Multivariate joint frailty model for the analysis of nonlinear tumor kinetics and dynamic predictions of death.

The Response Evaluation Criteria in Solid Tumors are used as standard guidelines for the clinical evaluation of cancer treatments. The assessment is based on the anatomical tumor burden: change in size of target lesions and evolution of nontarget lesions (NTL). Despite unquestionable advantages of this standard tool, Response Evaluation Criteria in Solid Tumors are subject to some limitations such as categorization of continuous tumor size or negligence of its longitudinal trajectory. In particular, it is of interest to capture its nonlinear shape and model it simultaneously with recurrent progressions of NTL and overall survival. We propose a multivariate nonlinear mechanistic joint frailty model for longitudinal data, recurrent events, and a terminal event. In the model, the tumor size trajectory is described using an ordinary differential equation that accounts for the natural growth and treatment-induced decline. We perform a simulation study to validate the method and apply the model to a phase III clinical trial in colorectal cancer. In the results of the analysis, we determine on which component, tumor size, NTL, or death the treatment acts mostly and perform dynamic predictions of death. We compare the model with other models that consider parametric functions or splines for the tumor size trajectory in terms of goodness of fit and predictive accuracy.