If you can find a death certificate for Nancy Agnes or one of her siblings that lists parents names, this may be possible. Unfortunately,
mandatory registration in PA did not occur until 1906 -- however, some localities issued death certificates on a regular basis in 1870. Pittsburgh is one of those cities, however, I do not believe
Allegheny City did it until the early 1880s.
Allegheny County followed suit in the 1890s if my memory serves me correctly -- but I cannot swear to it. I have no idea regarding
Beaver County. A second avenue is to find a printed county history that has biographies. Since William John
Sloan was a physician in East Liverpool, OH -- there may be a bio of him in one of the
Columbiana County histories. If so, these generally listed when the family came to the US and the forebeares of the line. Good luck.
Jim