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 \(_\) (Hill coefficient) for patients with ADTKD-MUC1 was higher (i.e., 10.23) than for ADTKD-UMOD (i.e., 6.34), whereas \(_\) 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, \(_\) and \(_\). Other model structural parameters, i.e., DPT50 and DPmax, also affect the change in the longitudinal trajectories of eGFR decline, along with \(_\) and \(_\). 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 [32,33,34,35]. 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, \(_, _\), 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 \(_\) increased to 1.25. For MUC1 base model, ω values were estimated on parameters DPT50, \(_, _\), 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 \(_\) 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 \(}_,_, _\) and DP0. Only eGFR_FCV (β_eGFR_FCV_ \(}_\)) 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_ \(}_\)) increases DPT50 by 0.93 years (approximately 11 months), suggesting a slower initial decline in eGFR compared to younger individuals. Regarding the parameter \(_, _\), 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 \(_\) by 1.14, resulting in a steeper decline in eGFR as the disease progresses. For DP0, eGFR_FCV (β_eGFR_FCV_ \(\text0\)) 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\(}_\), \(_, _\) and DP0\(.\) Individuals with higher eGFR_FCV (β_eGFR_FCV_\(}_\)) increases DPT50 by 0.04 years (approximately 0.5 months). Older AFCV (β_AFCV_\(}_\)) increases DPT50 by 0.97 years (approximately 12 months). Regarding the parameter\(_, _\), patients with higher eGFR_FCV (β_eGFR_FCV_\(\gamma 1,\upbeta \_\text\_\text\_\gamma 2\)) experience a decrease in \(_\) by 0.7 and a decrease in \(_\) by 1.13. For DP0, eGFR_FCV (β_eGFR_FCV_\(\text0\)) 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 (\(_\)) steepens once they reach their inflection point. Our analysis suggests that the initial decline in \(_\) for UMOD and MUC1 is similar. Once the inflection point is reached, MUC1 exhibits a significantly higher progression rate than UMOD via \(_\) (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_ \(}_\), 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_ \(}_\)), 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 [36,37,38]. 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_ \(}_,\upbeta \_\text\_\gamma 2\), 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.