Pharmacokinetics of metformin in patients with chronic kidney disease stage 4 and metformin‐naïve type 2 diabetes

Abstract The pharmacokinetics of metformin therapy in patients with chronic kidney disease stage 4 (CKD‐4) were studied using data from the largest Phase I consecutive cohort trial yet performed in this population. Eighteen metformin‐naïve men and women with Type 2 Diabetes and creatinine clearance (CrCl) in the range 18‐49 mL/min (eGFR 15‐29 mL/min/1.73 m2) were allocated to daily immediate‐release metformin of 250 mg, 500 mg, or 1000 mg. A first‐dose profile and trough concentrations for 4 weeks were taken on all patients. Pharmacokinetic (PK) parameters were estimated by fitting a first‐order compartment model with absorption in a peripheral compartment to concentrations measured 24 hours post–first dose. Single‐dose PK parameters time to maximum concentration (t max) and maximum concentration (C max) were consistent with previous observations in patients with normal renal function (healthy and diabetic), as was the association between CrCl and apparent total oral clearance (Cl/F). However, patients with a CrCl below 32 mL/min had trough concentrations that were consistently above the steady‐state minimum implied by the population PK model. This suggests the model may not apply to patients with CrCl below 32 mL/min. Metformin in doses of 500‐1000 mg/day could be taken by CKD‐4 patients. However, the single‐compartment model breaks down as CrCl declines below 32 mL/min suggesting that metformin levels should be monitored regularly in progressive stage 4 CKD.

largely based on case reports 3 and the fact that phenformin, a precursor of metformin of the same therapeutic class but with different mechanisms of action, undoubtedly did cause significant rates of lactic acidosis. 4 Many large observational studies have failed to find evidence of metformin-associated lactic acidosis. Scale  Despite the literature cited above, use of metformin in this population remains controversial 10,11 and contrary to national guidelines in many jurisdictions. 8 However, small studies 12 and ones reporting only steady-state concentrations 13,14 show that therapeutic levels should be achievable. A simulation study by Duong et al 15  population. Here, we report the pharmacokinetic (PK) results of that study and assess the impact of kidney function on single-dose PK profiles.

| Subjects and protocol
Eligibility criteria and study protocol are described elsewhere. 16 Briefly, metformin-naïve men and women aged 30- Days 1,4,5,11,18,25,29, and 32 with baseline information collected at Visit 1 (Day 1). The intervention consisted in a single dose of metformin in an immediate-release tablet taken orally before breakfast after an overnight fast. On visit days the drug was to be taken after the visit prior to the first meal. Visits were held in the morning.
A consecutive cohort design was chosen because this was a safety and tolerability Phase I study (this group had not been prescribed metformin) with pharmacokinetic evaluation on different doses. The study size was chosen to be consistent with other pharmacokinetic studies in the nonrenal population; no a priori power calculation was performed.
The New Zealand Health and Disability Ethics Committee approved this study (reference number NTX/11/12/112) and all participants gave written informed consent prior to enrolment. Safety monitoring (including for signs of acidosis) was done by an independent physician.

| Outcomes
The primary safety outcome of the trial was the development of acidosis assessed via fasting levels of venous lactate, bicarbonate, and pH. This was reported on in Dissanayake et al. 16

| Other measures
Estimated glomerular filtration rate was calculated from serum creatinine (Cr), gender, age (in years), and ethnicity using the following formula:

| Methods
Basic descriptive statistics were used to summarize patient demographics and baseline status. More complex methods (described below) were used to characterize population pharmacokinetics.
All statistical analysis was done using the R Environment for Statistical Computing version 3.1.2. 21 Nonlinear modeling was done using the MASS, 22 car, 23 and nlme 24 packages; plots were generated using the ggplot2 package. 25 The 0.05 level of significance was used for all statistical tests.

| Pharmacokinetics: single-dose hourly concentrations
Population pharmacokinetic (popPK) parameters were estimated using a nonlinear mixed effects model. 26 where D is the dose in mg, t is time postdose in hours, and k a and K are the absorption and elimination rate constants, respectively. Cl/F is the apparent total oral clearance, where F is the relative bioavailability of the drug (0 < F ≤ 1). Mathematically, Cl/F is equivalent to the ratio of the dose to the area under the concentration-time curve (AUC 0-∞ ). 28 Cl/F and k a were fitted as patient-specific random intercepts. Actual sampling times were used for all pharmacokinetic evaluations.
Maximum concentration (C max ), time to C max (t max ), AUC 0-∞ , and absorption and elimination half-lives (t ka 1=2 ; t K 1=2 , resp.) were derived from the nonlinear mixed effects model estimates of the parameters in Equation (1). Comparison of observed and fitted values and examination of standard residual diagnostics showed the model was a good fit to the data.
Concentration as a function of both dose and CrCl (L/h) was modeled by modifying Equation (1) as follows: where CrCl is the baseline measurement. The factor (CL/F)ʹ was fitted as a patient-specific random effect and is equivalent to Cl/F in Equation (1) divided by patient-specific baseline CrCl. This model was used to generate predicted C max values for future patients with a range of baseline CrCls. We used Akaike's Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to compare models (1) and (2).

