All patients included in the intention-to-treat (ITT) analysis set (ITT correction phase) were assessed (n = 2369), with a total of 25,764 serum K+ observations. Serum K+ concentrations measured more than 240 h (10 days) after the last intake of experimental drug (active or placebo) were not included in the analysis (12 observations). Three serum K+ observations were considered to be outliers [extreme values based on the standard deviation (SD) of serum K+ for each patient] and were excluded from the analysis. For the longer clinical studies (ZS-005 and D9482C00001), the observations beyond 28 days from the start of maintenance dosing were excluded.

Patients’ baseline demographics and characteristics are presented in Table 1. Overall, the mean (SD) patient age was 66.0 (12) years, 61% were male, 68% were White, 34% had CHF, and 62% had diabetes. Mean (SD) serum K+ at baseline was 5.49 (0.43) mmol/L.

Between-study differences in patient race resulted in differences in baseline clinical characteristics. Body weight and rates of CHF were lower in the three studies that predominantly or exclusively enrolled Asian patients (D9480C00002, D9482C00001, and D9482C00002; Table 1).

The distributions of continuous and categorical covariates in the SZC dataset are shown in Supplementary Fig. S1. No continuous covariates were sufficiently correlated to cause concern for model estimation, and no continuous characteristics appeared to covary with categorical groups (except for the effect of Asian race as described above).

A semi-mechanistic longitudinal mixed-effects model was used to describe serum K+ concentration after SZC dosing. Parameter estimates and their precision for the base model are presented in Table 2.

Shrinkage in ETA (the discrepancy of an individual parameter from the typical population value, a distribution of mean of 0 and variance OMEGA; 18.9% Kin and 35.2% EC50) and EPS (random variability associated with individual observations, a distribution with a mean of 0 and variance SIGMA; 5.1%) were reasonable.

Inspection of model diagnostics showed that the model described the data adequately. GOF plots showed no bias in predictions across serum K+ value, time, or dose in the stable regimen studies or in those using maintenance dose titration (Supplementary Figs. S2 and S3).

Parameter estimates of the final covariate model are presented in Table 2. The sigmoid Emax exposure response was characterized by a high value for the EC50 (32.8 g) and a Hill coefficient of 1.36.

Inspection of model diagnostics showed good agreement between the observed data and the model. Specifically, GOF plots showed no bias in predictions across serum K+ value, time, or dose in the stable regimen studies or in those using maintenance dose titration (Supplementary Figs. S4 and S5). The full model empirical Bayesian estimates of the random effect on Kin (ETA1) and EC50 (ETA2) were consistent across the categorical and continuous covariates studied, including correction and maintenance phase dose (Supplementary Fig. S6), and shrinkage in ETA (16.4% Kin and 46.5% EC50) and EPS (4.7%) remained reasonable.

The model was deemed acceptable for use in dose–response simulation and the empirical Bayesian estimates appropriate for covariate impact analysis. VPCs are shown in Supplementary Figs. S7 and S8.

From the base model to the full covariate model, most parameters remained similar or decreased (between patient and residual variance); however, the estimate of EC50 increased from 15.3 to 32.8 g and the estimate of Emax increased from 43.4 to 63.3%.

The predicted placebo-adjusted dose–response of serum K+ changes from baseline at 48 h and 4 weeks are shown in Fig. 2. In the correction phase, the predicted placebo-adjusted dose–response of serum K+ change from baseline after 48 h appeared nearly linear. In the maintenance phase, the predicted placebo-adjusted dose–response for a regimen of SZC 10 g TID dosing for 48 h followed by 0–15 g QD for 4 weeks appeared nearly linear at 28 days.

