A Comparison of Joint Models for Longitudinal and Competing Risks Data, with Application to an Epilepsy Drug Randomized Controlled Trial

Abstract

Summary. Joint modelling of longitudinal data and competing risks has grown over the past decade. Despite the recent methodological developments, there are still limited options for fitting these models in standard statistical software programs, which prohibits their adoption by applied biostatisticians. We summarize four published models, each of which has software available for model estimation. Each model features a different hazard function, latent association structure between the submodels, estimation approach and software implementation. Of the four models considered here, the model specifications and association structures are substantially different, thus complicating model-to-model comparison. The models are applied to the 'Standard and new anti-epileptic drugs' trial of anti-epileptic drugs to investigate the effect of drug titration on the treatment effects of lamotrigine and carbamazepine on the mode of treatment failure. Notwithstanding the vastly different association structures, we show that the inference from each model is consistent, namely, that there is a beneficial effect of lamotrigine on unacceptable adverse events over carbamazepine and a non-significant effect on the hazard of inadequate seizure control. The association between anti-epileptic drug titration and treatment failure was significant in most models. To allow for the routine adoption of joint modelling of competing risks and longitudinal data in the analysis of clinical data sets, further work is required on the development of model diagnostics to aid model choice.

Competing risks joint models using R-INLA

“…In particular, spatial/spatio-temporal random effects can be included in the cause-specific hazard functions and/or the longitudinal submodel to develop, for example, a spatial competing risks joint model. The works of Hickey et al (2018) on the SANAD trial, Huang et al (2010) on outlying values in the longitudinal submodel, Rajeswaran et al (2018) on multivariate longitudinal data and the model presented by Elashoff et al (2008) are some examples in the literature that can be applied with our approach through R-INLA. A thorough presentation of all the possibilities is not possible in this article but we believe that the general method presented herein catalyses future research, especially different instances of competing risks joint models motivated from a modeling perspective.…”

A tractable Bayesian joint model for longitudinal and survival data

“…30 Williamson et al 31,32 were the first to analyze this dataset using a competing risk model without longitudinal information. Later, Williamson et al 33 proposed a joint modeling approach and more recently Hickey et al 12 compared different specifications of competing risks joint models for these data.…”

“…Applications of joint models abound in a number of areas of medical statistics. [11][12][13] In this paper, we propose a numerically tractable and interpretable alternative formulation of joint models, where we allow the longitudinal process to be modeled using GLMMs, while the survival process is specified through a parametric GH structure. This formulation allows for a direct interpretation of the parameters, as they are formulated at the hazard scale, as well as a separation of the roles of the parameters that affect the time scale, from those that affect the hazard scale.…”

Genetics of physiological dysregulation: findings from the long life family study using joint models

“…Joint models is an active area of research in statistics with numerous extensions of the basic model (analyzed in this paper) suggested in the literature that cover a wide range of research applications such as latent classes, competing risks, multivariate models, nonlinear models, dynamic predictions, stochastic processes, etc. (see books [15,16] and recent review papers and tutorials [25][26][27][28][29][30][31][32][33]). Such extended models can be applied to analyze dynamic characteristics of composite measures such as DM with various outcomes in more comprehensive ways.…”