The pharmacokinetics of metformin in patients receiving intermittent haemodialysis

Abstract

The aims of this study were to characterise the population pharmacokinetics of metformin in patients receiving haemodialysis, and to determine the doses that will maintain median metformin plasma concentrations below 5 mg L⁻¹ for a typical individual. Metformin plasma concentrations from 5 patients receiving thrice weekly intermittent haemodialysis followed by metformin 500 mg postdialysis were fitted to a published pharmacokinetic model. Additional models to describe the dialytic pharmacokinetics of metformin were explored. Doses of 250 and 500 postdialysis were simulated from the model for a typical haemodialysis patient. The published 2‐compartment pharmacokinetic model with an additional parameter to describe haemodialysis clearance provided a reasonable fit to the data. Deterministic simulations from the model for a typical individual suggest that metformin doses of 250–500 mg postdialysis and 250 mg given once daily should maintain median metformin plasma concentrations below 5 mg L⁻¹.

What is already known about this subject

• Metformin use in patients with renal impairment is controversial due to concerns that elevated plasma concentrations will increase the risk of lactic acidosis.

• In theory, dose reduction to maintain plasma concentrations below 5 mg L⁻¹ should mitigate risk of lactic acidosis.

• The dosing for patients who require intermittent haemodialysis has not been well‐studied.

What this study adds

• A published 2‐compartment pharmacokinetic model with an additional parameter to describe haemodialysis clearance provided a reasonable fit to the data.

• Deterministic simulations from the model for a typical individual suggest that metformin doses of 250–500 mg postdialysis or 250 mg given once daily should maintain median metformin plasma concentrations below 5 mg L⁻¹.

• We consider the doses proposed here to be preliminary until the interdialytic pharmacokinetics and the typical variability expected in dialysis patients for metformin can be clarified.

1. INTRODUCTION

Metformin is widely considered to be the first line treatment for Type 2 diabetes mellitus (T2DM). T2DM patients are at an increased risk of chronic kidney disease (CKD). Those patients who eventually progress to end stage renal disease will require renal replacement therapy, such as haemodialysis (HD).

The safe use of metformin in patients with CKD is a matter of considerable debate. Traditionally, metformin was contraindicated in patients with moderate to severe renal impairment due to concerns that elevated plasma concentrations would increase the risk of lactic acidosis. Recent work suggests that metformin may be reasonable to use in patients with chronic kidney disease, provided that doses are appropriately reduced to maintain plasma concentrations below 5 mg L⁻¹, the nominal upper limit of the therapeutic range.1 As a consequence, published renal dosing guidelines have been recently amended to include metformin dosing for patients with an estimated glomerular filtration rate as low as 30 mL min⁻¹,2 or even 15 mL min⁻¹ in some cases.3

The pharmacokinetics of metformin have been well described, including recent work on patients with CKD.4, 5, 6, 7, 8 In brief, metformin has a variable oral availability averaging about 50%, has negligible binding to plasma proteins, and a volume of distribution in the order of 300 L (once bioavailability is considered).5 There is evidence to suggest distribution into tissues and deep compartments, including red blood cells.1 Metformin is cleared almost entirely by the kidneys and undergoes extensive tubular secretion resulting in a renal clearance that exceeds glomerular filtration rate. Renal clearance has been found to be reduced in patients with poor kidney function.4, 5, 6, 7, 8

The use of metformin in patients who require intermittent HD has not been well studied. This leaves prescribers with no guidance about potentially safe and effective dosing. The aims of the present study are to characterise the population pharmacokinetics of metformin in patients receiving HD, and to provide some initial dose predictions that should maintain plasma concentrations <5 mg L⁻¹.

2. METHODS

2.1. Patients

Patients with Type 2 diabetes receiving intermittent HD were recruited from HD centres within the Southern Adelaide Local Health Network, South Adelaide, Australia. Patients were included if they were age ≥18 years and receiving HD 3 times a week for a period of >3 months. Patients with moderate to severe heart failure, liver failure, alcohol abuse, major psychiatric disorders, who were medically unstable, or who were unable or unwilling to self‐monitor and record blood glucose levels were excluded. The study was registered under the Australian New Zealand Clinical Trials Registry (ANZCTR number 12612000352808) and approved by the Southern Adelaide Clinical Human Research Ethics Committee (application 324.11). The study was conducted in accordance with the Helsinki declaration. All participants gave written and informed consent.

