Shared random-effect models for the joint analysis of longitudinal and time-to-event data: application to the prediction of prostate cancer recurrence

Sène, Mbéry; Bellera, Carine A.; Proust-Lima, Cécile

Journal de la société française de statistique, Tome 155 (2014) no. 1, pp. 134-155.

Dans la dernière décennie, la recherche en modélisation conjointe s’est développée très rapidement dans le domaine des biostatistiques et de la recherche médicale. Ce type de modèles permet d’étudier simultanément un marqueur longitudinal et un temps d’événement corrélés. Parmi eux, les modèles à effets aléatoires partagés, qui définissent un modèle mixte pour le marqueur longitudinal et un modèle de survie pour le temps d’événement incluant les caractéristiques du modèle mixte comme variables explicatives, ont reçu le plus d’attention. En effet, ces modèles étendent naturellement le modèle de survie avec variables explicatives dépendantes du temps et offrent un cadre flexible pour explorer le lien entre le biomarqueur longitudinal et le risque d’événement.

L’objectif de cet article est de passer brièvement en revue la méthodologie du modèle à effets aléatoires partagés et de détailler son implémentation et son évaluation à travers un exemple réel d’étude de progression de cancer de la prostate après une radiothérapie. En particulier, différentes spécifications de la dépendance entre le biomarqueur longitudinal, l’antigène spécifique de la prostate (PSA), et le risque de rechute clinique sont investiguées pour bien comprendre le lien entre la dynamique du PSA et le risque de rechute clinique. Ces différents modèles conjoints sont comparés en termes de qualité d’ajustement et d’adéquation aux hypothèses du modèle conjoint mais aussi en termes de pouvoir prédictif en utilisant la cross-entropie pronostique. En effet, en plus de mieux comprendre le lien entre la dynamique de PSA et le risque de rechute clinique, la perspective dans les études sur le cancer de la prostate est de fournir des outils pronostiques dynamiques de rechute clinique basés sur toute l’histoire du biomarqueur.

In the last decade, joint modeling research has expanded very rapidly in biostatistics and medical research. This type of models enables the simultaneous study of a longitudinal marker and a correlated time-to-event. Among them, the shared random-effect models that define a mixed model for the longitudinal marker and a survival model for the time-to-event including characteristics of the mixed model as covariates received the main interest. Indeed, they extend naturally the survival model with time-dependent covariates and offer a flexible framework to explore the link between a longitudinal biomarker and a risk of event.

The objective of this paper is to briefly review the shared random-effect model methodology and detail its implementation and evaluation through a real example from the study of prostate cancer progression after a radiation therapy. In particular, different specifications of the dependency between the longitudinal biomarker, the prostate-specific antigen (PSA), and the risk of clinical recurrence are investigated to better understand the link between the PSA dynamics and the risk of clinical recurrence. These different joint models are compared in terms of goodness-of-fit and adequation to the joint model assumptions but also in terms of predictive accuracy using the expected prognostic cross-entropy. Indeed, in addition to better understand the link between the PSA dynamics and the risk of clinical recurrence, the perspective in prostate cancer studies is to provide dynamic prognostic tools of clinical recurrence based on the biomarker history.

Keywords: Joint models, Shared random-effect models, Dynamic predictions, Prognostic cross-entropy, Predictive accuracy, Prostate cancer
Mot clés : Modèles conjoints, Modèles à effets aléatoires partagés, Prédictions dynamiques, Cross-entropie pronostique, Pouvoir prédictif, Cancer de la prostate

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