MODELLING LONGITUDINAL AND SURVIVAL DATA WITH MULTIPLE BIOMARKERS

Abstract

Background: Existing joint model for longitudinal and survival data captured both types of data, but there is dearth of information about methodologies that captured simultaneously the trajectories of multiple biomarkers over time. This study developed a joint statistical model that captured concurrent trajectories of multiple biomarkers using longitudinal and survival data. Data from the Mayo Clinic trial on Primary Biliary Cirrhosis was used to validate the model. The dataset comprised 424 patients that met eligibility criteria, with 312 actively participated in the trial. An additional 112 cases that participated not in the trial consented to basic measurements and survival monitoring 

Methods: The joint model was developed by integrating a longitudinal sub-model (longitudinal outcomes over time) and a survival sub-model (the time until a specified event occurs) and compared with Mayor’s models. The longitudinal sub-model was represented by a linear mixed-effects model and the survival sub-model by the Cox proportional hazards model. The two sub models were   connected using a shared random effect to capture the correlation between longitudinal trajectory and event risk.  The model parameters were   estimated using the Expectation-Maximization algorithm and diagnostic checks were carried out to validate the model.

Results: The results revealed consistent trends in serum bilirubin levels, significant differences in serum cholesterol between placebo and D-penicillamine groups, and gender-related disparities in survival outcomes. A 55% observed survival rate highlighted positive health outcomes, while an 8% incidence of liver transplants underscored the complexity of the targeted medical conditions. An even distribution of participants between interventions ensured a fair comparison, emphasizing the efficacy of D-penicillamine while acknowledging the challenging nature of the addressed health conditions. Gender-specific analyses showed significant associations, with females exhibiting a hazard of survival approximately 0.4913 times that of males. 

Conclusion: The survival model identified significant associations between survival time and biochemical measurements with high predictive accuracy. 

Keywords: Statistical Models, longitudinal data, survival data, biomarkers, clinical trial