The influence of the microstructure geometry of patterned sapphire substrates (PSS) on the light extraction efficiency (LEE) of GaN light-emitting diodes (LEDs) is numerically analyzed. Cone structures of various dimensions are studied, along with dome and mixed microstructures. LEE is found to mainly depend on the microstructure surface slope. LEE rises quickly with slope and flattens out when the slope exceeds 0.6. Scaling down the microstructure has little effect on LEE. Light rays are found to travel longer distances in PSS LEDs, as compared with LEDs grown on a flat substrate. Keeping GaN absorption loss low is important for LEE optimization.