CO8.3 - Shared frailty excess hazard modelling in presence of between clusters heterogeneity and inappropriate life tables: an example from chronic kidney disease epidemiology
Modélisation du taux en excès avec un terme de fragilité partagée en présence d'hétérogénéité entre clusters et de tables de mortalité inappropriées: un cas d'usage en épidémiologie de la maladie rénale chronique
Abstract
Background and objective(s) In chronic-disease epidemiology, researchers may focus on disease-related mortality rather than overall mortality. When cause of death information is unavailable, disease-related mortality can be estimated using the relative survival approach. This method assumes that the observed mortality can be decomposed into mortality due to the disease, the excess mortality, and mortality due to others causes, the expected mortality. In the overall survival framework, a shared frailty is often used as a multiplicative effect on the hazard to account for the between cluster heterogeneity. Recent developments in relative survival methodology have introduced a cluster-level frailty applied only to excess hazard. However, directly translating a frailty model for observed hazard into the relative survival framework would involve a joint shared frailty, meaning that heterogeneity would affect both the excess and the expected hazards. The presence of heterogeneity acting on expected hazard can be due to the use of inappropriate life tables as proxy of the expected mortality. The objective was to propose excess hazard models in the presence of clusters heterogeneity and inappropriate life tables. Material and Methods Two shared frailty models accounting for the between cluster heterogeneity acting on expected and excess hazards were developed; one without (M1) and one with (M2) a fixed-correction parameter used to rescale the background mortality. The parameters were estimated using the maximum likelihood method. A large simulation design considered various functions for the baseline excess hazard, various numbers of clusters and sample size, medium and high strengths of the between cluster heterogeneity. The proposed models were also compared with existing cluster-level frailty excess hazard models [1] (M3 & M4). Bias, root mean square errors, empirical coverage rate and Akaike Information Criterion (AIC) were used as performance criterion. Finally, the models were also applied on dialyzed patients from the French Epidemiologic and Information Network in Nephrology (REIN). Results Overall, the simulated results were satisfactory and highlighted specific configurations where the proposed models performed best. A large number of clusters and of individuals per cluster is preferable, in order to obtain unbiased estimates of the parameters. Models also performed best when the cluster heterogeneity is lower. The simulations have also shown that using a fixed correction of the background mortality is also not recommended below 5,000 individuals. Moreover, when the simulation design assumed a frailty acting on both hazards, M1 and M2 led to poor performance. The AIC was able to discriminate between the compared models. In the application study, we explored the variations in excess hazard by French départements. M2 was favored by the AIC (M1: 50,752/ M2: 50,739/ M3: 50,753/ M4: 50,745), leading to a smaller standard deviation estimate of the between départements heterogeneity 0.17 [0.14,0.21] and a larger correction parameter of the French life tables 1.83 [1.49,2.25]. Conclusion Translating an overall shared frailty hazard model into its complement in the excess hazard framework provides a new tool to address inappropriates life tables settings in chronic disease epidemiology.
