In our retrospective study, a total of 41 PMN patients who received RTX treatment from March 2019 to December 2021 at Department of Nephrology, Peking University Third Hospital were included. Most patients received monthly mini-dose of 100 mg RTX, whereas some of them received 200–500 mg RTX for a few months with the intention to better control disease progress. Due to COVID-19 epidemic, part of patient population experienced a gap up to 10 months and received RTX infusion again afterwards. The trial was consistent with the Good Clinical Practice (GCP) standards and was registered at Chinese clinical trial registry (ChiCTR2200057381).

The trough and peak RTX blood samples were collected before and after RTX infusion, respectively. RTX concentrations were detected by ELISA kit purchased from Abcam (Cambridge, MA, United States). RTX PK observations below the limit of quantification (3 ng/mL) were excluded from the analysis. CD20⁺ B cell count was measured before every RTX intravenous (IV) infusion. CD20⁺ B cell depletion was defined as an absolute count < 5/μL in peripheral blood (Cravedi et al., 2007). Serum anti-PLA2R titer was assessed by an ELISA kit purchased from Euroimmune, Lubeck, Germany.

PPK/PD models were constructed by nonlinear mixed-effects modeling methods to describe the PK characteristics and variability for RTX concentration and CD20⁺ B cell count (Supplementary Figure S1). The observed RTX concentrations were converted to molar units. The CD20⁺ B cell counts were transformed to CD20 concentration in molar units by multiplying 94000 CD20 molecules per cell and dividing by Avogadro’s constant (Ginaldi et al., 1998).

A total of four structural PPK models were developed as follows. At first, a basic two-compartment model was constructed as reported by many previous studies that is characterized by linear elimination (Ng et al., 2005; Regazzi et al., 2005; Li et al., 2007; Blasco et al., 2009). Based on the basic two-compartment model, two additional models were constructed with nonlinear elimination approximation described by Michaelis-Menten elimination (Tout et al., 2017) and time-varying elimination (Li et al., 2012), respectively. Finally, a mechanistic target-mediated drug disposition (TMDD) model with quasi-steady-state (QSS) approximation was constructed. In this model, the free RTX in central compartment is directly eliminated by a first-order elimination rate constant (k _el ). In addition, central compartment RTX distributes to and from peripheral compartment by first-order distribution rate constant k _pt and k _tp , respectively. In plasma, RTX binds to CD20 antigen (R) with a second-order rate constant (k _on ) to form drug-receptor complex (RC), whereas RC dissociates at a first-order rate (k _off ) and internalizes for degradation (k _int ). CD20 is reported to be a non-internalizing receptor, and the elimination of CD20 and the subsequent depletion of CD20⁺ B cells is thought to be via ADCC and CDC effect (Boross and Leusen, 2012). Thus, the internalization rate constant k _int was replaced by the RTX-CD20 complex target-mediated elimination rate constant (k _tmd ), which is assumed to be the maximal rate of elimination observed for mAbs in clinical use (Glassman and Balthasar, 2017). On the other hand, CD20⁺ B cell is synthesized at a zero-order rate (k _syn ) and degraded at a first-order rate (k _deg ) in the absence of RTX binding. Due to its non-internalization character, the turnover rate of CD20 was assumed to be similar to the disappearance rate of B cells from circulation (∼3.9% per day) (Macallan et al., 2005). The RTX-CD20 complex elimination rate constant (k _tmd ) is much greater than the dissociation rate constant k _off (Bondza et al., 2017). Thus, QSS approximation of TMDD model was used, where QSS constant k _ss is defined as the sum of dissociation constant k _D and the quotient of k _tmd and dissociation rate constant (k _off ) (Gibiansky et al., 2008). Models were evaluated with objective function value (OFV), while the model with the lowest OFV and better fitting of the diagnostic plots was selected as structural model.

Between-subject variability (BSV) was modeled in an exponential form (Eq. 1): P i = T V P × e η i (1) where P i is the ith individual value of the parameter; TVP is the typical value of the population parameter; η _i is the empirical Bayes estimates of BSV for the ith individual that is normally distributed with mean zero and variance ω².

The residual variabilities were assessed as an error model in a proportional form (Eq. 2): C i j = C i j ∧ × 1 + ε p r o (2) where C i j and C i j ∧ is the ith observed and predicted concentration for the jth individual, respectively; ε p r o is the proportional error component that is normally distributed with mean zero and variance σ².

Covariates with high correlation (correlation coefficient > 0.3) were taken into consideration for further the covariate analysis, including age, sex, eGFR, etc. Continuous and categorical covariates were established by a power function and a linear function (Eqs 3, 4), respectively: P i = θ 1 × C o v c o n C o v m e d i a n θ 2 (3) P i = θ 1 × 1 + θ 2 × C o v c a t (4)

Where P _i is the parameter for the ith individual; C o v c o n and C o v c a t is the value of continuous and categorical covariate for the ith individual, respectively; θ 1 is the typical value for the population parameter; θ 2 is the estimated value for the covariate effect.

