The Allegheny County Medical Examiner's Office said James Edwards, 52, and his 19-year-old daughter, Laurin Edwards, died at the scene, the Pittsburgh Tribune-Review reported.
Charlene Edwards, 51, and the couple's son, Jimmy, 21, were hospitalized in critical condition, the newspaper said. They are expected to survive.
Police said it appears James Edwards went from room to room in the Shaler, Pa., home and shot his wife, son, and daughter before turning the gun on himself. Charlene Edwards called 911 at about 3:10 a.m. to report the shooting.
The family dog also died in the rampage.
"We're in the early stages of the investigation in trying to determine what caused this," Lt. Andrew Schurman was quoted as saying. "It looks like the children were in their respective rooms."
Shaler police did not have any prior reports of domestic problems at the home, the newspaper said.
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