Background: Joint models (JM) have emerged as a promising statistical framework to concurrently analyse survival data and multiple longitudinal responses. This is particularly relevant in clinical studies where the goal is to estimate the association between time-to-event data and the biomarkers evolution. In the context of oncological data, JM can indeed provide interesting prognostic markers for the event under study and thus support clinical decisions and treatment choices. However, several problems arise when dealing with this type of data, such as the high-dimensionality of the covariates space, the lack of knowledge about the function structure of the time series and the presence of missing data, facts that may hamper the accurate estimation of the JM.
Methods: We propose to apply JM for the analysis of bone metastatic patients and infer the association of their survival with several covariates, in particular the N-Telopeptide of Type I Collagen (NTX) dynamics. This biomarker has been identified as a relevant prognostic factor in patients with metastatic cancer, but only using static information in some specific time points.
Results: We extended this analysis using the full NTX time series for a larger cohort of patients with bone metastasis, and compared the results obtained by the JM and the extended Cox regression model. Imputation based on fuzzy clustering was used to deal with missing values and several functions for NTX evolution were compared, such as rational, exponential and cubic splines.
Conclusions: The JM obtained confirm the association between NTX values and patients' response, attesting the importance of this time series, and additionally provide a deep understanding of the key survival covariates.
Keywords: Bone metastasis; Cancer studies; Fuzzy clustering; Joint models; Longitudinal analysis; Survival analysis.