Enriching the Analysis of Chronic Kidney Disease with Statistics and Its New Frontiers

Approximately 15% of adults in the United States (U.S.) are afflicted with chronic kidney disease (CKD). For CKD patients, the progressive decline of kidney function is intricately related to hospitalizations due to cardiovascular disease and eventual `terminal' events, such as kidney failure and mortality. To unravel the mechanisms underlying the disease dynamics of these interdependent processes, including identifying influential risk factors, as well as tailoring decision-making to individual patient needs, we develop a novel Bayesian multivariate joint model for the intercorrelated outcomes of kidney function (as measured by longitudinal estimated glomerular filtration rate), recurrent cardiovascular events, and competing-risk terminal events of kidney failure and death. The proposed joint modeling approach not only facilitates the exploration of risk factors associated with each outcome, but also allows dynamic updates of cumulative incidence probabilities for each competing risk for future subjects based on their basic characteristics and a combined history of longitudinal measurements and recurrent events. We propose efficient and flexible estimation and prediction procedures within a Bayesian framework employing Markov Chain Monte Carlo methods. The predictive performance of our model is assessed through dynamic area under the receiver operating characteristic curves and the expected Brier score. We demonstrate the efficacy of the proposed methodology through extensive simulations. Proposed methodology is applied to data from the Chronic Renal Insufficiency Cohort study established by the National Institute of Diabetes and Digestive and Kidney Disease to address the rising epidemic of CKD in the U.S. 

Background: Chronic kidney disease (CKD) is slowly progressive, with clinically-relevant end-points of interest (e.g. kidney failure/dialysis, transplantation, death) occurring many years after diagnosis, making the design of trials to evaluate treatments to slow the progression of kidney disease challenging. Recent work has demonstrated the utility of a 3-year slope in patient's estimated glomerular filtration rate (eGFR) as a high-quality surrogate marker for the clinical end-points of interest, thereby allowing for shorter clinical trials. Existing research has focused on relaxing the linear trend assumption on the eGFR slope, accounting for informative censoring (via fitting a shared parameter model, for example), and evaluating heterogeneous treatment effects (HTE) given predetermined subgroups. Yet, none have explored data-driven subgroup identification and HTE estimation.

Methods: We propose a Bayesian method that incorporated a Bayesian decision tree for HTE into a shared-parameter model that combines a survival model for censoring time with a two-slope spline model that characterizes the rate of decline in eGFR. Our proposed approach simultaneously estimates the eGFR slope in the presence of informative censoring and provides interpretable clinical decisions for subgrouping patients according to their treatment effect on eGFR slope.

Results: We apply our model to analyze the Modification of Diet in Renal Disease (MDRD) Trial, observing strong Bayesian evidence that patients with a baseline eGFR above 34.32 benefit more from the intensive systolic blood pressure control compared to patients with a baseline eGFR below 34.32, with a posterior frequency of 81\% for observing a higher treatment effect estimation in the former group.

Conclusion: Our proposed model can effectively capture even subtle HTE while avoiding over-fitting when no heterogeneity exists, making it valuable for downstream analyses such as treatment recommendations.