The use of the Joint Models to improve the accuracy of prognostication of death in patients with heart failure and reduced ejection fraction (HFrEF)

The work presented in this thesis has been developed during a scholarship at the Scientific Directorate - Unit of Biostatistics of the Galliera Hospital in Genoa under the supervision of Dr. Matteo Puntoni. This scholarship was partially supported by a grant from Ministry of Health, Italy "Bando Ricerca Finalizzata - Giovani Ricercatori" (Project code: GR-2013-02355479) won by Dr. Puntoni for conducting a cancer research study. The main objective of my research was to apply the Joint Model for longitudinal and survival data to improve the dynamic prediction of cardiovascular diseases in patients undergoing cancer treatment. These patients are usually followed after the start of the therapy with several visits in the course of which different longitudinal data are collected. These data are usually collected and interpreted by clinicians but not in a systematic way. The innovation of my project consisted in a more formal use of these data in a statistical model. The Joint Model is essentially based on the simultaneous modelling of a linear mixed model for longitudinal data and a survival model for the probability of an event. The utility of this model is twofold: on one hand it links the change of a longitudinal measurement to a change in the risk of an event, on the other hand the prediction of survival probabilities using the Joint Model can be updated whenever a new measurement is taken. Unfortunately, the clinical study on cancer therapy for which the project was thought is still ongoing at this moment and the longitudinal data are not available. So, we applied the developed methods based on Joint Model to another dataset with a similar clinical interest. The case of study presented in the Chapter 6 of this thesis is developed after a meeting between Dr. Puntoni and me and Dr. Marco Canepa of the Cardiovascular Disease Unit of the San Martino Hospital in Genoa. The necessity of the last one was to prove that the longitudinal data collected in patients after a heart failure could be used to improve the prognostication of death and, more in general, the patient management and care with a personalized therapy. The last one could be better calibrated by a dynamic update of the prognosis of patients related to a better analysis of the longitudinal data provided during each follow-up visit. The Joint Model for longitudinal and survival data solves the problem of the simultaneous analysis of the biomarkers collected at each follow-up visits and the dynamic update of the survival probabilities each time a new measurements are collected (see Chapter 4). The next step, developed in the Chapter 5, was to find a statistical index that was simple to understand and practical for clinicians but also methodologically adequate to assess and prove that the longitudinal data are advantage in the prognostication of death. To do this, two different indexes seemed most suitable: the area under the Receiver Operating Characteristic Curve (AUC-ROC) to assess the prediction capability of the Joint Model, and the Net Reclassification Improvement (NRI) to evaluate the improvement in prognostication in comparison with other approaches commonly used in clinical studies. In Section 5.3, a new definition of time-dependent AUC-ROC and time-dependent NRI in the Joint Model context is given. Even if a function to derive the AUC after a Joint Model was present in literature, we needed to reformulate it and implement in the statistical software R to make it comparable with the index derived after the use of the common survival models, such as the Weibull Model. Regarding the NRI, no indexes are present in the literature. Some methods and functions were developed for binary and survival context but no one for the Joint Model. A new definition of time-dependent NRI is presented in Section 5.3.2 and used to compare the common Weibull survival model and the Joint Model. This thesis is divided in 6 chapters. Chapters 1 and 2 are preparatory to the introduction of the Joint Model in Chapter 3. In particular, Chapter 1 is an introduction to the analysis of longitudinal data with the use of Linear Mixed Models while Chapter 2 presents concepts and models used in the thesis from survival analysis. In Chapter 3 the elements introduced in the first two chapters are joined to defined the Joint Model for longitudinal and survival data following the approach proposed by Rizopoulos (2012). Chapter 4 introduces the main ideas behind dynamic prediction in the Joint Model context. In Chapter 5 relevant notions of prediction capability are introduced in relation to the indexes AUC and NRI. Initially, these two indexes are presented in relation to a binary outcome. Then, it is shown how they change when the outcome is the time to an event of interest. Ending, the definitions of time-dependent AUC and NRI are formulated in the Joint Model context. The case of study is presented in the Chapter 6 along with strength and limitations related to the use of the Joint Model in clinical studies.