The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. The bootstrap method for estimating the standard error of the kappa statistic in the presence of clustered data is evaluated. Such data arise, for example, in assessing agreement between physicians and their patients regarding their understanding of the physician-patient interaction and discussions. We propose a computationally efficient procedure for generating correlated dichotomous responses for physicians and assigned patients for autologous cartilage tissue implantation, compared with microfracture for treatment of distal femoral cartilage lesions simulation studies. The simulation result demonstrates that the proposed bootstrap method produces better estimate of the standard error and better coverage performance compared to the asymptotic standard error estimate that ignores dependence among patients within physicians with at least a moderately large number of clusters. An example of an application to an autologous cartilage tissue implantation, compared with microfracture for treatment of distal femoral cartilage lesions prevention study is presented. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data.Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time of autologous cartilage tissue implantation, compared with microfracture for treatment of distal femoral cartilage lesions.