If two or more covariates were highly correlated, only the most clinically and practically relevant covariate was tested on the PK parameter in the analysis. These covariates were further screened using the SCM implemented in PsN.

Goodness-of-fit (GOF) plots were used to evaluate the final model, which defined as the combination of four plots including the observed concentration (DV) versus the population predicted concentration (PRED) or individual predicted concentrations (IPRED) and conditional weighted residuals (CWRES) versus PRED or time. The predictive performance of the final model was evaluated using visual predictive checks (VPCs), which were repeated 1000 times to compare the DV data and simulated value with the 95% confidence intervals for the 5^th,50th and 95th percentiles.

The results of bootstraps with 500 replicates were finally used to assess the final model. The RSEs of the parameter estimates and the condition number of the model were also considered.

Using the established model, we carried out simulations for both standard dosage and monthly mini-dose to predicted RTX concentrations and CD20⁺ B cell counts under different regimen groups. In addition, mini-dose with larger infusion interval was also simulated.

To explore the relationship between CD20⁺ B cell counts and anti-PLA2R titer, the individual anti-PLA2R titer data at descending stage was extracted, while serology relapse data that was defined as two consecutive ascending anti-PLA2R titer data was excluded. Anti-PLA2R titers detected with interval longer than 3 months or after 12 months since the first RTX infusion were excluded as well. The anti-PLA2R titer data was plotted versus time and described using an exponentially decrease function (Eq. 5). For patients experienced relapse and second round of anti-PLA2R reduction, two exponentially decrease functions using respective data were used. a n t i − P L A 2 R   t i t e r = A × e − k e , P L A 2 R × t (5)

Non-compartmental analysis was conducted for the simulated results using typical PK parameters. The area under the concentration-time curve (AUC), the elimination half-life (t_1/2), the apparent clearance (CL/F) and apparent volume of distribution during the terminal phase Vz (Vz/F) were determined.

All the modeling and simulation were carried out with the first order conditional estimation method with interaction that is implemented within NONMEM 7.2 and aided by PsN. The dataset was treated and processed by R package. Pirana was used for documentation of the development process. Non-compartmental analysis was conducted using Phoenix WinNonlin V8.3.3 (Certara, Princeton, NJ, United States).

A summary of subject demographic characteristics is shown (Table 1). A total of 31 male (75.6%) and 10 female (24.4%) patients were enrolled. The ages of the patients ranged from 19 to 76 years, with weight ranging from 50 to 101 kg (75.3 ± 11.3 kg). The albumin concentration and urine protein at baseline is 25.8 ± 5.7 g/L and 8.0 ± 3.6 g/day, respectively. The anti-PLA2R antibody titer ranged from 5.4–2695 U/mL (260.3 ± 453.2 U/mL), while 17 patients had a high anti-PLA2R antibody titer (>150 U/mL). The ratio of CD19⁺ B cell depletion at month 3 was 80% (33/41). The mean follow-up period was 15.9 (6–44) months. The cumulative dose of rituximab at month 6, month 12 and last follow-up was 578 ± 350, 923 ± 544 and 1060 ± 705 mg, respectively. The urinary protein levels decreased and serum albumin levels increased gradually after rituximab treatment, while the eGFR remained relatively stable. The remission rate was 21.2% (7/33) with 0% complete remission (CR) at 3 months, 50% (19/38) with 5.3% CR (2/38) at 6 months, 72.7% (24/33) with 18.2% CR (6/33) at 12 months, and 81.6% (30/38) with 28.9% (11/38) CR at last follow-up, respectively. Rate of relapse was 7.9% (3/38) at last follow-up.

A total of 171 RTX concentration, 220 CD20⁺ B cell count and 276 PLA2R titer data from 41 PMN patients were collected. Most patient receive multiple doses of 100 mg RTX infusion with at least 1 month apart, while part of them received 200–500 mg RTX infusion.

Four PPK models were constructed to describe RTX PK profile, including two-compartment model with linear, time-varying and Michaelis-Menten. An additional PPK/PD model described by TMDD model with QSS approximation was established. Among four models, TMDD model best captured the RTX concentration and CD20⁺ B cell count profile with lowest OFV (Supplementary Table S1), and was thus selected as structural model. The model has included both specific elimination (k_tmd) and non-specific elimination (k_el). The contribution of both proteolysis and urinary loss have been considered in our model, although it is difficult to exactly evaluate their respective contribution due to limited data.

More than 30 baseline physiological parameters were used for covariates screening. Notably, covariates have been identified for RTX in many other diseases, such as body weight, sex, age on clearance and body surface area on central volume (Wang et al., 2020). However, no covariates were identified in our study. Thus, the final model was replaced by the base structural model and the results of estimated model parameters were presented (Table 2).

