Statistical methods and designs in clinical oncology

The RECIST criteria 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 non-target lesions, ie. appearance of new lesions and progression of non-target lesions. Despite indisputable advantages of this standard tool, RECIST 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 heterogeneous among patients and model it simultaneously with recurrent events of non-target disease evolution and overall survival. This complex analysis is achievable using multivariate joint frailty models for longitudinal and survival data. We propose a new 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 (ODE) that accounts for the natural growth and treatment induced decline. We perform a simulation study to validate the proposed method and apply the model to a real dataset of a phase III clinical trial for metastatic colorectal cancer. In the results of the analysis, we determine on which component: tumor size, NTL or death, the treatment acts mostly and evaluate the predictive abilities of the components for death. We compare this model with models that consider parametric functions or splines for the SLD trajectory in terms of goodness-oft and predictive accuracy.