Population pharmacokinetics and dose optimisation of colecalciferol in paediatric patients with chronic kidney disease

Aims The prevalence of vitamin D deficiency is high in children with chronic kidney disease (CKD). However, current dosing recommendations are based on limited pharmacokinetic (PK) data. This study aimed to develop a population PK model of colecalciferol that can be used to optimise colecalciferol dosing in this population. Methods Data from 83 children with CKD were used to develop a population PK model using a nonlinear mixed effects modelling approach. Serum creatinine and type of kidney disease (glomerular vs. nonglomerular disease) were investigated as covariates, and optimal dosing was determined based on achieving and maintaining 25‐hydroxyvitamin D (25(OH)D) concentration of 30–48 ng/mL. Results The time course of 25(OH)D concentrations was best described by a 1‐compartment model with the addition of a basal concentration parameter to reflect endogenous 25(OH)D production from diet and sun exposure. Colecalciferol showed wide between‐subject variability in its PK, with total body weight scaled allometrically the only covariate included in the model. Model‐based simulations showed that current dosing recommendations for colecalciferol can be optimised using a weight‐based dosing strategy. Conclusion This is the first study to describe the population PK of colecalciferol in children with CKD. PK model informed dosing is expected to improve the attainment of target 25(OH)D concentrations, while minimising the risk of overdosing.

Conclusion: This is the first study to describe the population PK of colecalciferol in children with CKD. PK model informed dosing is expected to improve the attainment of target 25(OH)D concentrations, while minimising the risk of overdosing.

K E Y W O R D S
chronic kidney disease, colecalciferol, population pharmacokinetics

| INTRODUCTION
Vitamin D deficiency is widely prevalent in patients with chronic kidney disease (CKD), and contributes to abnormalities in calcium, phosphate and parathyroid hormone homeostasis with increasing recognition of its key role in the pathogenesis of CKD-mineral and bone disorder. [1][2][3] International clinical practice guidelines provide consensus support for determining vitamin D status and correction of deficiency through vitamin D supplementation. 3,4 Circulating total 25-hydroxyvitamin D (25(OH)D) is used clinically to assess an individual's vitamin D status. It reflects vitamin D supply from cutaneous biosynthesis and exogenous intake, and is not under any negative feedback control. [5][6][7] Current CKD guidelines recommend initiation of vitamin D supplementation as for the general population, 4,6 with some expert panels recommending a target 25(OH)D concentration of at least 30 ng/mL. 3,8 Vitamin D supplementation is not without risks. While symptomatic vitamin D toxicity has been defined at 25(OH)D concentrations >100 ng/mL, 3 population based cohort studies have suggested an association between increased mortality and 25(OH)D concentrations >48 ng/ mL. 9,10 A more cautious supplementation approach is therefore adopted in children with reduced renal reserve including those with CKD. 3 Despite its widespread use, the optimal dosing regimen of vitamin D supplementation required to correct and maintain adequate 25(OH)D concentrations in children is not known. Rich sampling pharmacokinetic (PK) studies are limited; the few studies in adults were conducted using large single doses of vitamin D, and studies involving children have focused on those with nutritional rickets. [11][12][13][14] Moreover, clinical studies have reported notable variations in individual response to vitamin D supplementation even when identical dosing regimens are compared in similar patient groups. 15 These highlight the need for further PK data to guide dose optimisation in the paediatric population.

The Colecalciferol Supplementation in Children with Chronic
Kidney Disease trial (C3 trial) was a prospective open-label, multicentre, randomised controlled trial to test the efficacy of 3 different dosing regimens of colecalciferol (vitamin D 3 ) for 12 months in children with CKD. 16,17 In the current study, these data were used to develop a population PK model to allow better understanding of colecalciferol PK, and through PK simulation, we pro-

| Patients and data collection
Data from the C3 trial were used for the population PK analysis. 16,17 Participating sites were located in India (between 8 and 18.5 16,17 Children were randomised 1:1:1 to oral colecalciferol 3000 IU daily, 25 000 IU weekly or 100 000 IU monthly for 3 months (maximum of 3 courses) as part of the intensive replacement phase. Those who achieved 25(OH)D concentrations ≥ 30 ng/mL moved to the maintenance phase and received 1000 IU daily thereafter for up to 9 months. Data of children whose 25(OH)D concentrations fell below What is already known about this subject • Vitamin D deficiency is prevalent in children with chronic kidney disease.
• Current dosing recommendations for vitamin D are based on limited pharmacokinetic data and the optimal dosing strategy is not known. 30 ng/mL on the maintenance therapy but who continued to be followed up and prescribed the same colecalciferol product as in the trial were also included in this secondary analysis. Children received colecalciferol granules (D 360 granules, Torrent Pharmaceutical Limited, India) packaged and supplied by a central pharmacy. 16

| Analytics
Samples for 25(OH)D were drawn at assumed steady state. To minimise invasiveness, PK sampling was aligned with routine outpatient visits and occurred every 3 months. All samples were sent on the same day at ambient temperature to a central laboratory for analysis.