2.2. Study protocol

The study was conducted over a period of 4 weeks. During this time, each participant continued their usual thrice‐weekly dialysis schedule. No replacement fluids were administered during the HD session. Urine output was monitored to determine anuric status. The study design, HD schedule and sampling schedule are summarised in Figure A1.

Metformin 500 mg was administered immediately post‐HD (3 times a week) for the first 3 weeks of the study (first to ninth HD sessions). During the last week of the study (10^th to 12^th HD session), no metformin was administered to the participants. Metformin plasma concentrations were measured pre‐ and post‐HD throughout the study starting from the second to the 12^th HD session. Plasma concentrations were measured hourly during the second, third and ninth HD sessions. Additional metformin concentrations were also measured 2 and 4 hours after dialysis for the first and ninth HD sessions. Samples collected during dialysis were drawn from the dialysis circuitry (prefilter) while samples taken during the interdialytic period were by venepuncture. Serum lactate and bicarb (bicarb) were measured before and after HD sessions 1 and 9, and predialysis before HD sessions 2, 3, 6, 10 and 12.

2.3. Metformin assay

Metformin plasma concentrations were measured by the Department of Clinical Pharmacology at Flinders University, South Adelaide, Australia using ultra‐performance liquid chromatography–mass spectrometry. The assay was found to be linear between 0.1 and 5 mg l⁻¹ (R ² = .9997). The lower limit of quantification was reported to be 0.02 mg/L and the with‐in run coefficient of variation was <8%.

2.4. Software

A population analysis was conducted using nonlinear mixed effects modelling analysis in NONMEM (version 7.3). The first‐order conditional estimation and interaction method was used. The convergence criterion was set to 3 significant digits. An Intel‐5 processor and a GNU Fortran 95 compiler (GCC 4.6.0) were employed for the analysis. The model runs were executed using PsN v 4.8.0. Pre‐ and postprocessing were conducted using R v3.5.1 (2018, The R Foundation) and MATLAB v2018b (Math Works Inc). Statistical analyses and plotting were conducted in Prism v8.0.1 (2018, GraphPad).

2.5. Model fitting

The data collected for this study were not intended to describe the interdialytic pharmacokinetics of metformin and provides scant information for model building. Therefore, a published population pharmacokinetic metformin model developed in Type 2 diabetic patients with varying degrees of renal impairment was fit to the data.4 Duong et al.⁴ estimated both renal (using measured urine concentrations) and nonrenal clearance for metformin. Since metformin is believed to be almost entirely cleared renally, the nonrenal clearance was deemed to capture unabsorbed and scant elimination by other routes.5 The model for nondialytic clearance is therefore given by;

$${\mathrm{CL}}_{\text{nondialytic}}={\mathrm{CL}}_{\text{renal}}+{\mathrm{CL}}_{\text{nonrenal}}$$

For the purpose of this study, CL_renal was fixed to zero (since all patient are anuric) and only CL_{non − renal} was estimated.

As per Duong et al.,⁴ residual unexplained error was described by a combined (i.e. both additive and proportional) model. The parameter variability between individuals was assumed to follow a log‐normal distribution.

No formal model building or covariate analysis was conducted to describe nondialytic pharmacokinetics. The published parameter values provided by Duong et al.4 were used as the initial estimates in the model runs.

The intradialytic pharmacokinetics of metformin was explored using 3 candidate models for metformin dialytic clearance; (i) an additional clearance parameter (CLHD) to account for the enhanced elimination during each HD session (set to zero during the interdialytic period); (ii) a fractional effect model to investigate the influence of dialyser type on CLHD; and (iii) an empirical model describing the influence of blood flow rate, dialysate flow rate and mass transfer area coefficient (KoA) on HD clearance, as described by Michaels.9 The latter model is given by

$$\text{CLHD}=BFR\left[\frac{e^{\left[{\displaystyle \frac{K_{0}A}{BFR}}\left(1‐{\displaystyle \frac{BFR}{DFR}}\right)\right]‐1}}{e^{\left[{\displaystyle \frac{K_{0}A}{BFR}}\left(1‐{\displaystyle \frac{BFR}{DFR}}\right)\right]‐{\displaystyle \frac{BFR}{DFR}}}}\right]$$

where CLHD is metformin dialytic clearance, BFR is the blood flow rate, DFR is the dialysate flow rate, and KoA is the mass transfer area coefficient (an estimated parameter in the model). To account for the change in volume of distribution during HD, a fractional change parameter was tested on metformin central and peripheral volume.

