Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data

Abstract

SummaryIn clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients.

Combining optical coherence tomography with visual field data to rapidly detect disease progression in glaucoma: a diagnostic accuracy study

“…Other approaches, such as the joint modelling of incident VF loss with the rate of change in structural measurements, as suggested by Medeiros et al, 66 and multivariate non-linear mixed-effect methods, with credible intervals for progression in individual patients, may be helpful to provide additional evidence, and non-parametric approaches need to be explored in detail. 123,124 A limitation that is hard to address when evaluating alternative progression criteria in real-world trial data is that the data are censored as a consequence of the progression criterion that were applied in the trialonce a participant is identified as progressing, he or she exits the study and the data series is curtailed. If an alternative progression criterion fails to identify progression in a censored series, it is not possible to know whether that criterion may have identified progression in that participant had the data not been censored.…”

Modelling Survival Events with Longitudinal Covariates Measured with Error

“…To demonstrate the proposed methods we use the primary biliary cirrhosis ( set can be found in Ding and Wang (2008) and Fleming and Harrington (1991).…”

A Kernel Smooth Approach for Joint Modeling of Accelerated Failure Time and Longitudinal Data

“…The extension of the joint model approach can be seen in Henderson, Diggle and Dobson (2000), Wang and Taylor (2001), Brown, Ibrahim, and Degruttola (2005), and Ding and Wang (2008). For insightful information about joint model, we refer to Tsiatis and Davidian (2004), Yu, Law, Taylor, and Sandler (2004), and Hsieh , Tseng, and Wang (2006).…”