| Pharmacokinetics: repeat dose and trough concentrations
We used the following formulae for minimum, mean, and peak concentrations under repeat dosing (c min,ss , c avg,ss , and c max,ss , respectively) 28 Confidence intervals for average c min,ss , c avg,ss , and c max,ss and average values of each under specific baseline CrCls were formed by applying the delta method to the parameter estimates produced by models in Equations (1) and (2).

| Observed trough concentrations
Observed trough concentrations were compared with confidence intervals for average c min,ss , c avg,ss , and c max,ss implied by the popPK  were computed by applying the delta method to the variance-covariance matrix of the estimated fixed effects regression coefficients and applying the relevant quantiles of the standard normal distribution.
They represent a 95% confidence interval for the average value of the response for a given set of values for the explanatory variables.
It is possible that on some visits some patients violated protocol and took metformin before having their predose blood test. These would be suspected if one or two observed trough-level concentrations per patient were within the 95% confidence interval for the steady-state maximum concentrations while the patient's other observations were within the confidence interval for the minimum. Values meeting these criteria were identified and labeled in plots. However, because there is no independent way to assess whether or not this occurred no data points were removed from any statistical analyses. It is likely therefore that the within-and between-subjects variances are overestimated (leading to wider confidence intervals) in regression models for the observed trough concentrations. This is a conservative approach.
In exploratory analysis, log concentrations were modeled as a function of dose, CrCl, and BMI. A linear mixed effects model with random intercepts for patient was used to account for repeat observations on each patient. Starting with a model with all two-way interactions, nonsignificant terms were eliminated sequentially beginning with interactions. All but the main effects of CrCl and dose were significant and only these two explanatory variables were retained.

| Metformin assay
A high-performance liquid chromatographic assay was used to measure metformin concentration in plasma. This was described and validated by Zhang et al 30 The limit of quantification was approximately 20 μg/L and the coefficient of variation estimated by Zhang et al 30 from intra-and interday assay variance was <9.0%.

| Materials
We used generic metformin (active ingredient metformin hydrochloride) which was prescribed by the conducting clinician to each patient.

| Single dose
There were 102 concentrations (5-6 per patient) available for PK analysis recorded over 24 hours after the first single dose. All postbaseline measurements were above the minimum quantifiable amount. Maximum observed concentrations, AUC 0-∞ , and time to maxima are reported elsewhere. 16 Pharmacokinetic parameter estimates and summaries of best linear unbiased predictors (BLUPs) are in Table 2 Note that the C max and t max values reported in Dissanayake et al 16 (Table 2) are empirical medians, whereas the values in Table 2 in this article are estimates (with confidence intervals) from the compartment model. Model-based estimates of average serum concentrations at steady state were derived from this single-dose popPK model. Confidence intervals for these parameters have the same interpretation as those for the PK parameters (see above). Estimated population averages for c min,ss , c avg,ss , and c max,ss are in Table 3

| Single dose
To account for variation in kidney function the popPK compartment model was refitted after including CrCl as a premultiplier to Cl/F. In this model it is the (Cl/F)-to-CrCl ratio rather than Cl/F that is estimated by the corresponding fixed effect. The estimated average (Cl/ AIC and BIC for this model were −48.9 and −30.6, while for the model without CrCl they were, respectively, −57.0 and −38.7. As 'smaller is better', these criteria preferred the model without CrCl. Nevertheless, estimates of k a and K from the two models were quite similar (Table A3) and residual diagnostics indicated the CrCl model was still a good fit, hence we proceeded to use it to estimate dose recommendations for various levels of CrCl (Section 3.3.3).

