Progressive familial intrahepatic cholestasis (PFIC) is a group of rare, inherited liver diseases that affect children and are characterised by impaired bile flow. Since PFIC is a paediatric ultra-rare disease, conducting randomised controlled trials is particularly challenging, making observational data essential for improving clinical management. This thesis analyses a large multinational observational retrospective data cohort with long-term follow-up of PFIC patients. The aim is to improve our understanding of PFIC and support more informed decision-making in patient care through the investigation of two key aspects of disease monitoring and progression. First, the thesis explores longitudinal trajectories of relevant biochemical parameters, serum bile acid levels and platelet counts, in patients with a specific subtype of PFIC, PFIC2, using latent class linear mixed models. This approach effectively identified distinct longitudinal patterns of serum bile acids and platelet counts in patients with PFIC2. These patterns highlight significant heterogeneity in the progression of laboratory parameters over time. Second, a comparative analysis of event-free survival is conducted between two European regional cohorts of PFIC patients, North-West Europe and South-Central Europe. Hypothesising that there are no differences in event-free survival of PFIC patients despite different care settings. This is achieved through a weighted survival analysis combining inverse probability treatment weighting with the Kaplan-Meier estimator and the Cox proportional hazards model. The results suggest there are no significant regional differences in event-free survival among PFIC2 patients between the two cohorts. Furthermore, a sensitivity analysis and permutation test have been performed, which also support this result. Together, these findings contribute to a more detailed understanding of disease progression in PFIC patients and provide practical tools and insights that can inform patient monitoring and clinical decision-making in the absence of randomised trials.

Latent profile analysis is a statistical modeling approach used to identify hidden subpopulations (i.e., latent profiles) within a population. These latent profiles are identified based on values of observed continuous variables, also known as profile indicators. While LPA is getting more popular in education sciences and psychology to group people based on similar characteristics, very little is known about the mathematical formulation. In this thesis, the mathematical foundations of LPA is introduced and explained. This leads to a discussion on the assumptions for the model.
After investigating the mathematical foundations of LPA, we applied LPA to identify different profiles of motivation in a student population at Delft University of Technology. We used a set of survey data measuring four types of motivation (i.e., profile indicators). Results of the analysis showed that there are four different student motivational profiles, each consisting of a different combination of the four types of motivation.