Model discrimination was guided by: (i) the global fit to the data using a reduction in the objective function value by 3.84 units (χ², P < .05) for nested models with 1 degree of freedom; (ii) goodness of fit plots; (iii) the biological plausibility of parameter estimates; and (iv) the standard errors of parameters. The models were evaluated using individual fit plots. The usual method of assessing model fit using a visual predictive check was not possible because of the different dialysis start and stops times in the data.

Outliers were defined as plasma concentrations with a CWRES > 5 and were excluded.

2.6. Serum lactate and bicarb concentrations

The relationship between serum lactate and metformin plasma concentrations, and serum bicarb and metformin, was explored using linear regression. In addition, lactate and bicarb concentrations during and in the absence of metformin therapy (at baseline and after stopping metformin in week 4) were compared using a 2‐sided (unpaired) t test.

2.7. Metformin dose predictions

The dialytic and nondialytic pharmacokinetic model for metformin was implemented in MATLAB (v. 2018b). Deterministic simulations to predict the median metformin plasma concentrations for a typical patient receiving a 4 hour HD session 3 times a week were conducted. Metformin doses of 250 and 500 mg given immediately postdialysis and once daily were explored. Plasma concentrations were predicted over a time period of 31 days.

2.8. Nomenclature of targets and ligands

Key protein targets and ligands in this article are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS Guide to PHARMACOLOGY.

3. RESULTS

Five patients with T2DM were recruited, providing 184 metformin plasma concentrations. Four data points were excluded leaving a final dataset with 180 concentrations. The 4 excluded concentrations were noted to be post or predialysis concentrations that were incongruent with the remaining data. Two of the 4 had a CWRES > 5. In 1 case (patient 3), plasma concentrations increased in the absence of a recorded dose. No concentrations were below the limit of quantitation. Plots of the raw data, including the excluded concentrations, for each participant, are presented in Figure A2. Baseline demographics, laboratory measurements, and details of the HD protocol for each participant are presented in Tables A1–3. All patients were anuric and none were receiving metformin therapy prior to the study.

There was no discernible relationship between serum lactate and metformin concentrations (R ² = .007, P = .55) and a trend towards higher, rather than lower, serum bicarb with increasing metformin concentrations (R ² = .077, P = .05). No lactate concentrations exceeded 5 mmol/L. Further details are provided Figure A3. The lactate and bicarb concentrations were similar to that seen in dialysis patients during treatment with metformin and when not receiving metformin.

There was a large inter‐ and intrasubject variability in the metformin plasma concentrations (see Figure A2). No metformin plasma concentrations were below the lower limit of quantification. Ten predialysis concentrations were >5 mg L⁻¹.

The published 2‐compartment pharmacokinetic model with first order absorption and elimination, as well as an additional clearance parameter to account for drug elimination during dialysis, provided a reasonable fit to the data (Figure 1 and Figure A4). F1 is not identifiable in the absence of intravenous data and was fixed to 0.55 in all runs, as per Duong et al.4 A fractional effect parameter was added to account for the assumed difference in nonrenal clearance observed in subject 1. A similar parameter did not improve the fit for subject 5. Other models to describe the pharmacokinetic changes of metformin during dialysis did not improve the fit and were not retained. This included a parameter to explain between‐subject variability in CLHD, which was poorly estimated. The parameter estimates of the final model are provided in Table 1 and key model building steps are presented in Supplemental Table A4. The details of the final model for metformin intra‐ and interdialytic pharmacokinetics are shown in Figure A5. Note that the between subject variability for interdialytic pharmacokinetic parameters were fixed to the values reported by Duong et al.4 to improve model stability. The differences in the parameter estimates between those reported by Duong et al.4 and those estimated here may be explained by differences in the patient populations.

