Lamar Odom's family says his condition is improving after the former NBA star was found unconscious at a Nevada brothel a week ago.

Alvina Alston, publicist for Odom's aunt JaNean Mercer, said Monday that the former reality-TV personality is alert and undergoing testing, but there's no word yet on when he might be released from the hospital.

Mercer said in a statement that Odom is overcoming "insurmountable obstacles" and defying the odds.

The statement says, "Each day Lamar is getting stronger and reaching significant milestones in his recovery."

Odom was found in extremely critical condition at the Love Ranch brothel in Crystal, Nevada, on Oct. 13. The brothel said workers saw him drink alcohol and take supplements sold as "herbal Viagra."

His family, including estranged wife Khloe Kardashian, rushed to Las Vegas to be by his side.

On Saturday, his sister-in-law Kim Kardashian tweeted that he had smiled at her.

Mother-in-law Kris Jenner asked fans to continue to pray for Odom.

The Associated Press contributed to this report.