We show that a linear relation exists between the device sensitivity and the quality (Q) factor of a dual-waveguide coupled microring resonator optical biosensor when the optimal conditions are satisfied. We also show that the detection limit depends on the loss coefficient and signal-to-nosie ratio (SNR) of the overall system, rather than the circumference of the ring. For a microring resonator sensor whose Q factor is 20000, the detection limit is found to be about 10^{-7} with 30-dB SNR, which is in good agreement with reported experimental data. These results indicate that loss reduction is the top priority in the design and fabrication of highly sensitive microring resonator optical biosensors.