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This study investigates optical properties and carrier dynamics of InGaN-based light-emitting diodes grown on cone-shaped patterned sapphire (CSPS) and planar sapphire substrates. Edge-type threading dislocations were dramatically reduced in InGaN multiple quantum wells (MQWs) on CSPS substrates compared to the case of planar substrates. We observed a smaller Stokes shift and enhanced quantum efficiency for CSPS substrates. From time-resolved optical analysis, we found that the non-radiative (radiative) recombination rate of MQWs on CSPS is lower (higher) than that of MQWs on planar substrates, which is consistent with improved crystal quality (strain relaxation) of the MQWs on CSPS.