Paul Meier, who was among the most influential biostatisticians of his generation and helped bring mathematical rigor to medical research in the years after World War II, died Aug. 7 at his home in Manhattan.

He had suffered a disabling stroke about 10 years ago and died after a series of recent strokes. He was 87.

As a biostatistician, Dr. Meier brought probability theory, data analysis and logic to bear on problems in biology and medicine. In the late 1950s, he co-invented the “Kaplan-Meier estimator” as a way of depicting survival and other important outcomes in medical experiments. It has been used in tens of thousands of scientific studies.

In addition to introducing analytical techniques, he was an early and successful proponent of “randomization” in clinical trials. The idea of assigning subjects in a medical experiment to one treatment or another solely on the basis of chance horrified many physicians.

In developing ways to more easily figure out which treatments worked and which ones didn’t, Dr. Meier “must already have helped save tens of thousands of lives,” said Richard Peto, a leading biostatistician at the University of Oxford in England. “I and hundreds of others use his methods every week in our work.”

Dr. Meier’s claim to fame was the two-dimensional, X- and Y-axis graph that can be found in the New England Journal of Medicine, the Lancet and dozens of other medical journals each week.

The Kaplan-Meier curve is a way of illustrating what happens to a group of subjects over the course of an experiment in which everyone starts in the same state: alive, disease-free, unpregnant, et cetera. If the subjects receive different “interventions” that affect health — say, half are getting an active drug and the other half a placebo — the graph depicts the two subgroups’ experiences as two diverging lines.

The problem that Dr. Meier and his collaborator, Edward L. Kaplan, solved was how to calculate an outcome — such as the chance of surviving five years after a cancer treatment — when not everyone participates in the experiment for the same length of time.

That problem is not uncommon, because clinical trials are time-consuming affairs and it often takes months or years to enroll enough volunteers.

The consequence is that a five-year study of survival after a cancer treatment might have only 50 or 60 percent of its subjects observed for the full five years. The rest are in for less time. Kaplan and Dr. Meier derived a series of equations that allows every patient’s experience — death or survival for whatever length of time observed — to contribute to the ultimate calculation of survival.

“It was a very, very important advance,” said Steven N. Goodman, associate dean for clinical research at Stanford University’s medical school and editor of the journal Clinical Trials. “It seems so elementary now.”

Kaplan, then at the University of California Radiation Laboratory, and Dr. Meier, then at the University of Chicago, published their 24-page paper in the Journal of the American Statistical Association in 1958.

It took a while for the technique to catch on. In the first 10 years after publication, the paper was cited only six times. As of earlier this week, the 1958 paper had been cited in about 34,000 research papers. The technique is now so common, its origin is no longer cited when it’s used in most papers.

An equally important contribution was Dr. Meier’s espousal of randomization as an essential element in clinical trials.

If researchers handpick patients to test a new drug, it’s often difficult to tell whether a good or bad outcome is attributable to it. That’s because individual characteristics of the patients — including age, smoking habits and other illnesses — may be equally responsible for what happens.

However, when patients are randomly assigned to get one treatment or another, those “confounding variables” tend to cancel out, making it easier to detect the real effect — or lack of effect — of the treatment being studied.

“He, perhaps more than any other U.S. statistician, was the one who influenced drug regulatory agencies, and hence clinical researchers, to insist on the central importance of randomized evidence,” Peto said.

Dr. Meier was involved in issues of health policy from early in his career. In 1955, a polio vaccine made by the California pharmaceutical company Cutter Laboratories that inadvertently contained live virus killed 10 people and severely paralyzed 164 others, according to physician Paul Offit’s 2005 history of the incident. Seventy thousand other developed muscle weakness, Offit wrote.

Two years later, Dr. Meier published a scathing paper in the journal Science, “Safety Testing of Poliomyelitis Vaccine,” in which he described deficiencies in the production of vaccines by several companies. His paper was seen as a forthright indictment of federal authorities, pharmaceutical manufacturers and the National Foundation for Infantile Paralysis, which funded the research for a polio vaccine.

“Perhaps the most disturbing element of the entire program has been the disparity between the risks that were known to be involved and the repeated assurances of safety,” he wrote.

Paul Meier was born in Newark, N.J., on July 24, 1924. His father was an industrial chemist and his mother a high school principal.

He graduated in 1945 from Oberlin College in Ohio. He received a master’s degree in mathematical logic in 1947 and a doctorate in statistics in 1951, both from Princeton University.

Dr. Meier taught at Johns Hopkins University for about five years before moving to the University of Chicago in 1957. There he taught in the college, graduate school, law school and medical school.

He made a point of teaching the biostatistics course required of medical students “because he thought it was so important for doctors to understand how to read and evaluate research,” said his daughter, Diane Meier, a physician and palliative care specialist.

He married the former Louise Goldstone in 1948. In addition to his wife and daughter, both of New York, survivors include two other daughters, Karen Meier of San Jose and Joan Meier of Washington; and five grandchildren. An older brother, August, became a noted scholar of black history; he died in 2003.

Kaplan died in 2006 in Corvallis, Ore., after a long career as a mathematics professor at Oregon State University.

Dr. Meier left Chicago in 1992 and moved to New York City, where he was chairman of statistics at Columbia University and of biostatistics at the university’s school of public health. He was frequently consulted on statistical matters by the Food and Drug Administration and the Centers for Disease Control and Prevention.

He played the piano, flute and guitar, and sang folk songs, his daughter said. During his years in Chicago, he enjoyed sailing on Lake Michigan.

About 10 years ago, Dr. Meier suffered a stroke after undergoing a procedure to correct atrial fibrillation, an abnormal heart rhythm. He was left with a difficulty finding words, a problem that eventually forced him to retire from his academic positions.

“After his stroke, he was brave,” Janet Wittes, founder of Statistics Collaborative, a consulting firm in Washington, said in an e-mail. “He still came to meetings, contributed cogent comments and was unafraid to show his limitations.”