Current research in oncology aims at developing targeted therapies to treat the heterogeneous patient population. Successful development of a targeted therapy requires a biomarker that identifies patients who are most likely to benefit from the treatment. However, most biomarkers are inherently inaccurate. We present a simulation study to examine how the sensitivity and specificity of a single, binary biomarker influences the Cox estimates of hazard ratios in phase II clinical trials. We discuss how the bias introduced by marker inaccuracy impacts the decision of whether to carry a drug forward to a phase III clinical trial. Finally, we propose a bootstrap-based method for reducing the bias of the Cox estimator, in the presence of an inaccurate marker.