Predicted dose–response in the SZC correction and maintenance phases. CFB change from baseline, CI confidence interval, K+ potassium, QD once daily, SZC sodium zirconium cyclosilicate, TID three times a day. Graphs: Predicted population average (line) with 95% CI (shaded region). Table: Correction phase predictions were calculated using a TID regimen and the maintenance phase predictions were calculated based on a regimen of SZC 10 g TID for 48 h, followed by SZC 10 g QD for 28 days. The CI was determined by simulating 500 virtual trials of 1000 patients each, calculating the mean population dose–response and distribution, from which the 2.5 and 97.5% quantiles were determined

Dosing regimens in the correction and maintenance phase had similar predicted serum K+-lowering behavior based on predicted placebo-adjusted change from baseline (Fig. 2). No clinically meaningful difference in placebo-adjusted serum K+ change from baseline at 28 days was observed between maintenance regimens of SZC 5 g QOD and 2.5 g QD [− 0.19 (95% CI − 0.23 to − 0.14) versus − 0.17 (95% CI − 0.21 to − 0.13), respectively]. Simulated individual trajectories and median serum K+ over time after 48 h with 10 g TID followed by 4 weeks of 0–15 g QD are shown in Fig. 3.

Simulated serum K+ time course after 48 h of SZC 10 g TID dosing followed by 4 weeks of dosing with placebo (0 g), or SZC 5, 10, or 15 g QD. K+ potassium, QD once daily, SZC sodium zirconium cyclosilicate, TID three times a day. Individual data are shown in yellow (subset of 100 patients). Median (red solid line), 25 and 75% quantiles (red dashed lines), and 5 and 95% quantiles (red dotted lines) are based on 1000 simulated patients, with model uncertainty and residual variability

The full covariate modeling approach considered the following covariates: five on EC50: baseline serum K+, age, body weight, eGFR, and race; four on placebo (Kin) response: baseline serum K+, eGFR, heart failure, and diabetes; and one on serum K+ dynamics (Kout): sex.

The impact of covariates on the predicted 48 h and 28 day serum K+ placebo-adjusted treatment response (change from baseline) relative to the reference patient is displayed in Fig. 4. Greater SZC treatment response is associated with high baseline serum K+, more advanced age, lower body weight, lower eGFR, and Black/African American and Asian race, compared with the reference patient.

Predicted serum K+ change from baseline for selected covariates for the correction phase (48 h 10 g TID) and maintenance phase (48 h 10 g TID followed by 4 weeks 10 g QD). CHF congestive heart failure, eGFR estimated glomerular filtration rate, K+ potassium, QD once daily, SZC sodium zirconium cyclosilicate, TID three times a day. The vertical black line in each panel represents the placebo-adjusted treatment response of SZC 10 g for the reference patient: a nondiabetic, non-CHF, White male, 65 years of age, with eGFR of 45 mL/min/1.73 m2, body weight of 85 kg, and baseline serum K+ of 5.4 mmol/L. Dashed lines in each panel display the SZC 5 and 15 g placebo-adjusted treatment response in the reference patient

The placebo-adjusted predicted serum K+ changes from baseline of SZC 10 g TID for the 10 and 90% quantile of baseline serum K+, age, and body weight were all within the range defined by the SZC 5 and 15 g response of the typical patient (− 0.21 to − 0.76 mmol/L). A stronger impact was observed for eGFR with SZC treatment response, predicted to be − 0.37 mmol/L and − 0.71 mmol/L for patients with eGFR of 88 mL/min/1.73 m2 and 17 mL/min/1.73 m2, respectively, compared with −0.48 mmol/L for the reference patient with eGFR of 45 mL/min/1.73 m2. Point estimates for Black/African American race (− 0.69 mmol/L) and Asian race (− 0.55 mmol/L) were likewise estimated within the 5–15 g range of the reference patient response.

The impact of heart failure status and diabetes status was very minor, with a predicted placebo-adjusted change from baseline of − 0.48 and − 0.49 mmol/L, respectively, compared with − 0.48 mmol/L for the reference patient who had neither medical condition. Taken together, the predicted treatment responses suggest that no SZC dose adjustment is needed for the intrinsic and extrinsic covariates considered.