The Curve That Changed the World

Let’s start with a statistic: almost 2,000 citations a year. One paper by Paul Meier, the Ralph and Mary Otis Isham Distinguished Service Professor emeritus of statistics, pharmacological and physiological sciences, medicine, and the college, has been cited more often, by a wide margin, than any other paper in the field. At last count it was the fifth most cited research paper of all time, in any field. With about 34,000 citations to date, Kaplan, E. L., and Meier, P. (1958), “Nonparametric Estimation from Incomplete Observations,” has been cited by another scientific publication about once, on average, for every day of Meier’s long life—he was born in 1924—and still counting.

Sadly, however, that ratio can only increase. Citation counting will continue, but the numbering of days stopped on Sunday, August 7th, when Professor Meier, a world-class statistician who made “extraordinary contributions to statistics and to society,” according to Columbia University – and everyone else – passed away peacefully at his Manhattan home.

The Kaplan-Meier estimator is used ubiquitously in medical studies to estimate and depict the fraction of patients living for a certain amount of time after treatment. This is not as simple as it sounds. Survival curves are complicated by the uncooperative way in which research subjects often behave. Some leave a study part of the way through. Others elect not to die before the study ends. These are known as “censored observations.” The Kaplan-Meier estimate is a simple way to compute the survival curve despite such troublesome behavior.

There was almost a Kaplan estimator and a Meier estimator. Each had submitted a separate manuscript to the Journal of the American Statistical Association, but the editor recommended that their papers be combined into one. It took them four years. “At one place he solved a problem that I couldn’t solve,” Meier later recalled in an interview [pdf]. “Other places I solved problems he couldn’t.” Finally published in 1958, it was only cited 25 times over the next ten years. Then, boosted by statisticians’ increased computing power, it caught on. It has since been applied to data from clinical trials of therapies for every disease from cancer to cardiology to concussion.

Friends and colleagues point out that this was only one of Meier’s fundamental contributions. He published many more studies, was a persistent and outspoken advocate for randomization in clinical studies, helped design some of the 20th Century’s most important clinical trials and trained many of the leaders in the field.

“Paul was a friend and colleague as well as one of the most influential statisticians of an important era,” recalled Stephen Stigler, the current chair of statistics at the University of Chicago. “He left an indelible mark on us, and through his research on the world’s clinic analytical practice. He will be missed and cannot be replaced.”

“I have been so fortunate and privileged to know this truly great, wonderful, helpful, kind man who was always so generous with his skills and wise advice,” said toxoplasmosis expert Rima McLeod, professor of ophthalmology and visual sciences at the University. “He is one of the founding fathers and giants of statistics in the past century. He was at the same time simply a modest, helpful, supportive and warm colleague who only let you know how special he was by the quality and content of what he said and wrote.”

He was key, she added, in the “design, establishment, and implementation of the only randomized clinical trial of treatment of congenital toxoplasmosis. This study established that treatment in the first year of life markedly improves outcomes for many of those with this disease, leading to normal, productive lives rather than significant medical problems. It changed the face of this disease and improved the lives for many persons.”

“His many published works and writings have had a huge influence on the application of statistics to medical research—particularly the design, conduct, and analysis of randomized clinical trials—and in the advancement of evidence-based medicine in general,” wrote Theodore Karrison, research associate at the University and director of the biostatistics lab, who had trained with Meier.

“Paul was the type of person who cared deeply about others and would go out of his way to help people whenever he could, whether it was a student struggling with difficult statistical concepts, an individual coping with an illness, a colleague making a hard career choice, or simply someone who needed help with a thorny administrative problem. I’ve always looked up to Paul as an example of how one should strive to be, both professionally and as a human being.”

Karrison offered a brief summary (further condensed here) of some of Meier’s key contributions:

1954—”On the Theory of the Indicator-Dilution Method for Measurement of Blood Flow and Volume,” provided the mathematical basis for a technique available at that time to measure cardiac output.

1958– The Kaplan-Meier paper describing a novel method for estimating survival rates when some patients have been followed until death but others are still alive.

1960s—Co-authored a number of papers with medical colleagues, including research on cervical and uterine cancer, the risks of hormonal contraceptives and radiation exposure, and outcomes following surgery for breast cancer.

1975—Published “Statistics and Medical Experimentation,” in which he discussed the importance of randomization and other issues in the design of clinical trials, including the inherent ethical issues.

1979—A paper on when to terminate a clinical trial delved further into the question of what constitutes compelling evidence of treatment efficacy and the ethical considerations arising during the accumulation of such evidence.

1980s to 2011–collaborated on numerous clinical trials in the areas of cardiovascular disease, including multicenter studies of cardiovascular death, cancer, and infectious diseases.

As Karrison wrapped it up, Meier made “outstanding contributions to the application of statistical methods to medical research—contributions that have led to the proper and efficient evaluation of new medical therapies, to the betterment of many patients’ lives.”

Meier came to the University of Chicago from Johns Hopkins in 1957 and stayed until 1992, when he left Chicago to head the Division of Biostatistics at Columbia University. He received many awards, such as being named fellow of the American Academy of Arts and Sciences, the Royal Statistical Society, and the John Guggenheim Memorial Foundation, and senior member in the Institute of Medicine of the National Academy of Sciences.

Meier’s last PhD student, Rick Chappell, now a professor of statistics at the University of Wisconsin, gets the last word. At professional meetings, he recalled, Meier “often astonished me by giving comments from the audience which, though spontaneous, displayed a depth of reasoning and perfect eloquence which few others could have matched with any amount of advanced preparation.”

“The last time I saw him,” he added, was at a Society for Clinical Trials meeting accompanied by his daughter Joan. “We were interrupted by yet another colleague asking how he was. (Answer: “Aging!”) Joan, giving kind words or hugs, turned to me and said, “I knew he was famous, but people loved him!”

“Yes,” Chappel said, “we did.”


Kaplan, E., & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations Journal of the American Statistical Association, 53 (282) DOI: 10.2307/2281868

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