A novel adaptive transmission scheme for discrete Fourier transform modulated filter bank based transceivers for underlay cognitive radio is proposed aiming to minimize the secondary user average bit-error rate (BER) for bit-interleaved coded modulation subject to a stochastic chance-based interference constraint. For a given confidence level, exact expressions for the BER are derived based on assumed perfect channel state information on conditionally Gaussian channel coefficients. Simulations are used to evaluate the BER performance. It is shown that the achievable performance gains as compared to a non-adaptive scheme can be substantial depending on the channel statistics and interference levels.