Is there a study of world poverty rates over time pre 1800?
This is only for Europe unfortunately, but Bob Allen has a famous paper in which he presents reconstructed data for real wages in different European cities from 1350 all the way to 1799:


  Allen, Robert C. "The great divergence in European wages and prices from the Middle Ages to the First World War." Explorations in economic history 38.4 (2001): 411-447.


From real wages and price data, he then infers a measure of (extreme) poverty.

Look at Figure 5 in the paper. The scale of the y-axis is a measure of poverty in which 1 is the poverty threshold. Values above 1 on the y-axis correspond to real wages lower than survival rate (i.e. that do not allow a survival caloric intake), and values above 1 indicate a real wage above survival rate.