Quantifying clinical and genetic factors influencing rate and severity of autosomal dominant tubulointerstitial kidney disease progression

Abstract

Autosomal dominant tubulointerstitial kidney disease (ADTKD), caused by mutations in UMOD and MUC1 genes, leads to tubular damage and fibrosis, ultimately resulting in kidney failure (KF). This study investigated clinical and genetic factors influencing the rate and severity of ADTKD progression by developing quantitative models. An estimated glomerular filtration rate (eGFR) of 10 mL/min/1.73 m² was used to define KF, corresponding to dialysis initiation. Natural history data from the Wake Forest University School of Medicine study were used to develop the models for UMOD (n = 371) and MUC1 (n = 233) disease types (age ≥ 18 years). Longitudinal change in eGFR and time-to-KF were quantified using nonlinear mixed-effects and parametric time-to-event modeling approaches, respectively, in Monolix (version 2024R1). Sigmoid I_max functions with steepness parameters varying before and after inflection points best captured eGFR decline. Patients with UMOD and MUC1 disease variants exhibited a similar initial shallow steepness ($\approx$ 1), but after inflection, each declined rapidly. MUC1 patients progressed faster than UMOD during the post-inflection phase (γ₂ = 10.23 vs. 6.34). eGFR at first clinic visit (eGFR_FCV) and age at first clinic visit (AFCV) significantly affected between-subject variability in eGFR decline. A Weibull hazard function best described the time to KF. In UMOD, males reached Te (the age at which approximately 36.8% of individuals remain free from KF) 4 years earlier than females on average (β_Te_Male = -0.07), indicating faster progression in males. Older AFCV was associated with slower progression to KF (β_Te_AFCV = 0.59 for UMOD and 0.81 for MUC1). These models may help enable quantitative data-driven subgroup analysis in the future, optimizing inclusion/exclusion criteria for ADTKD clinical trials.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10928-025-09989-0.

Introduction

Autosomal dominant tubulointerstitial kidney disease (ADTKD) is a genetic kidney disease characterized by tubular damage and interstitial fibrosis without glomerular lesions. Estimating the overall prevalence is currently challenging due to limited clinical recognition. After autosomal dominant polycystic kidney disease (ADPKD) and Alport syndrome, ADTKD is likely the third most prevalent genetic kidney disease [1, 2]. Individuals with ADTKD endure progressive chronic kidney disease (CKD) and ultimately kidney failure (KF) that requires dialysis or kidney transplantation; yet, throughout the progression of disease there is only normal-to-mild proteinuria and no change in kidney dimension or volume [3–5]. Progression to KF is inevitable, and rate of progression is highly variable [5]. Autosomal dominant inheritance, generally slow progression to severe CKD, and bland urinary sediment are the major findings in individuals with ADTKD [6]. Because there is no specificity in clinical, biological, and pathological findings, ADTKD is often underdiagnosed unless family history of disease is recognized [5].

Mutations in several genes have been identified as causes of ADTKD. Based on published studies, ADTKD-UMOD and ADTKD-MUC1 are the most common subtypes of ADTKD [5, 7, 8]. The most common mutated gene associated with ADTKD is UMOD, a gene responsible for the production of the most abundant protein in normal urine, uromodulin [4, 9, 10]. Uromodulin is a kidney-specific protein involved in regulating electrolytes, urine concentration, blood pressure control, and immunomodulation [11, 12]. Mutations in the UMOD gene cause the misfolding of uromodulin in the endoplasmic reticulum of tubular epithelial cells. The misfolded protein is improperly transported to the cell surface, preventing its secretion into the urine. Consequently, urinary uromodulin levels are reduced, which can be measured and may serve as a potential biomarker for the disease in the future [3, 5]. The next common mutated gene that causes ADTKD is MUC1, a gene responsible for the production of the transmembrane epithelial protein mucin-1. Mucin-1 is expressed in the lungs, stomach, intestine, and kidney and involves signal transduction, immunomodulation, and epithelial mucus barrier protection [13–15]. The mutant mucin-1 protein is misfolded and accumulates in the endoplasmic reticulum (ER) and other intracellular compartments of tubular epithelial cells. This accumulation triggers cellular stress, leading to dysfunction and ultimately apoptosis of tubular cells [3, 5]. ADTKD is less often caused by mutations in genes such as REN, HNF1β, SEC61A1, and DNAJB1, in which the latter two disease types are exceedingly rare [3, 16].

Hyperuricemia is more prevalent in ADTKD-UMOD than ADTKD-MUC1. Individuals with ADTKD-UMOD may present with gout in their early teenage years, and CKD becomes present in their late teens or early twenties. In ADTKD-MUC1, CKD generally starts in the early twenties, and gout is less prevalent [5]. The hallmark pathophysiology of ADTKD-UMOD is accumulation of aggregated mutant uromodulin protein in the endoplasmic reticulum, which leads to endoplasmic reticulum (ER) stress that cascades to inflammation, cell death, and interstitial fibrosis. The pathophysiology of ADTKD-MUC1 involves the accumulation of aggregated mutant mucin1 protein in the endoplasmic reticulum Golgi intermediate compartment (ERGIC) that ultimately causes tubulointerstitial damage and cell death [3].

