Silicon photonics which is compatible with mature complementary metal oxide semiconductor (CMOS) fabrication process has been extensively demonstrated for monolithic integration of photonic and electrical circuits. We show that an integrated silicon Mach-Zehnder modulator (MZM) may be used for advanced modulation formats despite the nonlinear dependence of refractive index change with applied voltage in the free-carrier depletion modulator. We experimentally demonstrated the use of a silicon MZM for direct detection optical orthogonal frequency division multiplexing (DDO-OFDM) modulation with advanced data formats of quadrature phase-shift keying (QPSK), 8 phase-shift keying (8PSK) and 16-quadrature amplitude modulation (16-QAM). The measured bit error rate performance of the back-to-back and 50 km single mode fiber transmission of each format is well below the forward error correction limit.