A new study argues that more than 4% of all defendants who have been sentenced to death -- and who remain under threat of execution -- are probably innocent.

In a paper published Monday in the journal PNAS, a team of researchers statistically examined the cases of 7,482 death row convictions from 1973 to 2004.

Using a so-called survival analysis mathematical model, study authors estimated that if all death-sentence defendants remained under sentence of death indefinitely, at least 4.1% would be exonerated.

"The great majority of innocent defendants who are convicted of capital murder in the United States are neither executed nor exonerated," wrote Samuel Gross, a law professor at the University of Michigan Law School, and colleagues. "They are sentenced, or resentenced to prison for life, and then forgotten."By the same token, authors concluded that althoug the number of innocent people who have been executed was "comparatively low," the percentage of innocent people who have had their death sentences commuted to life is even greater.

Specifically, the cases of defendants actively awaiting execution on death row receive the most intense scrutiny of all criminal convictions. Prisoners who have had their sentences reduced to life in prison receive much less scrutiny, authors argued.Gross, whose colleagues included biostatisticians from the American College of Radiology and the University of Pennsylvania Medical School, said the differing rates had to do with the unique workings of the U.S. justice system.

"Courts and executive officials explicitly recognize that it is appropriate to take the possibility of innocence into account in deciding whether to reverse a conviction for procedural error or commute a death sentence to life imprisonment.... As a result, those who are resentenced to punishments less than death are more likely to be innocent than those who remain on death row.""The threat of execution is the engine that drives the process of exonerating innocent death row prisoners, and it is likely that this process becomes more painstaking as inmates approach their execution dates," authors wrote.

In the time period examined, authors wrote that 943 people had been executed, or roughly 13% of the 7,482 death sentences imposed.

By contrast, 117, or roughly 2%, were exonerated. An additional 2,675, or roughly 36% of the total, had their sentences commuted. (The number of people who died on death row but who were not executed was 298, or 4%.)

Study authors wrote that the most charged question regarding capital punishment was how many innocent defendants have been executed.

"We cannot estimate that number directly but we believe it is comparatively low," authors wrote. "If the rate were the same as our estimate for false death sentences, the number of innocents executed in the United States in the past 35 years would be more than 50. We do not believe this has happened.

"Our data and the experience of practitioners in the field both indicate that the criminal justice system goes to far greater lengths to avoid executing innocent defendants than to prevent them from remaining in prison indefinitely."