The Kaplan-Meier estimator may not sound as if it is terribly important to most people’s lives. But if you have had a successful treatment for, say, cancer, or for diabetes, or for HIV/AIDS, or for heart disease, or for any one of dozens of other diseases or medical conditions, at any time over roughly the last fifty years, it may be that you owe your life to it and to one of the men who devised it. The statistician Paul Meier died this week. He was 87. It is estimated that his work and his advocacy in medical statistics have been responsible for saving millions of lives.
Hundreds of new and life-saving techniques have come into use over the past decades. Today it is standard that such drugs and treatments are tested by a randomised clinical trial. Some patients are given the new treatment, some are given the old; and the decision as to who gets which treatment is made randomly. That tells us whether the new treatment is better than the old one or not. It is also the only real way of finding out. The randomisation part of it is key; without that, it can give unreliable results.
Yet in the 1950s the usual technique was to give a new treatment to the patients whom it was thought would most benefit from it. It frequently happened that those were the patients whose chances of recovery were the best in any case, under the existing treatments as well as the new one. The result was all too often that new treatments were thought to be better than old ones but in fact were not.
‘When I said “randomize” in breast cancer trials I was looked at with amazement by my clinical colleagues’ said Meier in an interview in 2004. ‘ “Randomize? We know this treatment is better than that one” they said. I said “Not really…” ’ That drugs are now rigorously tested, and that those tests give good and unbiased evidence for or against their effectiveness, is in very large part due to Meier.
Another concern of his was the polio vaccine trial of 1954. The trial involved more than a million children and was the largest medical experiment in history,
‘Perhaps more than any other statistician he was the one who influenced US drug regulatory agencies, and hence clinical researchers, … to insist upon the central importance of randomised evidence’ said Sir Richard Peto, Professor of Medical Statistics and Epidemiology at Oxford, quoted this week in the New York Times. ‘That strategic decision half a century ago has already saved millions of lives, and those millions should be attributed to Paul.’
Meier’s advocacy of – insistence upon – randomised clinical trials was one part of his legacy. The Kaplan-Meier estimator was another. It has many other uses – it can plot anything whose time of survival is of interest, for example fruit before it blemishes, or mechanisms before they break down - but in particular it gives medical statisticians a simple way of comparing patients’ survival rates after different treatments. It has refinements but its basic principle is that the probability of a patient surviving up to the start of a certain time interval is the product of the probabilities of his not dying during each of many previous intervals. A fuller description, by Byron Jones, is in the December 2009 issue of Significance here. As a tool in medical research it is now universal.
Meier’s co-author, Edward Kaplan, died in 2006. Their journal article that introduced the method in 1958 remains one of the most cited research papers in statistics or in any other field, with about 34,000 citations so far. That is a very large number of citations; but the number of lives saved through Meier’s work is even greater.