Discovering heterogeneous treatment effects on slope-based endpoints in chronic kidney disease trials

Abstract

Background: Chronic kidney disease (CKD) is slowly progressive, with clinically-relevant end-points of interest (e.g. kidney failure, dialysis, transplantation, death due to kidney disease) occurring many years after diagnosis, making the design of trials to evaluate treatments that slow the progression of kidney disease challenging. Recent meta-analyses have shown that the 3-year total slope of estimated glomerular filtration rate (eGFR) may serve as a reliable surrogate for these hard clinical outcomes. 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 (HTEs) given predetermined subgroups. Yet, none have explored data-driven subgroup identification and HTE estimation.

Methods: We propose a Bayesian method that incorporates 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 total eGFR slope. Our proposed approach simultaneously estimates the total eGFR slope in the presence of informative censoring and identifies interpretable subgroups of patients who experience differential treatment effects on the total eGFR slope outcome.

Results: Simulation studies demonstrate that our method accurately recovers treatment-effect heterogeneity with low estimation error, yielding better subgroup-specific treatment recommendations in moderate-to-large samples. Our method also controls false positives when no true heterogeneity presents. We apply our approach to 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. Specifically, the posterior probability that the treatment effect is larger in the higher-eGFR subgroup is 81 %.

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

Supplementary Information: The online version contains supplementary material available at 10.1186/s12874-025-02646-7.

Keywords: Acute and chronic slopes; Bayesian decision tree; Informative censoring; Shared parameter model; Subgroup identification.

Fig. 1

Treatment effect estimations can be misleading if the heterogeneity in the control group slope is overlooked

Fig. 2

The “most representative tree” on the total treatment effect obtained in the MDRD study

Fig. 3

Spaghetti plot illustrating the group-wise mean trends, with dot-dashed lines representing the 95 credible bands, based on sub-sampled data for each treatment arm. The dashed line marks the boundary between the acute and chronic stages within the three-year observation period

Fig. 4

Assessment of the concordance between the two data subsets (60/40 split) across the 100 ’minimum distance trees.’ Each box represents the distribution of individual treatment effects estimated on the validation set (60% subset), conditioned on each subgroup identified from the discovery set (40% subset). The three subgroups are defined by evenly spaced quantiles of individual treatment effects calculated from the discovery set