| Repeat dose
To explore the relationship between CrCl and trough concentrations, we split the study cohort into two groups by comparing observed

| Dose recommendations
The popPK compartment model with CrCl can be used to estimate repeat-dose peak concentrations for a given dose and baseline CrCl.
They may be useful in determining the dose required to obtain a given steady-state concentration for a patient with known baseline

| DISCUSSION AND CONCLUSIONS
We conducted the largest consecutive dose-escalating study of metformin in patients with metformin-naïve T2DM and CKD-4 to date.
Eighteen patients with eGFR < 30 mL/min/1.73 m 2 were allocated to 1 of 3 dose groups: 250 mg/day, 500 mg/day, and 1000 mg/day.   F I G U R E 2 Repeat-dose serum metformin concentrations recorded at Visits 3-6 for each dose group 24 hours postdose (trough levels) for those patients with more than one observation above the upper limit of the 95% CI for the mean of the steady-state trough level (patients 1, 2, 4, 6, 7, 9, 10, 14, 16, 17, and 19). Number labels and lines indicate observed value; from top to bottom, ribbons show the 95% CIs for the means of the theoretical steady-state maximum, mean, and trough concentrations, respectively, for a population meeting eligibility criteria with average Cl/F and k a . Note that different vertical scales are used in each panel to allow the plots to be easily read F I G U R E 3 Repeat-dose serum metformin concentrations recorded at Visits 3-6 for each dose group 24 hours post-dose (trough levels) for those patients with no more than one observation above the upper limit of the 95% CI for the mean of the steady-state trough level (patients 3, 5, 8, 11, 12, 13, and 18). Number labels and lines indicate observed value; from top to bottom, ribbons show the 95% CIs for the means of the theoretical steady-state maximum, mean, and trough concentrations, respectively, for a population meeting eligibility criteria with average Cl/F and k a . Note that different vertical scales are used in each panel to allow the plots to be easily read patients with T2DM and impaired renal function and similarly found a single-compartment model to be appropriate.
The fixed effects parameters in our single-compartment model were the absorption and elimination rate constants (k a and K) and the apparent clearance (Cl/F). Fixed effect estimates for AUC 0-∞ , t max , C max , and the absorption and elimination half-lives (t ka 1=2 and t K 1=2 ) were derived using the delta method (Table 2). Patient-specific random intercepts were added for Cl/F and k a to account for the repeated measurements on patients. patients was similar to ours (moderate impairment group: CrCl 31-60 mL/min, n = 5; severe impairment group: CrCl 10-30 mL/min, n = 6). Mean t max s were 3.75 hours and 4.01 hours; the latter being larger than the upper limit of our confidence interval but comparable with empirical median t max s observed in our 500 mg and 1000 mg groups (4.0 hours in both; see ref. 16 Table 2). Sambol et al's 12 mean C max s were 4.12 mg/L and 3.93 mg/L, higher than our modeled (see above) and empirical median C max s for comparable doses (500 mg:

| Repeat dose
Patients with observed trough levels within the range predicted by the popPK model fitted only to the 24-hour concentrations had significantly higher CrCl at baseline than patients whose observed trough concentrations were consistently higher than the predicted range. Graham

| Dose recommendations
It remains unclear what the therapeutic range of metformin is in patients with impaired renal function. Frid et al 14

| Conclusion
This is the largest phase I pharmacokinetic trial yet performed in patients with CKD. The single-dose PK parameters t max and C max were consistent with previous observations in patients with normal renal function (healthy and diabetic). The association between CrCl and apparent clearance (Cl/F) of metformin was also similar to that observed in patients with normal renal function. However, Cl/F itself was much lower than in healthy patients and correspondingly steady-state minimum concentrations implied by our popPK model were higher.
Model-based steady-state concentrations appeared to fit the data well among a group of patients with high CrCl (median CrCl 41 mL/ min), but not among a group with low CrCl (median CrCl 24 mL/ min), suggesting that the first-order compartment model with absorption in a peripheral compartment breaks down as CrCl declines. We were probably able to detect this because, relative to previous studies, a much larger proportion of our study cohort (56%) had very low CrCl (<30 mL/min). Therefore, while the results suggest that 500-1000 mg per day could be taken by CKD-4 patients, metformin levels should be monitored regularly.

ACKNOWLEDGEMENTS
We are grateful to Middlemore clinical trials, Diabetes and Renal Services of Counties Manukau Health Auckland, New Zealand, for assistance with the conduct of this study; Dr. Michael Lam, nephrologist at Counties Manukau Health, who acted as the independent safety monitor; and Dr Chris Florkowski and Christchurch Laboratories New Zealand for assisting with metformin measurements. Funding was provided by the diabetes fund at Middlemore clinical trials.
We thank three anonymous reviewers for their insightful comments which led to meaningful improvements in the manuscript.  T A B L E A 3 Compartmental pharmacokinetic parameters of metformin administered in daily doses of 250, 500, and 1000 mg to patients with CKD-4. Estimates and predictions from the model with CrCl