Pharmacodynamics of rituximab on B lymphocytes in paediatric patients with autoimmune diseases

Aims Rituximab is a chimeric IgG‐1 monoclonal antibody that depletes B cells, aiding in the treatment of several conditions including autoimmune diseases. It is not licensed for use in children. This study aimed to quantify the B cell‐related pharmacodynamics of rituximab in children with autoimmune disease. Methods Routine electronic health record data were collected at a large paediatric tertiary hospital in London, UK. Dosing protocols were either 2 × 750 mg/m2 intravenous infusions of rituximab on days 1 and 15, or 4 × 375 mg/m2 infusions on days 1, 8, 15 and 22. Rituximab pharmacokinetics (PK) were not measured but CD19+ lymphocyte counts were taken before and after rituximab treatment. A dose–response model was constructed describing the life cycle of CD19+ lymphocytes, with rituximab assumed to increase the death rate. Rituximab effect was assumed to decay by first‐order kinetics. Results In total, 258 measurements of CD19+ lymphocyte counts were collected from 39 children with 8 autoimmune diseases. The elimination rate constant (% relative standard error) of rituximab effect decay was 0.036 (22.7%) days−1 and CD19+ turnover was 0.02 (41%) days−1 corresponding to half‐lives of 19 and 35 days respectively. Rituximab increased CD19+ death rate 35‐fold, with methotrexate and cyclophosphamide associated with further increases. Simulations suggested that a single infusion of 750 mg/m2 provides similar 6‐month suppression of CD19+ lymphocytes to current dosing. Conclusions Rituximab pharmacodynamics (PD) in paediatric autoimmune diseases has been described. Compared with rituximab alone, the additional effect of methotrexate or cyclophosphamide was statistically significant but small.

neutrophil cytoplasmic antibody-associated vasculitides. 1 Rituximab is not licensed for use in paediatric patients but has been administered off-label for autoimmune diseases such as juvenile systemic lupus erythematosus and lupus nephritis, anti-neutrophil cytoplasmic antibody-associated vasculitis, and rheumatoid factor positive juvenile idiopathic arthritis as well as nephrotic syndrome before and after transplantation and for induction and prophylaxis in antibody incompatible transplantation. Rituximab doses are individually adjusted by body surface area, although the impact of different doses and disease control in paediatric autoimmune disease is unknown.
Rituximab functions through depleting B cells that are considered to be major players in regulating immune responses to pathogens and autoantigens, 2 and hence has been used for controlling a range of B-cell malignancies including autoimmune diseases. The mechanism of action of rituximab is specific binding to the cluster of differentiation (CD) 20 antigen on the surface of B cells, which is a differentiation marker exclusively expressed in mature B cells. 3 In addition, rituximabmediated B lymphocyte clearance may act via a number of mechanisms, including complement-mediated toxicity, antibodydependent cell-mediated cytotoxicity, inhibition of cell proliferation and induction of apoptosis. 3 In assessing B cell counts, it is usual that CD19 surface antigens are measured, as CD19 is expressed continuously from the early pre-mature B cells to the early stages of plasma cell differentiation. 2 A single course of rituximab administration consists of 2 sets of intravenous infusions at 750 mg/m 2 given twice 2 weeks apart or 4 weekly infusions of 375 mg/m 2 given weekly. Treatment courses may be repeated based on clinical response. After administration, like most monoclonal antibodies, rituximab distributes and binds to FcRn receptors on the surface of endothelial cells to be protected from lysosomal degradation, which results in a long elimination half-life. 4 Following rituximab treatment, the B-lymphocyte depletion effect occurs rapidly, within 2 weeks, and persists for up to 6 months. 5,6 Whilst rituximab appears on the 2015 World Health Organisation Essential Medicines List, it costs £3493 per course in the UK 7 and adds to the financial burden facing the National Health Service (NHS).
Biosimilars of rituximab are now available with the cost savings of at least 10%. 8  For these patients, data on concomitant medications, basic demographics (diagnoses, age, sex) and CD19+ lymphocyte counts in peripheral blood measured by flow cytometry were collected. Ethical approval without the need for parent and patient consent was obtained for the retrospective analysis of the de-identified data (17/LO/0008).  Figure 1.

