InGaN-based light-emitting diodes (LEDs) exhibit a significant efficiency loss (droop) when operating at high injected carrier densities, the origin of which remains an open issue. Using atomistic first-principles calculations, we show that this efficiency droop is caused by indirect Auger recombination, mediated by electron-phonon coupling and alloy scattering. By identifying the origin of the droop, our results provide a guide to addressing the efficiency issues in nitride LEDs and the development of efficient solid-state lighting.