Currently, there is no specific treatment for patients with ADTKD and the disease can only be cured by kidney transplantation. While changes in estimated glomerular filtration rate (eGFR) can be used to measure the progression of ADTKD [17], factors contributing to the heterogeneity of the decline in eGFR are mainly unknown. For example, patients from the same immediate family can develop KF at substantially different ages [6]. Despite a clear need for therapies for ADTKD, the rarity, slow progression, and highly variable nature of this disease poses significant challenges in designing a successful clinical trial for this disease.

This study was conducted to quantify clinical and genetic factors that influence the rate and severity of ADTKD-UMOD and ADTKD-MUC1 disease progression by developing quantitative models that can inform future ADTKD clinical trial designs. Toward that end, existing natural history data were leveraged to develop ADTKD disease progression models for both UMOD and MUC1 disease types. The longitudinal changes in eGFR and progression timing to KF were quantified, including potential covariates contributing to the variability in the rate of disease progression. In order to utilize the developed models to inform clinical trial designs with respect to inclusion/exclusion criteria, baseline patient characteristics collected at screening visits were assessed in this study.

Methods

Data

Longitudinal individual-level natural history data were collected through the approved Wake Forest University School of Medicine study (WFUHS IRB0000352 Characteristics of Individuals with Inherited Kidney Disease). The Wake Forest Registry is comprised of over 1,100 families who have been referred since 1996. The registry contains data pertaining to demographics, pedigree, medical history, and laboratory values. Genetic testing was performed as previously described [18, 19]. Study data were collected and managed using Research Electronic Data Capture (REDCap) [20].

The target population in our disease progression modeling analysis was individuals with ADTKD UMOD and MUC1 who were at least 18 years old. The data set included longitudinal clinical assessment measures performed on 604 participants with a median follow-up time of 9 years (5th to 95th interval: 1–23 years). The data were randomly split into training and test sets at a 4:1 ratio while ensuring balanced covariate distributions. Specifically, we aimed to achieve a similar male-to-female ratio and maintain a comparable baseline eGFR distribution between the training and test sets.

Dependent and time variables

As changes in eGFR can be used as a biomarker that reflects ADTKD disease progression, it was chosen as the primary disease progression marker in the longitudinal modeling analysis. CKD-EPI_Scr, introduced by Levey et al. [21]., was used to calculate the eGFR measure using the collected serum creatinine (Scr), sex, and race information from the collected data. The CKD-EPI_Scr equation was chosen to calculate eGFR because it is considered most accurate and minimizes bias as a function of race [22]. Data with incomplete records (e.g., missing values in visit age and eGFR measures) were excluded. eGFR measurements, reported as less than 10 mL/min/1.73m², were censored using the likelihood-based M4 method in the longitudinal model analysis [23]. Time of KF was defined as the age at which the patient required dialysis, when the eGFR measure decreased to less than or equal to 10 mL/min/1.73m².

Age at assessment was chosen as the independent time variable in the longitudinal model and age at KF was used as the event time in TTE modeling analysis, given that the onset and rate of eGFR decline depend on aging, which also occurs in the absence of frank kidney disease [24–26]. Waas et al. confirmed that approximately 1 ml/min/1.73m² of eGFR loss happens per year in normal adult controls. This is due to the loss of functioning nephrons along with several risk factors that are associated with the decline in eGFR [24].

Covariates

As potential covariates influencing the rate and severity of disease progression, sex, race, ethnicity, eGFR collected at first clinical visit (eGFR_FCV), and age at first clinical visit (AFCV) for each individual were explored for both disease types. Kidd et al. hypothesized the presence of minor variants in the promotor regions of both Uromodulin and Mucin1 mutations that can influence the expression of mutated protein production and disease production [18]. Thus, the allele in phase with the UMOD mutation in a single nucleotide polymorphism (SNP), rs4293393 in the promoter region of the UMOD gene was also included as a covariate to compare the impact of adenosine (A) vs. guanosine (G) residue on disease progression. For the patients with the Mucin1 variant, the allele cysteine (C) vs. tyrosine (T) in SNP rs4072037 that is in phase with the MUC1 mutation was tested.

There were two additional available covariates to explore that are specific for UMOD: seventy-four sub-mutation types, and stratification by cysteine vs. non-cysteine amino acid presence in UMOD mutations. Exploratory data analysis was performed to find an optimal grouping strategy to combine some of the sub-mutation types. Given that there was limited supporting clinical evidence, the number of subjects available under sub-mutation types was counted and regrouped based on the frequency. The following covariates were explored in the TTE models: sub-mutation type (UMOD), sex and AFCV.

Disease progression model development

A nonlinear mixed-effects modeling approach was used to quantify the longitudinal changes in eGFR of the patients with ADTKD. For the model structure equations that describe the central trends in the eGFR decline with age, several mathematical functions, such as linear, quadratic, exponential, and sigmoid I_max functions, were tested.

Variability around the structural model was quantified at two levels of random effects: between-subject variability and residual error. The between-subject variability was explained using log-normal and logit-normal distributions for applicable structural parameters. Residual error was explained after testing the appropriateness of additive, proportional, and combined error models.

The age of KF diagnosis was quantified by a parametric TTE modeling approach for the UMOD and MUC1 disease types separately. KF event times (i.e., age at KF) were right-censored for individuals who had not reached KF by the end of the data collection period. Several hazard functions were tested as a structural model, such as gamma, Weibull, Gompertz, uniform, and exponential functions. The hazard function predicts the instantaneous rate of an event given that the event has not already occurred. Integrating the hazard function gives the cumulative hazard function. Exponentiating the cumulative hazard function gives us the survival function [27], which can then be interpreted as the probability that, in this work, KF had not occurred by the specified time.