Figure 1.

Individual fit plots for the 5 dialysis subjects. The grey dots (DV) represent the observed metformin plasma concentrations, the red line (IPRED) is the individual fit and the blue dotted line (PRED) represents the population fit. Conc = concentration

Table 1.

Parameter estimates for the published nondialytic model from Duong et al.4 and for the final dialytic and nondialytic model

Parameter	Duong et al4	Parameter estimates (RSE %)
θCLNR/F (L h−1)	1.6	0.49 (37.4)
θCLR/F (L h−1)	17	0 (FIX)
θCLHD (L h−1)	‐	11.4 (16.4)
θQ/F (L h−1)	13	5.2 (27.0)
θV2/F (L)	123	17.5 (16.5)
θV3/F (L)	335	48.6 (27.9)
${\theta }_{k_a}$ (h−1)	0.51	0.07 (15.4)
θCLNR ¯ ID1	‐	3.2 (59.7)
θF1	0.55 (FIX)	0.55 (FIX)
Between‐subject variability
ωCL (CV %)	69	69 (FIX)
ωV2 (CV %)	36	36 (FIX)
ωF1 (CV %)	29	29 (FIX)
Residual error
Proportional error	0.20	0.25 (7.3)
Additive error	0.05	0.01 (FIX)

θ_CLNR/F = apparent nonrenal clearance; θ_CLR/F = apparent renal clearance; θ_CLHD = haemodialysis clearance; θ_Q/F = apparent intercompartmental clearance; θ_V2/F = apparent central volume; θ_V3/F =apparent peripheral volume; ${\mathrm{\theta }}_{{\mathrm{k}}_{\mathrm{a}}}$ = absorption rate constant;θ_{CLNR ¯ ID1} = the fractional effect on clearance for patient ID 1; ω_CL = between subject variability of clearance; ω_V2 = between subject variability of the central volume compartment; ω_F1 = between subject variability for bioavailability; CV% = coefficient of variation; RSE = relative standard error (derived from the asymptotic standard errors produced by NONMEM)

Deterministic simulations from the model for a typical individual suggest that metformin doses of 250–500 mg postdialysis or 250 mg given once daily should maintain median metformin plasma concentrations below 5 mg/L (see Figure 2).

Figure 2.

Model predicted metformin plasma concentrations for metformin doses of 250 mg, 500 mg and 1000 mg given either postdialysis (a) or daily (B). The dotted horizontal line indicates the upper limit of the nominal therapeutic range (5 mg L⁻¹). The simulations represent the median concentrations for a typical individual. Conc = concentration

4. DISCUSSION

A published pharmacokinetic model for metformin, with an additional HD clearance parameter, was fit to data from 5 patients receiving 500 mg of metformin after each intermittent HD session. Preliminary predictions from the model suggest that a metformin dose of 250–500 mg postdialysis, or a 250‐mg daily dose, should maintain median plasma concentrations below the proposed upper end of the therapeutic range of 5 mg L⁻¹.

The primary concern with metformin use in renal disease, including those receiving renal replacement therapy, is that elevated plasma concentrations due to reduced drug elimination may increase the risk of lactic acidosis. However, a growing number of studies have shown that metformin is unlikely to be the sole cause of lactic acidosis outside of the overdose setting.10, 11, 12 A recent systematic review of metformin safety in dialysis patients, while inconclusive, found no obvious increased lactic acidosis risk or increased mortality in this population.13 Furthermore, elevated metformin plasma concentrations could be mitigated, in theory, with dose reduction provided that dosing decisions are supported by robust evidence on safety and efficacy. Our study provides an initial step towards this goal.

