Statistics2013 Poster
Kaplan-Meier Estimator
Bo Huang, Ching-Ray Yu and Christy Chuang-Stein
Pfizer Inc.
Statistics Saves Lives
The History of the Kaplan-Meier Estimator
In a paper published in the Journal of the American Statistical
Association in June 1958, Edward Kaplan and Paul Meier put
forth a new, efficient method for estimating patient survival
rates, taking into account the fact that some patients may have
died during a research trial while others will survive beyond the
end of the trial. The method, called the Kaplan-Meier estimator
(also known as the product limit estimator), is based on a
mathematical formula using information from those who have
died and those who have survived to estimate the proportion of
patients alive at any point during the trial. The estimator is
plotted over time. The resulting curve is called the Kaplan-Meier
curve, which is a series of horizontal steps of declining
magnitude that, when a large enough sample is taken,
approaches the true survival function for that population.
The Curve That Changed the World
- John Easton
• Paul Meier, 1924-2011, was the Ralph and Mary Otis Isham Distinguished
Service Professor emeritus of statistics, pharmacological and physiological
sciences, medicine. The 1958 paper has been cited more often, by a wide
margin, than any other paper in the field of statistics. At last count it was
the fifth most cited research paper of all time, in any field. It has been
cited by another scientific publication about once, on average, for every
day of Meier’s long life time.
• The Kaplan-Meier estimator is used ubiquitously in medical studies to
estimate and depict the fraction of patients who are alive at, for example
one year, after the onset of a treatment. Estimating the survival curve is
complicated by the fact that while some patients may still be alive at the
end of a study, others may have dropped out of the study early. The latter
are known as “censored observations” and are typically noted by tick
marks on the estimated K-M curve. The Kaplan-Meier approach estimates
the survival curve in the presence of censored observations
• The concept of K-M estimator is equally applicable to other clinical
endpoints such as the occurrence of a composite endpoint of vascular
death, non-fatal MI and non-fatal stroke.
Edward L. Kaplan and Paul Meier
According to Current Contents (1983), the seminal paper by
Kaplan and Meier began in 1952 when Paul Meier, then at
Johns Hopkins University, encountered Greenwood’s paper on
the duration of cancer. A year later, while at Bell Laboratories,
Kaplan became interested in the lifetimes of vacuum tubes in
the repeaters in telephone cables buried in the ocean. Kaplan
and Meier worked independently and submitted their
respective work to the Journal of American Statistical
Association. The journal encouraged them to submit a joint
paper. Kaplan and Meier spent the next 4 years to resolve
differences in their approaches and published a method that
ultimately became the standard nonparametric approach for
analyzing time to event data with censored observations.
Example 1: KM curves of overall survival of an experimental
drug vs the standard chemotherapy in a randomized phase III
study in patients with advanced melanoma
experimental drug
standard chemotherapy
Source: Marshall, Ribas and Huang, ASCO, 2010
Example 2: KM curve of progression-free survival in a
randomized placebo-controlled phase III trial of sunitinib in
patients with advanced pancreatic neuroendocrine tumors
Source: Raymond et al., NEJM, 2011
Publications and Citations Since 1975
Publications refer to research papers related to the Kaplan-Meier method.
Citations refer to all the medical and statistical papers that cite the 1958
seminal paper
Publications and citations are on different scales in the double-axis
figure
Source: Microsoft academic research
Selected Quotes in Honor of Meier’s Work at His Death in 2011
The KM curve has become the standard tool used by
medical researchers for determining the duration of
survival in thousands of studies, ranging from cancer to
AIDS to cardiovascular disease to diabetes, to name just
a few
-- New York Times (2011)
The KM estimate was a very, very important advance. It
seems so elementary now
-- Washington Post (2011)
Paul Meier’s work and the KM analysis have been
responsible for saving millions of lives
--- The Significance Magazine (2011)
The KM estimator is used ubiquitously in medical studies
to estimate and depict the fraction of patients living for a
certain amount of time after treatment. It has since been
applied to data from clinical trials of therapies for every
disease from cancer to cardiology to concussion
-- Science Life (2011)
Reference
• Kaplan EL, Meier P. Nonparametric estimation from incomplete
observations. J. Amer. Statist. Assn. 53:457–481, 1958.
• Kaplan EL. This week’s citation classic – Kaplan EL & Meier P. Nonparametric
estimation from incomplete observations (J. Amer. Statis. Assn 53: 47-481,
1958). Current Contents. 24: 14, 1983.
• Marshall M, Ribas A and Huang B. Evaluation of baseline serum C-reactive
protein (CRP) and benefit from tremelimumab compared to chemotherapy
in first-line melanoma. J. of Clin. Oncology, 2010 ASCO Annual Meeting
Proceedings. 28: No 15: 2609, 2010.
• Raymond E, Dahan L, Raoul JL, Bang YJ, Borbath I, Lombard-Bohas L, Valle J,
Metrakos P, Smith D, Vinik A, Chen JS, Horsch D, Hammel P, Wiedenmann B,
Van Cutsem E, Patyna S, Lu DR, Blanckmeister C, Chao R and Ruszniewski P.
Sunitinib malate for the treatment of pancreatic neuroendocrine tumors.
NEJM. 364: 501-13, 2011.
Reference (cont’d)
• Hevesi D. Paul Meier, Statistician Who Revolutionized Drug Trials. New
York Times. August 12, 2011
• Brown D. Paul Meier, biostatistician and co-inventor of a famous graph.
The Washington Post. August 10, 2011
• Champkin J. Paul Meier - Statistician who saved millions of lives.
Significance. August, 2011
• Easton J. The Curve That Changed the World. Science Life. August, 2011