After defining the structural model equations, the two different ADTKD disease types, i.e., UMOD and MUC1, were modeled separately because of the difference in the available covariate data lists. Covariate analysis was conducted, guided by the classic stepwise covariate modeling (SCM) approach using forward addition and backward elimination with p-values of 0.1 and 0.05, respectively. Continuous covariates were incorporated using a power model centered by their weighted mean values (Supplementary S1: Equation S1), and exponential functions were used for categorical covariates (Supplementary S1: Equation S2).

Model selections were guided by the Akaike information criterion (AIC), Bayesian information criterion (BIC), objective function value for nested models, convergence of the minimization criteria, including a successful covariance step, reasonable precision of the parameter estimates, goodness-of-fit plots (GOF), visual predictive check (VPC) plots, and the physiological plausibility of parameter estimates [28–30]. As a final step, selected models were validated using the holdout test data set by analyzing the visual predictive check plots.

Software

Data processing and visualization were performed in R (Version 4.3.2) [31]. Monolix (Version 2024 R1) was used for modeling analysis with the stochastic approximation expectation–maximization (SAEM) algorithm.

Results

Data summary

The final formatted data set, following the exclusion of incomplete records, included a total of 604 patients with ADTKD from 18 to 80 years of age with a total of 6,447 visit records. Among them, 371 and 233 were patients described as possessing UMOD and MUC1 disease types, respectively. Each step of the data formatting process and summary of the data were presented in Fig. 1 and Table 1. Supplementary S1: Figure S1.1 displays the maintained proportion of the categorical covariate, and Supplementary S1: Figure S1.2 displays the similar distribution of baseline eGFR in both UMOD and MUC1 disease types in the training and test sets compared to the overall dataset.

Fig. 1.

Data formatting process and summary of the data

Table 1.

Summary of formatted data

		Total	ADTKD-UMOD	ADTKD-MUC1
Number of individuals		604	371	233
Continuous Median (95% Interval)
Age at assessment	Years	44.76(23.23–65.63)	44.26(22.48–63.10)	45.65(24.03–69.11)
eGFR (CKD-EPI)	mL/min/1.73m2	34.14(10.62–87.38)	31.86(10–87.5)	38.18(12.69–86.83)
Age of gout	Years	32(14–60)	30(13–57)	52(25–72)
Age of KF	Years	51(28–69)	52(31–64)	49(27–74)
Baseline age	Years	37(18.50–59.79)	36.77(18.34–58.93)	37.68(20.56–64.99)
eGFR at baseline	mL/min/1.73m2	48.59(18.19–101)	45.35(14.56–94.83)	58.63(25.4–101.74)
Categorical Number of individuals
Sex	Female	356	215	142
	Male	247	156	91
Mutation type	UMOD	371	371	233
	MUC1	233
Mutations on promotor region	Phase A (UMOD)	359	359	-
	Phase G (UMOD)	12	12	-
	Phase C (MUC1)	136	-	136
	Phase T (MUC1)	35	-	35
	NA (MUC1)	62	-	62
Family of mutations (specific mutation subtypes under UMOD)	p.H177-R185 del (UMOD)	77	77	-
	p.V93-G97delinsAASC (UMOD)	34	34	-
	p.R178P (UMOD)	21	21	-
	p.C106F (UMOD)	50	50	-
	Other Mutations (UMOD)	189	189	-
	MUC1	232	-	233
Gout	Yes	209	178	31
	No	395	193	202
KF	Yes	193	105	145
	No	410	266	88

eGFR estimated Glomerular Filtration Rate, CKD-EPI Chronic Kidney Disease Epidemiology Collaboration, KF Kidney Failure, UMOD Uromodulin; and MUC1 Mucin1

Given that 92% of patients in the dataset were “American White”, race was not further considered as a covariate in the modeling analysis. Also, 89% were not Hispanic or Latinx in the dataset, so ethnicity was not considered as a covariate. The 74 sub-mutation types for UMOD were regrouped into 3 main mutation populations based on frequency into: p.H177-R185 del, p.V93-G97delinsAASC, pC106F, and the others. The influence of cysteine vs. non-cysteine amino acid involvement was excluded from the analysis since Kidd et al. found that it was not significantly associated with age of KF [18].

Longitudinal trajectory models quantifying the declines in eGFR in patients with ADTKD

For both ADTKD-UMOD and ADTKD-MUC1, a sigmoid I_max function (Eq. 1) with steepness parameters (i.e., ${\gamma }_i$) varying before and after inflection points (i.e., ${\text{DPT}}_{50}$) best captured the central trend of the longitudinal decline of eGFR with age among the tested model equations (Supplementary S1: Table S1.1).