The goodness-of-fit diagnostic plots of the final model were shown (Figures 1, 2). There was no obvious bias in the model fitting. The VPC and bootstrap results suggested that the model adequately describe the both the RTX concentrations and CD20⁺ B cell counts (Supplementary Figure S2). The general trend and the observed variability were well captured.

Mechanically, anti-PLA2R antibody is excreted by plasma cells, which is in turn transformed from activated B cells that express CD20, and eliminated through catabolism. Thus, once CD20⁺ B cells are depleted by RTX, the plasma B cell count slowly decreases and the production of anti-PLA2R is halted, leading to the subsequent decrease of anti-PLA2R titer. However, we failed to establish the quantitatively relationship between CD20⁺ B cell counts and anti-PLA2R titers. The major reason is that monthly (or even longer) monitor of CD20⁺ B cell counts is incapable to capture the descending process of CD20⁺ B cells as they are rapidly depleted in peripheral blood within 72 h after receiving RTX. Thus, the majority of CD20⁺ B cell count data was obtained either before RTX administration or after depletion (mostly 0/μL) (Supplementary Figure S3A). In addition, the relationship between the recovery of CD20⁺ B cell count and anti-PLA2R titer is controversial. The reemergence of CD20⁺ B cell may be followed either by the increase of anti-PLA2R titer (Supplementary Figure S3B) or not (Supplementary Figures S3C, D). Accordingly, these data are also helpless for modeling.

The anti-PLA2R titers of 36 in all 41 patients were analyzed without the integration of CD20⁺ B cell count. Notably, we found that the anti-PLA2R titer data can be well described using an exponentially decrease function whose R ² > 0.8 for all patient except one (R ² = 0.67). The function is parameterized with initial anti-PLA2R titer and individual elimination constant k _e,PLA2R , which is independent of CD20⁺ B cell counts. The mean k _e,PLA2R is 0.033 ± 0.017, corresponding to the mean half-life 21 days, similar with typical IgG4 antibody half-life. Similar phenomena were also observed in previous studies treated with standard dosage, where the k _e,PLA2R is 0.025 with a R ² of 0.98 using titers in the first 3 months (Ruggenenti et al., 2015). We conducted Pearson correlation analysis to explore the physiological factor that influence k _e,PLA2R . Unfortunately, no significant relationship (Pearson correlation coefficient > 0.7) was identified.

The simulations were carried out to compare the efficacy of standard dosage 1 (four weekly infusions of 375 mg/m2), standard dosage 2 (two 1000 mg infusion with 2 weeks apart) and mini-dose (six monthly 100 mg). RTX rapidly achieve peak concentration at 215, 332, and 39 μg/mL, whereas the trough concentration collected 1 week after first infusion is 52, 118 and 7.8 μg/mL for standard dosage 1, standard dosage 2 and mini-dose, respectively (Figure 3). The apparent clearance and half-life are 0.54 L/day and 14.7 days, respectively, as calculated by non-compartmental analysis for monthly mini-dose.

CD20⁺ B cell depletion was used as a surrogate for clinical efficacy, since the decrease of anti-PLA2R titer occur shortly after the depletion and is independent of B cell recovery as demonstrated above. One the other hand, B cell recovery can be regarded as a marker for safety since it is related with reduced infection incident, which is the predominate adverse effect of RTX in PMN treatment. Though the concentration is much lower for mini-dose, the ability to deplete CD20⁺ B cell is similar (Figure 4). Under all three dosages, the depletions of CD20⁺ B cells occur within 24 h, and slowly recover after last dose. Notably, the duration of depletion is longer for mini-dose than standard dose. CD20⁺ B cell count increases back to more than 5/μL in ∼ 5.5 months for both standard dosages after first infusion, while the depletion can last for more than 7 months for mini-dosage. On the other hand, it takes shorter time for mini-dosage to recover back to normal (90% of baseline CD20⁺ B cell count) than standard dosages (10 months vs 12 months after last dose). Thus, the mini-dose outperforms standard dose with lower total doses (600 mg vs 2000–2400 mg), longer depletion duration (7 months vs 5.5 months) and faster recovery (10 months vs 12 months).

To explore the possibility to further reduce the dosage with larger interval, we simulated the RTX concentration and CD20⁺ B cell count receiving 3 doses of 100 mg every 2 months. Although the RTX concentrations and time for CD20⁺ B cell depletion remain the same with monthly mini-dose in the first week, the duration of CD20⁺ B cell depletion is largely reduced. The median CD20⁺ B cell count increases up to more than 5/μL in less than 2 months. Thus, 100 mg every 2 months dosage is insufficient for long time CD20⁺ B cell depletion and thus should not be recommended for PMN treatment.