Evaluation of study designs to test the intact nephron hypothesis

Introduction: Renal dose adjustment generally assumes a linear relationship between renal drug clearance (CLR) and glomerular filtration rate (GFR). The theory underpinning this practice is the Intact Nephron Hypothesis (INH) [1]. A recent review by our group suggested that the INH may not be a suitable general model for renal drug clearance, particularly for drugs that are clearly largely by tubular secretion where a non-linear relationship between CLand GFR is expected [2]. To date, the study designs required to detect a deviation from the INH in renal drug studies have not been explored.

Aim: To evaluate Phase 1 renal drug study designs recommended by the United States Food and Drug Administration (FDA) [3] and the European Medicines Agency (EMA) [4] for testing the INH.

Methods: The FDA and the EMA guidelines for Phase 1 pharmacokinetic studies in patients with renal impairment were evaluated for their performance to discriminate between linear (under INH scenario) and nonlinear (under non-INH scenario) relationship between CLand GFR, when latter was true. The key difference between the two guidelines is the recommended method for estimating renal function. The FDA recommends a serum creatinine based equation for estimating GFR (eGFR) and the EMA recommends using an exogenous marker for measured GFR (mGFR). Two models were proposed to describe the relationship between CLRand eGFR or mGFR:

  1. M1: a linear model based on the INH scenarioCLR= THETA(1) * GFR
  1. M2: a nonlinear model based on the non-INH scenarioCLR= THETA(1) * GFR ^ THETA(2)

where, GFR is either eGFR or mGFR for the FDA or EMA guidelines, respectively; THETA(1) is the linear coefficient parameter and THETA(2) is the exponent parameter.

A series of stochastic-simulation and estimations were conducted to assess the performance of the designs based on the FDA and the EMA guidelines in terms of their ability to identify a departure from the INH. The number of subjects for each simulated study was n = 4, 8, 12, 16, 20, 24, 48, 72, 120, 240, 480, 1080. The studies were replicated 1000 times. Alpha-error, power, relative standard error (RSE) and bias were calculated to assess the designs based on the FDA and the EMA guidelines.

Results: Study designs under the EMA guideline with ≥ 8 subjects had power ≥ 80% to correctly detect non-linear relationship between CLRand GFR. Under the FDA guidelines, ≥ 80% was achieved only with ≥ 24 subjects. For M2, the true model, the RSE of THETA(1) was < 17% for all designs with power ≥ 80%, while TEHTA(2) was not precisely estimated with an RSE of 59. To achieve RSE of < 25% for THETA(2) at least n=48 and n=72 subjects were required for designs under the EMA and the FDA guidelines, respectively. The estimated parameters for all the tested designs with power > 80% were unbiased.

Conclusions: The present study evaluated the designs recommended by the FDA and the EMA guidelines for testing the INH. The FDA guideline would require 3 times more subjects to achieve ≥ 80%power to detect non-linear relationship between CLRand GFR compared to the EMA design. Under non-INH scenario, with number of subjects recommended by the EMA guidelines (n = 24), designs under both the guidelines would will not be able to estimate the parameters precisely and therefore will be unlikely to establish the true relationship between CLRand eGFR or mGFR.


  1. Bricker NS, Morrin PA, Kime SW, Jr. The pathologic physiology of chronic Bright’s disease. An exposition of the “intact nephron hypothesis”. Am J Med. 1960;28:77-98.
  2. Pradhan S, Duffull SB, Walker RJ, Wright DFB. The intact nephron hypothesis as a model for renal drug handling. Eur J Clin Pharmacol. 2018. doi:10.1007/s00228-018-2572-8.
  3. Food and Drug Administration, Center for Drug Evaluation and Research (CDER). Guidance for industry: pharmacokinetics in patients with impaired renal function – study design, data analysis, and impact on dosing and labeling. 2010.
  4. European Medicines Agency, Committee for Medicinal Products for Human Use (CHMP). Guideline on the evaluation of the pharmacokinetics of medicinal products in patients with decreased renal function. 2016.