steepness factor.
↵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.
- Copyright © 2005 by American Physiological Society