We study a general class of piecewise Cox models. We discuss the computation of the semi-parametric maximum likelihood estimates (SMLE) of the parameters, with right-censored data, and a simplified algorithm for the maximum partial likelihood estimates (MPLE). Our simulation study suggests that the relative efficiency of the PMLE of the parameter to the SMLE ranges from 96% to 99.9%, but the relative efficiency of the existing estimators of the baseline survival function to the SMLE ranges from 3% to 24%. Thus the SMLE is much better than the existing estinators. To assess the appropriateness of the model assumption, we propose a simple diagnostic plotting method. This method enables us to determine an appropriate cut point. We apply the piecewise Cox model to our cancer research data.