Metformin has not been extensively studied in patents with end stage renal disease who require renal replacement therapy. A few pharmacokinetic studies, representing a total of only 14 patients, were found in the published literature.6, 14, 15, 16 Duong et al.6 reported details of a single patient receiving a metformin dose of 250 mg daily during haemodiafiltration therapy. The clearance of metformin during haemodiafiltration was reported to be 149 mL min⁻¹ (8.9 L h⁻¹). Elevated metformin or lactate concentrations were not observed. Smith et al.14 studied the pharmacokinetics of metformin in 4 Type 2 diabetic patients receiving intermittent thrice weekly haemodiafiltration with metformin 500 mg after each session. Individual metformin clearance values were during haemodiafiltration were reported to be 78–196 mL min⁻¹ (4.7–11.8 L h⁻¹). Similarly, Roberts et al.15 found a mean metformin clearance during HD in a single patient of 157 mL min⁻¹ (9.42 L h⁻¹). Lalau et al 16 found metformin clearance values during HD ranging from 68 to 176 mL min⁻¹ (4.1 to 10.6 L h⁻¹).

There are several case reports involving the acute management of metformin toxicity or intentional overdose, some reporting metformin plasma concentrations measurements during dialysis (e.g.17, 18). The available evidence suggests that metformin is moderately dialysable with a dialysis clearance in the range of 70–230 mL/min.6, 14, 15, 16, 17, 19 The percentage of the daily dose removed has been reported to be 9–35% for a 4–6‐hour HD session.6, 14

The interdialytic pharmacokinetics of patients receiving metformin predicted by our model are speculative, given the sparse data available between dialysis sessions. While the published 2‐compartment model from Duong et al.⁴ is probably reasonable, we were required to fix the estimates of between‐subject variability in our work to the published values. This means that we assume the same variability in metformin pharmacokinetics during the interdialytic period in patients receiving and not receiving dialysis. Whether this is a reasonable assumption is not known. The impact of rebound concentrations postdialysis and altered absorption or distribution in a dialysis have not been well studied.

To visualise the model predictions between and during HD sessions, a single predicted plasma concentration profile is presented in Figure A6 for a typical individual taking a 500‐mg dose postdialysis. The model predicts a peak plasma concentration at about 4 hours and an initial distribution phase that is essentially complete by about 12 hours. This is followed by a slow, and modest, decline in plasma concentrations until the next dialysis session. This decline is estimated in the model as a small nonrenal clearance (approximately 0.5 L h⁻¹); however, since metformin is cleared entirely by the kidneys, it is not known if nonrenal clearance may actually represent other processes (e.g. slow distribution). It is noteworthy that the data reported by Smith et al.14 showed a relatively stable plasma concentrations across the interdialytic period from 4 hours postdialysis for most of the patients studied. Our data, depicted in Figure A7, show a predominate decline in plasma concentrations over the same time period in most patients. The reason for this discrepancy is unclear. We suggest that further work to clarify the interdialytic pharmacokinetics of metformin during intermittent dialysis is warranted before dosing can be reliably predicted.

The results from our analyses should be interpreted in light of some additional limitations. We have studied 5 patients, who will not represent the population of T2DM patients and therefore the work should be viewed as a preliminary. Stochastic simulations, to determine the probability of exceeding 5 mg L⁻¹ across the range of expected plasma concentration–time profiles, from this model may therefore give an unreliable picture of the expected range of possible concentrations, limiting the inferences from our work to deterministic simulations for a typical individual rather than inferences about all HD patients. In addition, we cannot speculate whether our model predicts the pharmacokinetics of metformin in HD patients receiving larger doses than 500 mg as these were not studied. Our model predictions were not evaluated against external data. Extractable data from published plots or data tables collected under similar conditions could not be located. The published data from Smith et al.14 was collected in patients receiving haemodiafiltration where there is additional elimination due to convective processes so was not used to evaluate our model. Finally, metformin concentrations were not measured before and after the dialyser in the dialysis circuitry, nor in the dialysate, so the extraction ratio of metformin or percentage of the dose removed by dialysis could not be determined.

A published pharmacokinetic model for metformin was fit to data from 5 end‐stage renal disease patients receiving metformin 500 mg postdialysis. Predictions from the model for a typical individual suggest that metformin doses of 250–500 mg postdialysis or 250 mg given once daily should maintain median metformin plasma concentrations below 5 mg L⁻¹. This result must remain preliminary until the interdialytic pharmacokinetics of metformin can be further clarified.

COMPETING INTERESTS

There are no competing interests to declare.

