That’s one reason that, despite the rigorous monitoring of clinical trials, 16 novel medicines were withdrawn from the market from 2000 through 2010, a figure equal to 6 percent of the total approved during the period. The pharmacogenomics of each of us — the way our genes influence our response to drugs — is unique.

HUMAN drug trials are typically divided into three phases. In the first, researchers evaluate the safety of a new experimental compound in a small number of people, determining the best way to deliver it and the optimal dosage. In Phase 2, investigators give the drug to a larger number of patients, continuing to monitor its safety as they assess whether the agent works.

“Works” in this stage is broadly defined. Seeing that the drug has any positive effect at all — say, that it decreases the level of a blood marker associated with a disease — is often enough to move a drug to Phase 3. Even so, most experimental drugs fail before they get to Phase 3.

The few that make it to Phase 3 are then tested for safety and efficacy in hundreds or thousands of patients. This time, the outcomes for those taking the new drug are typically compared head-to-head with outcomes for those getting a placebo or the standard-of-care therapy. Generally, the Food and Drug Administration requires that two “adequate and well-controlled” trials confirm that a drug is safe and effective before it approves it for sale, though the bar can be lower in the case of medicines aimed at life-threatening conditions.

Rigorous statistical tests are done to make sure that the drug’s demonstrated benefit is genuine, not the result of chance. But chance turns out to be a hard thing to rule out. When the measured effects are small — as they are in the vast majority of clinical trials — mere chance is often the difference between whether a drug is deemed to work or not, says John P. A. Ioannidis, a professor of medicine at Stanford.

In a famous 2005 paper published in The Journal of the American Medical Association, Dr. Ioannidis, an authority on statistical analysis, examined nearly four dozen high-profile trials that found a specific medical intervention to be effective. Of the 26 randomized, controlled studies that were followed up by larger trials (examining the same therapy in a bigger pool of patients), the initial finding was wholly contradicted in three cases (12 percent). And in another 6 cases (23 percent), the later trials found the benefit to be less than half of what was first reported.