Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time‐to‐Event Data

• Published in: Biometrics Vol. 67; no. 3; pp. 819 - 829
• Main Author: Rizopoulos, Dimitris
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.09.2011; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: Accuracy; Area under the curve; Bayes estimators; BIOMETRIC METHODOLOGY; Biometrics; biometry; Biometry - methods; CD4 Lymphocyte Count; CD4-Positive T-Lymphocytes - pathology; Data analysis; data collection; Datasets; Discrimination; Estimate reliability; Estimators; HIV Infections - blood; HIV Infections - mortality; Human immunodeficiency virus; Humans; Induced substructures; Longitudinal data; Longitudinal Studies; Maximum likelihood estimation; Modeling; patients; prediction; Probability; ROC methodology; Shared parameter model; Standard error; Survival Analysis; Time; Time series; Time-dependent covariates
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2010.01546.x

In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time‐to‐event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time‐to‐event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time‐to‐death using their longitudinal CD4 cell count measurements.