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Joint Modelling of Longitudinal and Survival Data on Breast Cancer

With the primary motivation to contribute to the understanding of the progression of breast cancer, within the Portuguese population, we propose a more complex statistical model assumptions than the traditional analysis.The analysis preformed has as main objective to develop a joint model for longitudinal data (repeated measurements over time of a tumour marker) and survival (time-to- event of interest) of patients with breast cancer, being death from breast cancer the event of interest. The data analysed gathers information on 540 patients, englobing 50 variables, collected from medical records of the Hospital. We conducted a previous independent survival analysis in order to understand what the possible risk factors for death from breast cancer for these patients. Followed by an independent longitudinal analysis of tumour marker Carcinoembryonic antigen (CEA), to identify risk factors related to the increase in its values. For survival analysis we made use of the Cox proportional hazards model and the flexible parametric model Royston-Parmar. Generalized linear mixed effect models were applied to study the longitudinal progression of the tumour marker. After the independent survival and longitudinal analysis, we took into account the expected association between the progression of the tumour marker values with patient?s survival, and as such, we proceeded with a joint modelling of these two processes to infer on the association between them, adopting the methodology of random effects. Results indicate that the longitudinal progression of CEA is significantly associated with the probability of survival of these patients. We also conclude that as the independent analysis returns biased estimates of the parameters, it is necessary to consider the relationship between the two processes when analysing breast cancer data.
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