The importance of developing personalized risk prediction estimates has become increasingly evident in recent years. In general, patient populations may be heterogenous and represent a mixture of different unknown subtypes of disease. When the source of this heterogeneity and resulting subtypes of disease are unknown, accurate prediction of survival may be difficult. However, in certain disease settings the onset time of an observable intermediate event may be highly associated with these unknown subtypes of disease and thus may be useful in predicting long term survival. Throughout this dissertation, we examine an approach to incorporate intermediate event information for the prediction of long term survival: the landmark model. In Chapter 1, we use the landmark modeling framework to develop procedures to assess how a patient’s long term survival trajectory may change over time given good intermediate outcome indications along with prognosis based on baseline markers. We propose time-varying accuracy measures to quantify the predictive performance of landmark prediction rules for residual life and provide resampling-based procedures to make inference about such accuracy measures. We illustrate our proposed procedures using a breast cancer dataset. In Chapter 2, we aim to incorporate intermediate event time information for the prediction of survival. We propose a fully non-parametric procedure to incorporate intermediate event information when only a single baseline discrete covariate is available for prediction. When a continuous covariate or multiple covariates are available, we propose to incorporate intermediate event time information using a flexible varying coefficient model. To evaluate the performance of the resulting landmark prediction rule and quantify the information gained by using the intermediate event, we use robust non-parametric procedures. We illustrate these procedures using a dataset of post-dialysis patients with end-stage renal disease. In Chapter 3, we consider improving efficiency by incorporating intermediate event information in a randomized clinical trial setting. We propose a semi-nonparametric two-stage procedure to estimate survival by incorporating intermediate event information observed before the landmark time. In addition, we present a testing procedure using these resulting estimates to test for a difference in survival between two treatment groups. We illustrate these proposed procedures using an AIDS dataset.

Dans les études longitudinales en cancer, une problématique majeure est la description de l’évolution de la maladie d’un patient ou la prédiction de son état futur, à partir de mesures répétées d’un marqueur biologique. La modélisation conjointe permet de répondre à ces objectifs, mais elle a principalement été développée pour l’étude simultanée d’un marqueur longitudinal Gaussien et d’un unique temps d’événement. Afin de caractériser les transitions entre événements successifs qu’un patient peut connaître, nous étendons la méthodologie classique en introduisant un modèle conjoint pour un processus longitudinal Gaussien et un processus multi-états Markovien non homogène. Le modèle suppose que les temps de transition individuels sont indépendants conditionnellement aux covariables incluses. Nous proposons aussi un score test afin de tester cette hypothèse. Ces développements sont appliqués à deux cohortes d’hommes avec un cancer de la prostate localisé traité par radiothérapie. Le modèle permet de quantifier l’impact des dynamiques de l’antigène spécifique de la prostate, et d’autres facteurs pronostiques mesurés à la fin du traitement, sur chaque intensité de transition entre états cliniques prédéfinis. Cette thèse fournit ensuite des outils statistiques et des lignes directrices pour le calcul de prédictions dynamiques individuelles d’événements cliniques, dans le cadre de risques compétitifs. Enfin, un dernier travail amène une réflexion sur la modélisation conjointe de données longitudinales ordinales et de données de survie, avec une technique d’inférence innovante. Ainsi, ce travail introduit des méthodes statistiques adaptées à divers types de données longitudinales et d’histoire d’événements, qui permettent de répondre aux besoins des cliniciens. Des recommandations méthodologiques et des outils logiciels sont associés à chaque développement, pour une utilisation pratique par les communautés clinique et statistique. / In longitudinal studies in cancer, a major problem is the description of the patient’s disease evolution or the prediction of his future state, based on repeated measurements of a biological marker. Joint modelling enables to meet these objectives but it has mainlybeen developed for the simultaneous study of a Gaussian longitudinal marker and a single event time. In order to characterize the transitions between successive events that a patient may experience, we extend the classical methodology by introducing a joint model for a Gaussian longitudinal process and a non-homogeneous Markovian multi-state process. The model assumes that individual transition times are independent conditionally to included covariates. We also propose a score test to assess this assumption. These developments are applied on two cohorts of men with localized prostate cancer treated with radiotherapy. The model quantifies the impact of prostate specific antigen dynamics, and other prognostic factors measured at the end of treatment, on each transition intensity between predefined clinical states. This thesis then provides statistical tools and guidelines for the computation of individual dynamic predictions of clinical events in the context of competitive risks. Finally, a last work leads to a reflection on joint modelling of longitudinal ordinal data and survival data with an innovative inference technique. To conclude, this work introduces statistical methods adapted to various types of longitudinal data and event history data, which meet the needs of clinicians. Methodological recommendations and software tools are associated with each development, for practical use by the clinical and statistical communities.