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A modified ray-tracing model is applied to analyze the dependence of external quantum efficiency and far-field radiation pattern of AlGaInN light-emitting diodes (LEDs) on various device parameters. Considerable increase (about 1.5 times) in the efficiency is predicted for LEDs with highly reflective p-contact as compared to those with the semitransparent p-contact. It is shown that the LED's efficiency degrades with the increasing of the optical loss in AlGaInN epitaxial layers as well as with increasing of the LED chip area. The ways of improving the external efficiency of large-area (and thus, powerful) LEDs are discussed including utilization of a textured (light-scattering) backside of sapphire substrate or a diffusive interface between epitaxial layers and p-contact.