| Population kinetic-PD modelling
Equations for the K-PD model are written as below: (1) Here, A 1 has initial conditions of 0, with addition of a dose amount in mg added with every dose event, and k e representing elimination What is already known about this subject • Rituximab is unlicensed for paediatric autoimmune diseases, but frequently used off-label.
• Rituximab pharmacokinetics have been described in children in oncology, but few pharmacokinetic or pharmacodynamic data are available in children with autoimmune diseases.
What this study adds • The turnover half-life of CD19+ lymphocytes and drug effect decay were similar in paediatric patients with autoimmune diseases than those observed in other populations.
• Current dosing schemes could be reduced by half and still give a similar degree of CD19+ suppression rate constant of rituximab effect, k in : production rate of CD19+ lymphocytes, k out : elimination rate constant of CD19+ lymphocytes, E max : maximum increase in cell elimination rate in the presence of rituximab, ED 50 : dose at which produces 50% of the maximum effect, A 2 represents CD19+ lymphocytes. In the absence of rituximab at steady-state the baseline CD19+ count is given by k in /k out and we estimated baseline and k out as parameters, from which k in was derived.
The baseline parameter was used to initialize the CD19+ lymphocytes compartment. NONMEM code is provided in the supplementary material. Proportional, additive and combined additive and proportional residual error models were tested.
The following covariates were tested on the K-PD model parameters: age, sex and comedications (methotrexate, cyclophosphamide, azathioprine or mycophenolate mofetil). Other concomitant immunosuppressants were not considered since they were either taken by all patients (e.g. prednisolone or methylprednisolone) or by very few patients (e.g. 2 patients on tacrolimus) and their effects on CD19+ lymphocytes were unable to be identified. Since B-cell count is expected to fall with age, 10 asymptotic decrease in CD19+ lymphocyte production rate over age was examined via adding age on the k in parameter. Whether female children possessed higher CD19+ lymphocyte production rate was also tested. 10 Individual comedications were considered to increase apparent E max or to decrease apparent ED 50 .
A covariate was considered statistically significant when the reduction in -2log likelihood of the model was >3.84 for an additional 1 degree of freedom at the significance level of 0.05 using the likelihood ratio test. 11 CD19+ lymphocyte counts reported as zero were set to 5 × 10 6 Table 1. In total, 108 were reported as zero and so replaced with 5 × 10 6 /L (LLOQ/2).

| Population K-PD modelling
The M3 method was unstable and successful minimization was not achieved. The final structural model therefore employed the M6 method with LLOQ/2 to handle the zero counts, with a proportional residual error model best describing residual variability. A comparison of the observed data plotted against time after last rituximab dose compared with the population and individual predictions is given in Figure 2 and a VPC including prediction of the fraction of data below 10 × 10 6 /L is given in Figure 3. Further diagnostic plots, and NONMEM code of the final model are provided in the supplementary material.   Table 3.

| DISCUSSION
To our knowledge, this is the first study to investigate and quantify the PD of rituximab on CD19+ lymphocytes in paediatric patients.
The proposed K-PD model with turnover mechanism gave a good description of the life span of CD19+ lymphocytes after rituximab treatment (Figures 2, 3), with CD19+ lymphocyte counts measured from children with multiple autoimmune diseases. Our major finding is that a similar peripheral blood CD19+ lymphocyte response could be achieved using lower doses than at present, with a single 750 mg/m 2 dose producing >80% of the CD19+ lymphocyte suppression time as doubling the dose (Table 3). Since dosing also depends on other clinical measures (including adverse events such as opportunistic infection; off target effects such as neutropenia; and impact on disease activity) that were not available in our data, whether dose reductions are feasible based on these requires further investigation.
Another use of our model could be in assessment of the effect of rituximab biosimilars in paediatric populations.
Both methotrexate and cyclophosphamide were found to increase the maximum killing effect significantly, and age and sex did not affect the individual difference in CD19+ lymphocyte suppression following rituximab treatment. Through simulations, a single infusion of lower rituximab dose was able to suppress CD19+ lymphocytes to a mostly identical extent within 10 weeks and the suppression effect remained similar within 6 months ( Figure 4).
We did not measure rituximab concentrations in the study, and hence modelled a dose response, the so-called K-PD approach. 15 However, our model did estimate an apparent decay in rituximab effect, which it could be hypothesized might be similar to rituximab's half-life.
In adult patients with rheumatoid arthritis, a 2-compartment PK model with first-order elimination described the time course of rituximab serum concentrations, 16  and the value was consistent with these literature findings ( Table 2).
Collecting PK data of serum concentrations may be challenging in some settings, for example due to the fact that blood samples may be required after the patient is discharged, or complex assay methodology required for biological drug plasma quantification may not be available.
We have shown that, for rituximab, the K-PD modelling approach is able to uncover underlying PK information in the absence of PK data.
The turnover of CD19+ lymphocytes was characterized by zeroorder cell proliferation and first-order decay over time as a simplified representation of the underlying sequential development steps of B cell maturation in bone marrow, mitigation into spleen as transitional B cells, and differentiation into mature B cells. 19 The elimination half-life of B cells was estimated to be 34.7 days (Table 2) Based on the turnover mechanism of CD19+ lymphocytes, asymptotic increase on cell production rate over age was examined, although the changeover age was not found to be statistically significant. From infancy to adulthood, cell growth may differ between females and males due to oestrogen 10 but the sex difference was not a significant covariate in our study.  (Table 2); however, the comedication effect from either small molecule was overall negligible regarding the suppression of CD19+ lymphocytes over time.
A limitation of our work was the relatively limited sample size. A large proportion of our data were below the limit of detection, but the rather simple solution of replacing these values with half the limit worked well in that model simulated fractions matched those observed ( Figure 3).   for a proportion of the variability in cell death rate (k out ) ( Table 2).
Given the limited sample size low relative standard error values were reported for model parameters suggesting precise parameter estimates, except for ED 50 due to lack of observed information on residual doses within the body over time (  Ultimately, the findings from our study may be used as underlying prior PKPD knowledge against which biosimilars of rituximab could be compared using PK if serum measurements are available for biosimilars or using the PD endpoint as in the current study. Such a PD bioequivalence could inform rituximab biosimilar dosing in the paediatric population, and therefore allow more economic access to therapy in children with autoimmune diseases.

| CONCLUSIONS
The current study quantified the effect of rituximab on reducing