$${\text{eGFR}}_{\text{i}}={DP0}_{\text{i}}·\left(1,-,\left(\frac{{\text{DP}}_{\text{max},\text{i}}·{\mathit{Age}}_i^i}{{\text{DPT}}_{50,\text{i}}^i+{\mathit{Age}}_i^i}\right)\right)$$ 1

where Age is the age of an individual $i$ at the time the subject visited the clinic and their serum creatinine was measured for eGFR determination; ${DP0}_{\text{i}}$ (mL/min/1.73m²) represents the eGFR when Age = 0 for the individual$i$; however, it would be more accurate to interpret as the extrapolated eGFR value when the age is approximately 18 years. This is because the age range in the data set did not include any patients younger than 18 years old and the sigmoid Imax function shape shows a flat trajectory between Age = 0 and Age = 18. ${\text{DP}}_{\text{max},\text{i}}$ represents the fractional maximum change in eGFR for the individual$i$, which was modeled in a logit domain to constrain the values between 1 and 0; ${\text{DPT}}_{50,\text{i}}$ (age in years) represents the age at which half of the maximum change in eGFR occurs in the individual$i$; and ${\gamma }_i$ is the steepness of the curve (i.e., Hill coefficient for the individual i), where ${\gamma }_1$ is before (i.e., younger than) ${\text{DPT}}_{50}$ and ${\gamma }_2$ is after (i.e., older than) ${\text{DPT}}_{50}$. The model parameter, ${\text{DP}}_{\text{max}}$, represents the maximum fractional decrease in eGFR and was fixed to its maximum value of 0.99 (the highest biologically plausible value) for both the UMOD and MUC1 models due to high shrinkage.

For UMOD, the covariate selection was done for the following covariates: baseline eGFR, baseline age, SNP rs4293393 (A vs. G), sex, and the re-grouped common mutations. Baseline eGFR was significant on ${\gamma }_2$, and $DP0$ (Fig. 2A). Baseline age was significant for ${\text{DPT}}_{50}$ and ${\gamma }_2$ (Fig. 2C). The estimated age at which the eGFR value is half of its maximum decrease ${\text{DP}}_{50}$ was 39.76 years for a typical (mean) patient, with a maximum decrease ${\text{DP}}_{\text{max}}$ of 0.99. The correlations between the parameters, ${\gamma }_1$ and $DP0$ were also estimated to be −0.88.

Fig. 2.

Representative Simulation Results Visualizing the Influence of Significant Covariates in the Final Models, quantifying the Longitudinal Decline in estimated Glomerular Filtration Rate (eGFR) for ADTKD-UMOD and ADTKD-MUC1. Subjects were created from minimum to maximum values for each of the continuous covariates, such as eGFR_FCV (eGFR collected at first clinical visit) and AFCV (age at first clinical visit). Each subject was simulated with 10 replicates. Mean eGFR was calculated and plotted with standard errors. Each panel represents the predicted effects of the covariates on the longitudinal decline of eGFR: for UMOD, effects of eGFR_FCV (A), AFCV (C), and for MUC1, eGFR_FCV (B) and AFCV (D)

For MUC1, covariate selection was done for the following covariates: baseline eGFR, baseline age, SNP rs4072037 (C vs. T), and sex. Baseline eGFR was significant on${\text{DP}}_{50}$,${\gamma }_1,{\gamma }_2,$, and DP0 (Fig. 2B). Baseline visit age significant on ${\text{DP}}_{50}$ and ${\gamma }_2.$ (Fig. 2D). The estimated age at which the eGFR value is half of its maximum decrease ${\text{DP}}_{50}$ was 38.36 years for a typical patient, with a maximum decrease ${\text{DP}}_{\text{max}}$ of 0.99. The correlations between the parameters, ${\gamma }_1$ and ${\text{DP}}_{50}$ were also estimated to be −0.63.

The final parameter estimates of the longitudinal trajectory models are summarized in Table 2A and quantify the decline in eGFR in patients with ADTKD (Supplementary S2: Model Code 1 and 2). The predicted effect values of the associated covariates that significantly influenced the individual trajectories are also summarized for each disease type. The other sources of variability (i.e., between-subject and residual variability) were also quantified with reasonable precision. Visual inspections using goodness-of-fit, VPC, and individual fits (Supplementary S3) revealed good agreement between observed and predicted data (Figs. 3). The additional validation using the test data sets also showed good predictive performance for the models (Supplementary S1: Figures S1.3 & S1.4).

Table 2.

