\chapter{Introduction}
Advanced hepatocellular carcinoma (HCC) is the most common liver cancer that affects people worldwide. It has a poor survival primarly due to the lack of effective treatments for late stage patients, that represent the majority of cases at dignosis. Early detection is critical for this kind of cancer, even a little improvement may result be a significant one in survival rates.

Recent developments in methods for early detection of HCC patients have focused on the analysis of trajectories of multiple biomarkers, assuming for them and in particular for their changepoints a joint model. Longitudinal biomarkers are indeed an essential tool for screening test, because they totally respect desirable characteristics of the test. Indeed, they are non-invasive in order to reduce patients anxiety and clinical costs and they are also inexpensive, to allow a widespread use.

The model proposed here is an innovative extension of the fully Bayesian hierarchical joint model (mFB) outlined in \cite{tayob2018bayesian}. The extension consists in the inclusion of baseline covariates to the model on multiple biomarkers trajectories. The aim of the new proposed method is to find out whether pre-analysis clinical features, in addition to biomarkers levels, are able to improve early detection.

The accuracy of the new screening algorithm has to be evaluated before being applied in a prospective study. Therefore, simulation studies have been conducted to assess whether covariates could catch a variation component of biomarkers trajectories, variation that is not explained in the newest approach in \cite{tayob2018bayesian}. The hepatitis C antiviral long-term treatment against cirrhosis (HALT-C) trial contains valuable information about multiple longitudinal biomarkers in cirrhosis patients, with an extensive follow-up. The HALT-C dataset has indeed been used to evaluate the current screening algorithm once its accuracy has been ensured in the simulation phase.

This work will demonstrate that the new approach has a higher sensitivity than the old approach when covariates play an key role in predicting the biomarkers trajectories (section \ref{beta2}).
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The thesis is organized as follows: in chapter 2 the background is described, in particular there is the description of HALT-C Trial data. In chapter 3 diagnostic tests are explained and their main features are described; in addition a first sketch of the new screening approach is given. In chapter 4 all the elements of the new screening test are outlined, including the joint model for covariates-adjusted multiple biomarkers and the computational procedure implemented to obtain necessary posterior distributions for the computation of the posterior risk of disease. Chapter 5  reports results from multiple scenarios simulation studies. Once the new screening approach has been assessed on simulation studies, it has been applied to real data. Results of applying the new screening approach on the HALT-C Trial are also reported in section 5. Chapter 6 comments the results.