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PLoS One. 2014 Dec 11;9(12):e114839. doi: 10.1371/journal.pone.0114839. eCollection 2014.

Should we use standard survival models or the illness-death model for interval-censored data to investigate risk factors of chronic kidney disease progression?

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University of Bordeaux, ISPED, Centre INSERM U897 Epidemiology and Biostatistics, Bordeaux, France.
Inserm Unit 1018, CESP, Research Centre in Epidemiology and Population Health, Villejuif, France; University Paris-Sud 11, UMRS 1018, Villejuif, France.
Centre Hospitalier Universitaire de Bordeaux, Service de Néphrologie Transplantation Dialyse, Bordeaux, France; Unité INSERM 1026, Univ. Bordeaux, Bordeaux, France.



In studies investigating risk factors of chronic kidney disease (CKD) progression, one may be interested in estimating factors effects on both a fall of glomerular filtration rate (GFR) below a specific level (i.e., a CKD stage) and death. Such studies have to account for the fact that GFR is measured at intermittent visit only, which implies that progression to the stage of interest is unknown for patients who die before being observed at that stage. Our objective was to compare the results of an illness-death model that handles this uncertainty, with frequently used survival models.


This study included 1,519 patients from the NephroTest cohort with CKD stages 1-4 at baseline (69% males, 59±15 years, median protein/creatinine ratio [PCR] 27.4 mg/mmol) and subsequent annual measures of GFR (follow-up time 4.3±2.7 years). Each model was used to estimate the effects of sex, age, PCR, and GFR at baseline on the hazards of progression to CKD stage 5 (GFR<15 mL/min/1.73 m2, n = 282 observed) and death (n = 168).


For progression to stage 5, there were only minor differences between results from the different models. The differences between results were higher for the hazard of death before or after progression. Our results also suggest that previous findings on the effect of age on end-stage renal disease are more likely due to a strong impact of age on death than to an effect on progression. The probabilities of progression were systematically under-estimated with the survival model as compared with the illness-death model.


This study illustrates the advantages of the illness-death model for accurately estimating the effects of risk factors on the hazard of progression and death, and probabilities of progression. It avoids the need to choose arbitrary time-to-event and time-to-censoring, while accounting for both interval censoring and competition by death, using a single analytical model.

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