Final parameter estimates of disease progression models

Parameter	ADTKD-UMOD		ADTKD-MUC1
	Final estimates (%RSE)	Bootstrap estimates n = 500; median (95% CI)	Final estimates (%RSE)	Bootstrap estimates n = 500; median (95% CI)
A. Final parameter estimates of models predicting longitudinal changes in eGFR
Fixed Effects
TV_ ${\text{DP}}_{\text{max}}$	0.99		0.99
TV_ ${\text{DPT}}_{50}$	39.76(2.06)	39.53 (38.21–41.39)	38.36 (0.9)	39.25 (37.64–41.7)
β_eGFR_FCV_ ${\text{DPT}}_{50}$	-	-	0.04 (53.4)	0.07 (0.018–0.16)
Β_AFCV_ ${\text{DPT}}_{50}$	0.93 (2.05)	0.93 (0.88–0.97)	0.97 (2.41)	0.96 (0.91–1)
$TV\_\gamma 1$	1.12 (15.2)	0.91 (0.32–1.98)	0.9 (22.6)	1.19 (0.43–5.9)
β_eGFR_FCV_ $\gamma 1$	-	-	−0.67 (26.8)	0.097 (−0.97 – 1.16)
$TV\_\gamma 2$	6.34 (7.76)	6.35 (5.29–7.9)	10.23 (9.01)	11.18 (9.03–15.82)
β_eGFR_FCV_ $\gamma 2$	−0.68 (28.9)	−0.68 (−1.16 – −0.31)	−1.13 (16.4)	−1.07 (−1.56 – −0.4)
β_AFCV_ $\gamma 2$	1.14 (20.29)	1.22 (0.76–1.75)	0.28 (83.1)	0.37 (−0.16 – 1.08)
TV_ $DP0$	76.69 (1.48)	78.13 (70.05–82.72)	82.74 (1.66)	79.24 (61.55–84.71)
β_eGFR_FCV_ $DP0$	1 (1.38)	1 (0.98–1.03)	0.96 (4.34)	0.91 (0.66–1.01)
Standard Deviation of the Random Effects
Random Effects	[%CV] (%RSE)		[%CV] (%RSE)
ω_ ${\text{DPT}}_{50}$	0.07 [7.61] (6.07)	0.07 (0.05–0.09)	0.07 [7.63] (8.48)	0.076 (0.052–0.1)
ω_ $\gamma 1$	1.25 [194] (7.41)	1.27 (0.89–1.71)	0.21 [21.6] (51.4)	0.97 (0.2–1.47)
ω_ $\gamma 2$	0.8 [98.93] (7.41)	0.8 (0.68–0.94)	0.66 [74] (12.1)	0.63 (0.49–0.96)
ω_ $DP0$	0.13 [12.97] (10.4)	0.12 (0.07–0.18)	0.09 [9.5] (8.48)	0.14 (0.057–0.24)
Correlations
Correlation $\gamma 1$ and $DP0$	−0.88 (8.37)	−0.87 (−0.92 – −0.73)	−0.63 (105)	−0.88 (−0.93 – 0.28)
Error Model Parameters
additive	0.33 (27.5)	0.34 (0.01–0.86)	-	-
proportional	0.11 (3.19)	0.11 (0.08–0.12)	0.12 (1.70)	0.12 (0.11–0.14)
B. Final parameter estimates of the time-to-event of models predicting the survival function for kidney failure
Fixed Effects
$\mathit{Te}$	54.32 (1.86)	54.25 (51.97–56.85)	51.54 (1.97)	51.4 (49.16–53.9)
$p$	8.69 (7.50)	8.78 (7.76–10.01)	6.82 (8.81)	6.9 (6.19–8.14)
β_ $Te\_\text{Male}$	−0.07 (33.8)	−0.07 (−0.13–−0.016)	-	-
β_ $Te\_\text{AFCV}$	0.59 (6.05)	0.59 (0.52–0.67)	0.81 (7.01)	0.81 (0.7–0.94)

eGFR estimated glomerular filtration rate, FCV first clinical visit, AFCV age at first clinical visit, TV Typical Value (the population average parameter), ${\text{DPT}}_{\text{max}}$ maximum decrease in eGFR, ${\text{DPT}}_{50}$ age at which eGFR is half of its maximum decrease (years), $\gamma$ 1, Hill coefficient before DPT₅₀, $\gamma$ 2, Hill coefficient after DPT₅₀; $DP0$, extrapolated eGFR around age of 18 years (ml/min/1.73m²), TV typical value, ω standard deviation of inter-individual variability, β, exponent of covariate effects on specific parameters (Supplementary S1: Equation S1), $\mathit{Te}$ scale parameter (years), $p$ shape parameter, RSE relative standard error, CV coefficient of variation

Fig. 3.

Representative Evaluation Plots of the Final Longitudinal Models Quantifying the Decline in estimated Glomerular Filtration Rate (eGFR) for ADTKD-UMOD and ADTKD-MUC1. The figure represents the visual predictive check plots for A. UMOD and B. MUC1. VPCs show the median (red dashed curves) and 10th and 90th percentiles (lower and upper blue dashed curves, respectively) of the predicted profiles. The shaded areas indicate the 90% confidence intervals of each of the percentile curves

Time-To-Event models predicting the ages of KF of patients with ADTKD

For both ADTKD-UMOD and ADTKD-MUC1 disease types, the Weibull hazard function was selected (Eq. 2). The AIC values for the Weibull and Gamma models were comparable. Specifically, the difference in AIC between the two models was approximately 2 units for UMOD and 3 units for MUC1. Given these marginal differences, the Weibull model was selected by jointly considering multiple evaluation metrics (e.g., enhanced VPC plots in stratification analysis) and improved clinical interpretability of covariates, compared to the Gamma model. (Supplementary S1: Table S1.2). The Weibull model consists of scale and shape parameters:

$$\text{h}=\left(\frac{p}{\mathit{Te}}\right)\times {\left(\frac{t}{\mathit{Te}}\right)}^{p-1}$$ 2

where $\mathit{Te}$ (years) is the scale parameter representing the age at which the survival probability is approximately 0.368 (~ 0.4) that was derived from the mathematical properties of the survival function [32] (Supplementary S1: Equation S3). The shape parameter p provides a direct clinical interpretation of the risk trend over time, indicating whether the risk increases (p > 1), decreases (p < 1), or remains constant (p = 1).

In UMOD, males reached Te approximately 4 years earlier than females on average (β_Te_Male = −0.07), and patients with older AFCV were associated with slower progression to kidney failure (β_Te_AFCV = 0.59 for UMOD and 0.81 for MUC1).

