Optimizing Sample Size Calculation for Early-Stage CKD Trials Using eGFR Slope

The formula and tool developed in this study streamline sample size planning for CKD trials using eGFR slope. Frequent measurement effectively allowed for a smaller sample size in short trials, but this benefit is limited in long ones. Small expected slope differences require long-term trials, whereas short-term trials require large slope differences.

In CKD trials, the eGFR slope has emerged as a surrogate end point for earlier assessment of treatment effects. However, the influence of key design parameters-slope difference, trial duration, measurement frequency, and dropout patterns-on the required sample size remains unclear. The aim of this study was to derive a sample size formula that incorporated these factors and develop a practical tool for efficient calculation across diverse trial scenarios.

A sample size formula for comparing eGFR slopes in early-stage CKD trials was derived using a linear mixed-effects model and validated against a simulation-based method. Guided by National Kidney Foundation, US Food and Drug Administration, and European Medicines Agency workshop reports, the formula was applied to systematically examine the effects of these design parameters on sample size.

The derived formula yielded three key insights for early-stage CKD trials. First, frequent measurements allowed for a lower sample size in short-term trials but had a limited effect in longer ones ( e.g ., shortening the interval from 2 months to 1 month (with Δ = 0.8) allowed for a smaller sample size by approximately 440 participants in a 12-month trial versus approximately 30 participants in a 36-month trial). Second, long-term trials were preferable for small expected slope differences, whereas short-term trials required a sufficiently large slope difference for feasibility. Third, compared with a simple inflation approach, incorporating dropout patterns into the target sample size calculation reduced overestimation.

The derived formula quantified interactions among key trial design parameters. The effect of frequent measurements on required sample size was greater in short-term trials, whereas small expected slope differences required longer trial durations.