Dynamic predictions of kidney graft survival in the presence of longitudinal outliers

Abstract

In kidney transplantation, dynamic predictions of graft survival may be obtained from joint modelling of longitudinal and survival data for which a common assumption is that random-effects and error terms in the longitudinal sub-model are Gaussian. However, this assumption may be too restrictive, e.g. in the presence of outliers, and more flexible distributions would be required. In this study, we relax the Gaussian assumption by defining a robust joint modelling framework with t-distributed random-effects and error terms to obtain dynamic predictions of graft survival for kidney transplant patients. We take a Bayesian paradigm for inference and dynamic predictions and sample from the joint posterior densities. While previous research reported improved performances of robust joint models compared to the Gaussian version in terms of parameter estimation, dynamic prediction accuracy obtained from such approach has not been yet evaluated. Our results based on a training sample from the French DIVAT kidney transplantation cohort illustrate that estimates for the slope parameters in the longitudinal and survival sub-models are sensitive to the distributional assumptions. From both an internal validation sample from the DIVAT cohort and an external validation sample from the Lille (France) and Leuven (Belgium) transplantation centers, calibration and discrimination performances appeared to be better under the robust joint models compared to the Gaussian version, illustrating the need to accommodate outliers in the dynamic prediction context. Simulation results support the findings of the validation studies.

Robust joint modelling of longitudinal and survival data: Incorporating a time‐varying degrees‐of‐freedom parameter

“…When comparing the standard and robust joint models, it is evident that bias and inefficiency result from ignorance of longitudinal outliers and the assumption of Normality for the random terms. Previous research on time‐invariant robust joint models noted that failing to account for outliers in a joint modelling context can affect both the calibration and discrimination of dynamic predictions and thus may have a major impact on the treatment plans and prognosis of patients (Asar et al., 2021). The extent of the negative impact from Normality assumptions in the presence of outliers is highlighted through the simulation study we have undertaken in this paper.…”

“…Asar et al. (2021) considered the setting of for joint modelling. Under this approach, the dependence between and that was present in Approach 2 has been removed.…”

“…We do not present the details of either the likelihood function, nor HMC and NUTS, since, whereas the former is quite straightforward (e.g. see Asar et al., 2021), the second can be followed from the cited references.…”

“…In doing so, the heavier tails down‐weigh the detrimental impact of longitudinal outliers within the joint modelling framework. Initial research on robust joint modelling considered only the ‐outliers (Huang et al., 2010; Li et al., 2009; Taylor et al., 2013) and both ‐ and ‐outliers (Asar et al., 2021; Baghfalaki et al., 2014; McCrink, 2014; Song et al., 2012). Each of these studies found that the parameter estimates and corresponding standard errors are sensitive to the Normality assumptions when outliers are present, with t ‐distributional assumptions alleviating such bias.…”

Robust joint modelling of longitudinal and survival data with a time-varying degrees-of-freedom parameter

“…We do not present the details of neither the likelihood function, nor HMC and NUTS, since, whereas the former is quite straightforward (e.g. see 11 ), the second can be followed from the cited references.…”