The final parameter estimates of the time-to-event models are summarized in Table 2B (Supplementary S2: Model Code 4 and 5). VPC for UMOD stratified by AFCV and sex (Fig. 4) and VPC for MUC1 stratified by AFCV (Fig. 5). The additional validation using the test data sets also showed reasonable predictive performance for the models (Supplementary S1: Figure S1.6 and Figure S1.7). The VPC plots demonstrate reasonable agreement between the observed and simulated data, effectively capturing the events. Some deviations are noted and acknowledged as limitations in the discussion. To improve the clarity and visibility of the plots, the VPC plots of initial age ranges were included in the main text, and the remaining plots were included in the supplementary material (Supplementary S1: Figure S1.5).

Fig. 4.

Visual Predictive Check Plots for Time-to-Event Model Predicting Age of Kidney Failure (KF), Stratified by Significant Covariates of ADTKD-UMOD. Kaplan–Meier curves for UMOD are shown in Indian red (females) and forest green (males) solid lines, representing observed data. Dots (navy blue, forest green) indicate right-censored data points. The shaded gray area represents the 90% confidence interval of the model prediction, while the solid lines (navy blue, forest green), age at first clinical visit (AFCV) represent the model-predicted median. The plots are stratified by sex and AFCV in 10-year increments

Fig. 5.

Visual Predictive Check Plots for Time-to-Event Model Predicting Age of Kidney Failure (KF), Stratified by a Significant Covariate of ADTKD-MUC1. Kaplan–Meier curves for MUC1 are shown in solid lines, representing observed data. Dots indicate right-censored data points. The shaded gray area represents the 90% confidence interval of the model prediction, while the solid lines, age at first clinical visit (AFCV) represent the model-predicted median. The plots are stratified by AFCV in 10-year increments

Discussion

Understanding the heterogeneity of disease progression in patients with ADTKD is essential for efficient drug development. To our knowledge, this is the first comprehensive quantitative analysis of covariate effects that may influence the rate and severity of ADTKD progression by utilizing natural history data. In this study, we developed ADTKD-UMOD and ADTKD-MUC1 models that quantify the longitudinal progression of eGFR with age and time-to-event models that predict the age of KF. By applying the nonlinear mixed-effects modeling approach, the associated covariate effects were quantified simultaneously, focusing on the patient baseline characteristics that can be collected at screening visits.

Between the two ADTKD disease types, the typical value of the eGFR decline steepness parameter ${\gamma }_2$ (Hill coefficient) for patients with ADTKD-MUC1 was higher (i.e., 10.23) than for ADTKD-UMOD (i.e., 6.34), whereas ${\gamma }_1$ for ADTKD-UMOD and ADTKD-MUC1 is 1.12 and 0.9. These findings are consistent with those published by Olinger and Devuyst et al. that patients with ADTKD-MUC1 have a more severe kidney disease with a higher prevalence of KF and an earlier onset of KF compared to patients with ADTKD-UMOD [5]. From the pathophysiological view of tubular damage, MUC1 affects both the ascending loop of Henle and the collecting duct of the nephron, compared to UMOD, which affects only the ascending loop of Henle. In addition, the extrapolated value of eGFR at 18 years of age was slightly higher in MUC1 (i.e., the estimated typical value of $DP0$ were 76.69 ml/min/1.73 m² for UMOD and 82.74 ml/min/1.73 m² for MUC1).

It was challenging to explain the variability in the eGFR decline among individuals at different stages of disease progression in the various age groups. The decline rate of eGFR changes continuously with age. This rate is influenced mostly by the steepness of the curve, which is governed by the Hill coefficient parameters, ${\gamma }_1$ and ${\gamma }_2$. Other model structural parameters, i.e., DPT₅₀ and DP_max, also affect the change in the longitudinal trajectories of eGFR decline, along with ${\gamma }_1$ and ${\gamma }_2$. In prior work in other disease, accounting for baseline covariate values and baseline ages of individuals helped quantify the substantial variability that was encountered; hence, this approach was taken for the current work in ADTKD [32–35]. So, here the eGFR_FCV measures and AFCV of the ADTKD patients were added as additional covariates in both the UMOD and MUC1 models, and subsequently each played a major role in explaining the between-subject variability. For UMOD base model, ω values estimated on parameters DPT₅₀, ${\gamma }_1,{\gamma }_2$, DP0 were estimated as 0.3, 0.7, 1, 0.3. After accounting for covariates, ω values are reduced to 0.07, 0.8, 0.1, but ${\gamma }_1$ increased to 1.25. For MUC1 base model, ω values were estimated on parameters DPT₅₀, ${\gamma }_1,{\gamma }_2$, DP0 as 0.3, 0.7, 0.6, 0.2. After accounting for covariates, ω values are reduced to 0.07, 0.2, 0.09 but ${\gamma }_2$ stayed at 0.6.

In the UMOD variant, among the tested covariates, eGFR_FCV and AFCV were the most significant covariates to inform the parameters ${\text{DPT}}_{50},{\gamma }_1,{\gamma }_2$ and DP0. Only eGFR_FCV (β_eGFR_FCV_ ${\text{DPT}}_{50}$) was a significant covariate on $DP0$, and though it was correlated, it can be used to explain disease severity in patients when they enter the study. Older AFCV (β_AFCV_ ${\text{DPT}}_{50}$) increases DPT₅₀ by 0.93 years (approximately 11 months), suggesting a slower initial decline in eGFR compared to younger individuals. Regarding the parameter ${\gamma }_1,{\gamma }_2$, patients with higher eGFR_FCV (β_eGFR_FCV_ $\gamma 1$) experience a decrease by 0.7, indicating a less steep decline in eGFR. Older AFCV (β_AFCV_ $\gamma 2$) increases ${\gamma }_2$ by 1.14, resulting in a steeper decline in eGFR as the disease progresses. For DP0, eGFR_FCV (β_eGFR_FCV_ $\text{DP}0$) of 1 indicates the proportional relationship between observed eGFR_FCV and the predicted value in the model, ensuring consistency between clinical observations and model predictions.

