We present a comprehensive model of the dependence of the internal quantum efficiency (IQE) on both the temperature and the carrier density in InGaN-based blue and green light emitting diodes (LEDs). In our model, carriers are dominantly located and recombine both radiatively and nonradiatively inside randomly distributed In-rich areas of the InGaN quantum wells (QWs). In those areas, the carrier density is very high even at a small current density. We propose that the saturated radiative recombination rate is a primary factor determining the IQE droop of InGaNbased LEDs. In typical InGaN-based QWs, it is common for the total carrier recombination rate to be smaller than the carrier injection rate even at a small current density. This is mostly attributable to the saturation of the radiative recombination rate. The saturation of the radiative recombination rate increases carrier density in InGaN QWs, enlarges nonradiative carrier losses, and eventually gives rise to the large IQE droop with increasing current. We show how the radiative recombination rate saturates and the radiative recombination rate has influence on the IQE droop in InGaN-based QW LEDs.