Statistical Analysis of the Association between Bilirubin and Survival in Primary Biliary Cirrhosis



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Primary Biliary Cirrhosis (PBC) is a relatively rare chronic liver disease that mainly affects women. When someone’s immune system attacks the liver, the bile ducts are damaged and accumulated in the liver. Over time, it will lead to fibrosis and cirrhosis of the liver. PBC progresses differently among patients and its severity is indicated by repeated measurements of longitudinal biomarkers. In practice, insights on how biomarkers associate with death risk contribute to better adjustment of personal care and improvement of treatment regimen generally. In this project, we are interested in the association between the biomarker serum bilirubin and overall survival of PBC patients. When the liver fails to excrete bilirubin, high levels of this serum can cause jaundice of the skin, which is a common symptom of cirrhosis. This association is investigated with three different statistical approaches: Cox Proportional Hazards Model, Time-Dependent Cox Model, and Joint Model for Longitudinal and Time-ToEvent Data. For each of the three models, the following procedure is applied: univariate analysis, variable selection, and multivariate analysis. The study data comes from a PBC clinical trial conducted by the Mayo Clinic over 10 years from 1974 to 1984. The hazard ratios estimated from these three models are compared. Intuitively, the difference in the estimated hazard ratios can be explained by the different levels of information considered. The Cox Proportional Hazards model uses the baseline values of bilirubin. The Time-Dependent Cox model uses the current values of bilirubin by accounting for the changes of bilirubin over time. The Joint Model captures the internal progression of bilirubin and measurement errors. For applications where sample size is large and computational resources are available, Joint Models should be used because they reduce potential bias in parameter estimation relative to the other models in survival analysis.



Statistics, Survival Analysis, Biostatistics, Liver Cirrhosis, Longitudinal Analysis