Whereas the minor G allele mutation in the promotor region of UMOD gene can downregulate uromodulin production by approximately 50% compared to the A allele [18]. Kidd and Bleyer et al. hypothesized that the presence of a minor allele leads to decreased expression of mutant UMOD (mUMOD), which results in a slower progression of CKD and the later development of end-stage kidney disease (ESKD) [18, 36]. This highlights the genetic contributions to disease; further population specific studies are essential to clarify this mechanism precisely. It is noteworthy to mention the long-term clinical observation that age of gout onset could be a significant covariate in the UMOD variant. Gast et al. reported that ADTKD-UMOD is characterized by the early onset of hyperuricemia and gout [1]. This is due to the impaired activity of the TAL-based Na⁺-K⁺−2Cl⁻ cotransporter and the upregulation of Na⁺-coupled urate co-transporters as a compensatory mechanism, which results in hyperuricemia [3]. However, due to the limited availability of patient data on the age of gout onset, we were unable to assess its significance. In summary, for UMOD, patients with higher baseline eGFR exhibit slower and less steep kidney function decline. Individuals with older baseline age experience slower progression initially, but the rate of decline ($\gamma$) steepens once they reach their inflection point.

In MUC1, among the tested covariates, eGFR_FCV and AFCV were the significant covariates in the parameters${\text{DPT}}_{50}$, ${\gamma }_1,{\gamma }_2$ and DP0$.$ Individuals with higher eGFR_FCV (β_eGFR_FCV_${\text{DPT}}_{50}$) increases DPT₅₀ by 0.04 years (approximately 0.5 months). Older AFCV (β_AFCV_${\text{DPT}}_{50}$) increases DPT₅₀ by 0.97 years (approximately 12 months). Regarding the parameter${\gamma }_1,{\gamma }_2$, patients with higher eGFR_FCV (β_eGFR_FCV_$\gamma 1,\mathrm{\beta }\_\text{eGFR}\_\text{FCV}\_\gamma 2$) experience a decrease in ${\gamma }_1$ by 0.7 and a decrease in ${\gamma }_2$ by 1.13. For DP0, eGFR_FCV (β_eGFR_FCV_$\text{DP}0$) of 0.96 (approximately 1) indicates the proportional relationship between observed eGFR_FCV and predicted values in the model, ensuring consistency between clinical observations and model predictions. SNP rs4072037 and age of gout were not significant covariates in MUC1. Olinger and Devuyst et al. reported that gout has significantly earlier-onset and is more prevalent in UMOD compared to MUC1 [5]. In summary, for MUC1, patients with higher eGFR_FCV experience slower and less steep kidney function decline, but the rate of decline (${\gamma }_2$) steepens once they reach their inflection point. Our analysis suggests that the initial decline in ${\gamma }_1$ for UMOD and MUC1 is similar. Once the inflection point is reached, MUC1 exhibits a significantly higher progression rate than UMOD via ${\gamma }_2$ (10.2 vs. 6.3), indicating that rapid progression occurs during the later stages.

As reported in Table 2, the UMOD model required a combined error model incorporating both additive and proportional errors to account for residuals. This approach was necessary to capture both a fixed amount of variability in predictions and variability that scales with the magnitude of eGFR. For UMOD, error estimates of 0.3 (additive) and 0.1 (proportional) indicate a lower degree of error, with the proportional error demonstrating a lower %RSE compared to the additive component. In contrast, the MUC1 model required only proportional error to explain variability, with a value of 0.1 indicating a low degree of error and lower %RSE compared to the UMOD model. Bootstrap results have been estimated and incorporated into the results section for all models. As noted in the MUC1 model, a few parameters specifically, β_eGFR_FCV_ ${\text{DPT}}_{50}$, β_AFCV_ $\gamma 2$, and the correlation parameters were found to be statistically indistinguishable from zero. The estimate for β_eGFR_FCV_ $\gamma 1$, for example, lies close to the lower bound of its 95% confidence interval.

Despite the limited magnitude of these effects (e.g., ~ 0.04 for β_eGFR_FCV_ ${\text{DPT}}_{50}$), their removal resulted in an increase in AIC by at least 10 points. Additionally, the correlation between $\gamma 1$ and DP0 is necessary to ensure consistency in model structure and enable meaningful comparison with the UMOD model. Removing these covariates suggested a decrease in explanatory power of the model. Given both the statistical contribution and the clinical rationale provided by these covariates, we have chosen to retain them in the final model, along with their associated uncertainty.

