Answer by taking a quote from the following article:

Tierney was born on November 19, 1920 in Brooklyn, New York, the daughter of Howard Sherwood Tierney and Belle Lavinia Taylor. She was named after a beloved uncle, who died young. She had an elder brother, Howard Sherwood "Butch" Tierney, Jr., and a younger sister, Patricia "Pat" Tierney. Their father was a successful insurance broker of Irish descent, their mother a former physical education instructor.

Tierney had reportedly started smoking after a screening of her first movie to lower her voice, because she felt, "I sound like an angry Minnie Mouse." She subsequently became a heavy smoker. With difficult events in her personal life, Tierney struggled for years with episodes of manic depression. In 1943, she gave birth to a daughter, Daria, who was deaf and mentally disabled, the result of a fan breaking a rubella quarantine and infecting the pregnant Tierney while she volunteered at the Hollywood Canteen. In 1953, she suffered problems with concentration, which affected her film appearances. She dropped out of Mogambo and was replaced by Grace Kelly. While playing Anne Scott in The Left Hand of God (1955), opposite Humphrey Bogart, Tierney became ill. Bogart's sister Frances (known as Pat) had suffered from mental illness, so he showed Tierney great sympathy, feeding her lines during the production and encouraging her to seek help. Tierney consulted a psychiatrist and was admitted to Harkness Pavilion in New York. Later, she went to the Institute of Living in Hartford, Connecticut. After some 27 shock treatments, intended to alleviate severe depression, Tierney fled the facility, but was caught and returned. She later became an outspoken opponent of shock treatment therapy, claiming it had destroyed significant portions of her memory. In late December 1957, Tierney, from her mother's apartment in Manhattan, stepped onto a ledge 14 stories above ground and remained for about 20 minutes in what was considered a suicide attempt. Police were called, and afterwards Tierney's family arranged for her to be admitted to the Menninger Clinic in Topeka, Kansas. The following year, after treatment for depression, she was released. Afterwards, she worked as a sales girl in a local dress shop with hopes of integrating back into society, but she was recognized by a customer, resulting in sensational newspaper headlines. Later in 1958, 20th Century-Fox offered Tierney a lead role in Holiday for Lovers (1959), but the stress upon her proved too great, so only days into production, she dropped out of the film and returned to Menninger for a time.

Did anyone else in her family have similar health problems?
In 1943, she gave birth to a daughter, Daria, who was deaf and mentally disabled,