Abstract
BackgroundJoint 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.MethodsWe 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.ResultsWe 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.ConclusionsThe 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.
Highlights
Joint models (JM) have emerged as a promising statistical framework to concurrently analyse survival data and multiple longitudinal responses
It was considered that a value of NTX3 is elevated if it is larger than 100 nmol Bone collagen equivalents (BCE)/mmol creatinine and of NTX12 if it is larger than 64 nmol BCE/mmol creatinine
We extend this analysis to all types of cancer present in the cohort and we will include the whole N-telopeptide of type I collagen (NTX) time series function, and isolated time points, in order to evaluate the predictive accuracy of this biomarker
Summary
Joint models (JM) have emerged as a promising statistical framework to concurrently analyse survival data and multiple longitudinal responses This is relevant in clinical studies where the goal is to estimate the association between time-to-event data and the biomarkers evolution. Longitudinal studies are often conducted to investigate disease evolution, to assess the effect of certain interventions (e.g. drugs or surgery), or to explore the association between certain risk factors and a clinical outcome In these follow-up studies it is relevant to analyse the time until an event of interest occurs, such as death or disease relapse, and investigate the association between patient’s characteristic and the outcome In this context, survival analysis provides a statistical framework to analyse this type of data, through e.g. the estimation. Using features that do not fulfil both of these requirements usually leads to bias on the results [4]
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