When Ramiro Gonzales was sentenced to death in 2006 for the rape and murder of a young woman in Texas, it followed the testimony of a psychiatrist who suggested that Mr. Gonzales could very well commit a similar crime in the future if he remained alive.

But nearly two decades later, the psychiatrist, Dr. Edward Gripon, no longer stands by what he told the jury. In a subsequent report, he wrote that he had testified about a statistic that showed a high likelihood that those who commit sexual assaults will reoffend; the statistic turned out to be unfounded, he said, and after meeting with Mr. Gonzales a few years ago, he no longer believed he posed a threat.

The jury that heard Dr. Gripon’s initial testimony concluded that Mr. Gonzales should be sentenced to death, and despite desperate efforts by defense lawyers to highlight the psychiatrist’s new reservations, Mr. Gonzales was scheduled to be executed Wednesday evening by lethal injection.

The case has highlighted the unusual importance that Texas places on the contentious practice of predicting whether a person convicted of a capital crime is likely to be violent again.

Mr. Gonzales, 41, was accused of kidnapping the victim, Bridget Townsend, in 2001 when both of them were 18 years old and then sexually assaulting and killing her, a crime that went unsolved for more than a year. He confessed to the killing after he was sentenced to life in prison for the abduction and rape of another woman.

It was at the sentencing phase of his trial in the killing of Ms. Townsend that the focus turned to how likely it was that Mr. Gonzales would carry out further acts of violence if he were not executed but sentenced to life in prison. Texas is unusual in requiring death penalty juries to make a determination, beyond a reasonable doubt, whether the defendant is likely to be violent in the future and presents “a continuing threat to society.”