| Model development
Published data were used to guide model development. [18][19][20][21] In a modelbased meta-analysis of PK data in healthy or osteoporotic adult subjects, a model with a central and a peripheral compartment (2-compartment model) was found to best fit the data. 18 In contrast, 1-compartment models have been described in studies with sparse data. [19][20][21][22] Thus, both 1-and 2-compartment models were tested using both untransformed and log-transformed data. Body weight as the continuous covariate for apparent clearance and apparent volume parameters with allometric scaling was included a priori. 23 Between-subject variability terms were modelled and tested on each PK parameter using an exponential relationship as all PK parameters must be of positive values. Different error models were tested for estimation of residual variability. The selected base model was subsequently taken forward for covariate analyses by means of stepwise forward inclusion and backward elimination procedure. The specific covariates evaluated were those that had a mechanistic meaning: serum creatinine and type of kidney disease (glomerular vs. nonglomerular disease). Serum creatinine concentration was scaled by the expected sex-and age-adjusted normal serum creatinine concentration as applied in other paediatric studies. 23-28

| Model evaluation
Model evaluation was based on visual inspection of graphical diagnostics including predictions, residuals, as well as assessment of parameter estimates and precision of estimates. The comparison between 2 nested models (i.e., in covariate analyses) was performed based on the likelihood ratio test in which the difference in objective function value (OFV) is approximately χ 2 distributed. Covariates were tested using the stepwise covariate modelling approach. Covariates were sequentially added to the base model and retained if a decrease in the OFV >3.875 was seen. A backwards elimination was then executed whereby all covariates that had been identified as significant were added to the base model and removed singularly to evaluate their continued relevance. An increase in the OFV of >6.635 (corresponding to P-value <.01 in χ 2 distribution with 1 degree of freedom) was required to retain the covariate in the final model.
Both the base and the final models were evaluated using nonparametric bootstrap analysis (n = 1000) to assess the robustness of the parameter estimates. The final model was also evaluated using prediction-corrected visual predictive checks (pcVPC; n = 1000 simulations); the 5th, 50th and 95th prediction intervals, simulated from the posterior distribution of the final model parameter estimates, were overlaid with the 5th, 50th and 95th percentiles from the observed data. A well-performing model would see the observed percentiles within the 90% confidence interval of the simulated predictions.

| Simulations
Using the final model, 25(OH)D concentration-time profiles were simulated to assess current dosing recommendations (Table S1), 3   In covariate analysis, inclusion of serum creatinine on clearance did not improve the model, but the type of renal disease on clearance was found to improve the OFV by À4.83. However, this did not meet the statistical criteria for the backward elimination step, and therefore was not included in the final model. The mathematical representation of the final developed model is as follows: where CL/F is the apparent clearance, POPCL is the population estimate of clearance, V/F is the apparent volume of distribution and POPV is the population estimate of volume of distribution.  (Table 2). A pcVPC for the final model is presented in Figure 2; the similar distribution between simulated and observed data (with n = 36 [9.9%] observed concentrations outside of the predicted range) indicates that the final model developed was robust.

| Simulation
Simulations from the final model were generated to compare different

| DISCUSSION
We have developed the first population PK model of oral colecalciferol using data from an randomised controlled trial in children      Our study has a few limitations that should be considered when interpreting the results. Samples for 25(OH)D concentrations were aligned with routine 3-monthly outpatient visits to minimise patient burden and aimed at capturing steady state 25(OH)D concentrations. A study with sampling time points within the dosing intervals as well as different sampling time points between individuals would allow for better characterisation of colecalciferol PK, but the more intensive requirements would make such a study more challenging and limit patient numbers, especially in paediatrics. 23 Our model also assumed constant endogenous production of 25(OH)D, although the effect of seasonal variation is likely to be minimal considering study sites are located between 8 and 18.5 N of the equator. Furthermore, all children were assumed to be adherent based on caregiver reported adherence measurement. It should be noted that data on Fitzpatrick skin phototype was not available and our cohort included only children of Asian ethnicity; although data is limited, recent study has suggested that 25(OH)D clearance may differ by race. 43 We also acknowledge the discussions for and against the use of a priori allometric scaling in children, and that debate continues. 44

| CONCLUSION
Using a population modelling approach, our study illustrates the limitation of current colecalciferol dosing recommendations in children with CKD and proposes a weight-based dosing strategy for achieving and maintaining 25(OH)D concentrations in the target range.