Mixed‐effects models for slope‐based endpoints in clinical trials of chronic kidney disease

In March of 2018, the National Kidney Foundation, in collaboration with the US Food and Drug Administration and the European Medicines Agency, sponsored a workshop in which surrogate endpoints other than currently established event-time endpoints for clinical trials in chronic kidney disease (CKD) were presented and discussed. One such endpoint is a slope-based parameter describing the rate of decline in the estimated glomerular filtration rate (eGFR) over time. There are a number of challenges that can complicate such slope-based analyses in CKD trials. These include the possibility of an early but short-term acute treatment effect on the slope, both within-subject and between-subject heteroscedasticity, and informative censoring resulting from patient dropout due to death or onset of end-stage kidney disease. To address these issues, we first consider a class of mixed-effects models for eGFR that are linear in the parameters describing the mean eGFR trajectory but which are intrinsically nonlinear when a power-of-mean variance structure is used to model within-subject heteroscedasticity. We then combine the model for eGFR with a model for time to dropout to form a class of shared parameter models which, under the right specification of shared random effects, can minimize bias due to informative censoring. The models and methods of analysis are described and illustrated using data from two CKD studies one of which was one of 56 studies made available to the workshop analytical team. Lastly, methodology and accompanying software for prospectively determining sample size/power estimates are presented.