Huntsville, Texas - Barring a successful last-minute appeal, Texas will execute an autistic man this week whose murder conviction was based on what his lawyers say was a misdiagnosis of "shaken baby syndrome."

Robert Roberson (57) is scheduled to die by lethal injection at the state penitentiary in Huntsville on Thursday for the February 2002 death of his two-year-old daughter, Nikki.

Roberson's case has drawn the attention of the Innocence Project, which works to reverse wrongful convictions, best-selling novelist John Grisham, Texas lawmakers, and medical experts.

Also among those seeking to halt Roberson's execution is the man who put him behind bars – Brian Wharton, the former chief detective in the town of Palestine.

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"Knowing everything that I know now, I am firmly convinced that Robert is an innocent man," Wharton said at a recent press conference organized by Roberson's supporters. "The system failed Robert."

Grisham, author of the legal thrillers The Firm and A Time to Kill, also appeared at the event and said cases such as Roberson's "keep me awake at night."

"When you get into wrongful convictions, you realize how many innocent people are in prison," said Grisham, a former attorney.

"What's amazing about Robert's case is that there was no crime," added Grisham, a member of the board of the Innocence Project, which has helped free more than 250 innocent people from US prisons since it was founded in 1992.

Roberson's lawyers say the diagnosis of shaken baby syndrome, made at the hospital where his chronically ill daughter died, was erroneous and the cause of death was in fact pneumonia, aggravated when doctors prescribed a wrong medication.

Wharton, the former detective who is now a Methodist minister, said the conclusion by a hospital doctor that the toddler had died after being violently shaken "led the investigation from that point forward, to the exclusion of all other possibilities."

According to his lawyers, Roberson would be the first person executed in the US based on a conviction of shaken baby syndrome, which the American Academy of Pediatrics now classifies as abusive head trauma.

"In the two decades that have passed since Mr. Roberson's trial, evidence-based science has roundly debunked the version of the shaken baby syndrome hypothesis that was put before his jury," said Kate Judson of the Center for Integrity in Forensic Sciences.

More than 30 parents and caregivers in 18 states have been exonerated after being wrongfully convicted using "unscientific" shaken baby testimony, Judson said.

Roberson's attorney, Gretchen Sween, said his autism spectrum disorder, which was not diagnosed until 2018, was also not taken into account and contributed to his arrest and conviction.

During the medical crisis involving his daughter, Roberson "shut down, and his external lack of affect was judged as a lack of caring," Sween said.

The Texas Court of Criminal Appeals on Friday denied an emergency motion to stay Roberson's execution and order a new trial.

Another appeal is to be heard by a different state court on Tuesday, and lawyers for Roberson have also asked Texas Governor Greg Abbott and the Texas Board of Pardons and Paroles for clemency.

Citing the "voluminous new scientific evidence" that casts doubt on Roberson's guilt, a bipartisan group of 86 Texas state lawmakers has also urged the parole board and the governor to grant clemency.

There have been 19 executions in the US this year, including the September 24 execution in Missouri of Marcellus Williams, whose case was also championed by the Innocence Project amid serious doubts about his guilt.

The death penalty has been abolished in 23 of 50 states, while six others – Arizona, California, Ohio, Oregon, Pennsylvania, and Tennessee – have moratoriums in place.