The Weibull hazard function parameters selected for the time-to-KF models have clinical interpretability. The parameter Te, representing the age at which approximately 36.8% of individuals remain free from KF, is estimated to be 54 years (ADTKD-UMOD) and 51 years (ADTKD-MUC1). At this age, approximately 36.8% (~ 0.368) (Supplementary S1: Equation S3) of individuals remain free from KF, indicating that 63.2% are expected to have experienced the event by this time. Olinger and Devuyst et al. reported a shorter median renal survival for MUC1 compared to UMOD. Furthermore, the age at which approximately 50% of individuals remain free from KF, is reported to be 50 years (ADTKD-UMOD) and 48.3 years (ADTKD-MUC1). The heterogeneity of KF/disease progression between ADTKD disease types is intriguing. For UMOD, the progression to KF is highly variable and occurs between the ages of 20 and 70 [36–38]. The shape parameter, p, was estimated at 8.69 and 6.82 for ADTKD-UMOD and ADTKD-MUC1, respectively.

We used the full modeling approach, considering both statistical and clinical significance, and conducted a separate covariate analysis with the UMOD and MUC1 time-to-event models using available covariates. In our analysis for UMOD, sex was found to have a statistically significant covariate effect on Te, represented by the parameter estimate β_Te_Male = –0.07. This suggests that being male is associated with a ~ 7% reduction in Te, the age at which approximately 36.8% of individuals remain free from KF. On average, males are expected to reach Te approximately 3.8 (~ 4) years earlier than females (i.e., around 50.4 years of age). Additionally, the estimated age at which 50% of individuals remain event-free was 50 years for females and 46.5 years for males. Male patients were found to reach KF earlier than females, consistent with findings reported by Bleyer et al. and Maskowitz et al. [18, 36].

For MUC1, sex was not a significant covariate influencing the time to KF. AFCV has a moderately higher influence (β_Te_AFCV = 0.81 vs. 0.59) in delaying KF in MUC1. This positive association indicates that individuals who are older at the time of their first clinical visit tend to experience KF at a later age. One possible interpretation is that delayed symptom onset in older individuals may reflect a slower rate of disease progression. Furthermore, an increase in the number of subjects with UMOD sub-mutation types may enhance the estimation of their effects in future analyses.

There are some limitations in our study. Due to a lack of individual-level data of a healthy control group, disease-driven eGFR decline that happens in addition to the natural age-associated eGFR decline was not separately quantified. The developed models cannot be used to simulate patients younger than 18 years of age because the model parameters were estimated using the data collected from patients who were at least 18 years old. There were no records about other treatment information for gout in the data set. Mutation in the promotor region of UMOD gene, which is SNP Rs4293393 as a covariate, needs to be studied more to understand its influence on disease progression. The number of patients with the G allele was comparatively lower (n = 12) than that of other alleles in this study. Due to the limited availability of patient data with G allele, we were unable to assess its significance. This study predominantly had the American white population as study subjects; the influence of other races on disease progression could be included in the future. Greater diversity of mutations and patients with these mutations would improve distribution of data; future studies with these data may lead to better characterization of the probability of KF events.

In the VPC plots for longitudinal model, we acknowledge that our models underpredicted the 10th percentile profiles, particularly for MUC1, which would affect predictive performance. The observed discrepancy between the 10th percentile of the model predictions and the observed data is likely due to inherent variability in the dataset. In the validation VPC (Supplementary S1: Figure S1.3) for the MUC1 model, however, the observed 10th percentile remains well within the 90% prediction interval, indicating acceptable model performance in this region. In the VPC for TTE models, we acknowledge that the model fit for UMOD males aged 59–72 years is less accurate. Additionally, the predicted survivor functions for females aged 59–72 years and males aged 49–58 years deviate from the observed event-time trajectories when compared to other age groups, which is likely due to the limited number of KF events within these specific age ranges (Supplementary S1: Table S1.3). Increasing the sample size, particularly by capturing more events in these subgroups, may help improve model performance and address this limitation in future studies. The models accounted for variability explained by the available covariates and provided insights into the disease trajectory. We emphasize and acknowledge that a few parameter estimates (β_eGFR_FCV_ ${\text{DPT}}_{50},\mathrm{\beta }\_\text{AFCV}\_\gamma 2$, correlation) for MUC1 carry a degree of uncertainty, which should be taken into consideration when interpreting the model results.

In conclusion, the developed models demonstrated a satisfactory ability to predict the longitudinal decline in eGFR trajectories and time to KF using clinical characteristics for patients with ADTKD-UMOD and ADTKD-MUC1. These models were validated using a series of evaluation criteria for their reliability and robustness. The developed models will be the basis of a clinical trial simulation platform that can be used to optimize study designs, such as inclusion/exclusion criteria, trial duration, and sample size. Through simulation, prior to actual clinical trial execution, valuable insights that optimize trial success may be achieved for ADTKD.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

S.S.R, M.R., K.K, A.W. A.J.B., and S.K. wrote manuscript, M.R., J.R., K.B., A.J.B., and S.K. designed the research, S.S.R., A.W., D.Y.Y., and S.K. performed the research, S.S.R., M.R., K.K, A.W., D.Y.Y, J.R., K.B., A.J.B., and S.K. analyzed data, and S.S.R., A.W., D.Y.Y., and S.K. contributed new reagents/analytical tools.

Funding

Sail Bio, Inc. Cambridge, MA, USA (P0270000). A.J.B. has been supported by the Black Brogan Foundation, Slim Health Foundation, and Soli Deo Gloria Foundation.

Data availability

Data is provided within the manuscript or supplementary information files.

Declarations

Conflict of interest

The authors declare no competing interests.