CONTRIBUTORS

K.A.S., I.H.S.K. and D.F.B.W. drafted the manuscript; M.P.D. and T.R.J.R. designed and implemented the original dialysis study and data collection; K.A.S., I.H.S.K. and D.F.B.W. designed and conducted the pharmacometric analyses; M.P.D., T.R.J.T. and D.F.B.W. conducted the analysis of the lactate and bicarb; K.A.S., I.H.S.K., M.P.D., T.R.J.R. and D.F.B.W. reviewed and drafted the final manuscript.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on request from the principle investor. The data are not publicly available due to ethical restrictions.

APPENDIX A.

Figure A1.

Schematic of the haemodialysis study design. Each haemodialysis session lasted approximately 4 hours, with a metformin 500‐mg dose given immediately after each session (session 1–9). This is designated with an X. The arrows represent approximate times relative to the dialysis sessions of blood samples

Figure A2.

Individual plots of the raw metformin data for each subject. The grey shaded box represents each dialysis session. Data points depicted as red boxes are outliers excluded from the analysis on the basis of a CWRES > 5. Conc = concentration

Figure A3.

(A) Linear regression of serum lactate against metformin plasma concentrations. (B) Comparison of serum lactate values during and in the absence of metformin therapy using an unpaired t test (54 concentrations). The box represented the 25^th and 75^th quartiles of the data, the whiskers indicate the extremes (minimum and maximum) of the data. (C) Linear regression of serum bicarbonate and metformin plasma concentrations (52 concentrations). (D) Comparison of serum bicarbonate values during and in the absence of metformin therapy using an unpaired t test. The box represented the 25^th and 75^th quartile of the data, the whiskers indicate the extremes (minimum and maximum) of the data. Conc = concentration

Figure A4.

Goodness of fit plots for the final model. (A, B) Observed metformin plasma concentrations against the population predictions (A) and individual predictions (B). (C, D) CWRES (conditional weighted residuals) against the population predictions for metformin plasma concentrations (C) and time (D). Conc = concentration

Figure A5.

Details of the final model for metformin intra‐ and interdialytic pharmacokinetics. Cpt = compartment; k_a is the absorption rate constant; $\raisebox{1ex}{$\mathit{CL}$}\!\left/ \!\raisebox{-1ex}{$F$}\right.$ is the total apparent clearance of metformin; CL_HD = haemodialysis clearance; CL_NR = nonrenal (or other unexplained) clearance; CL_R = renal clearance (set to zero); CLcr = creatinine clearance (also set to zero); Q = intercompartmental clearance; V₂ = volume of the central compartment; V₃ = volume of the peripheral compartment; θ_{F ¯ CLNR ¯ ID1} = the fractional effect on nonrenal clearance for patient with ID1

Figure A6.

Model‐predicted metformin plasma concentration for a typical individual taking 500 mg of metformin postdialysis. The profile was generated at the first dose and assumes a 4‐hour dialysis starting at hour 44

Figure A7.

Paired metformin plasma concentrations across an interdialytic period. The left concentration was measured 4 hours after the dose of metformin (and therefore 4 hours after a dialysis session), the right concentration was measured just prior to the next dialysis session (44 hours later). D1 and D9 = study dialysis session numbers 1 and 9. D2 and D10 = study dialysis session numbers 2 and 10

Table A1.

Baseline demographics for the 5 haemodialysis subjects

Subject	1	2	3	4	5
Sex	Female	Male	Male	Female	Male
Age (years)	64	61	75	68	82
Height (m)	1.57	1.80	1.70	1.65	1.68
Weight (kg)	80	102	78	92	78
BMI (kg/m 2 )	32.5	31.5	27.0	33.8	27.6
Cause of renal failure	Reflux nephropathy	T2DM	Renal artery stenosis	T2DM	T2DM
Duration on HD (months)	18	22	8	17	22
Anuria	Yes	Yes	Yes	Yes	Yes
Comorbidities	T2DM, recurrent UTIs, IHD, obesity, HBP, hyperlipidaemia, hypothyroidism, gout, obstructive sleep apnoea	T2DM, HBP, hyperlipidaemia, gout	T2DM, IHD, AF, gout, hypertension, transitional cell cancer, stroke, urethral strictures, renal artery occlusion	T2DM, IHD, left carotid artery stenosis, hypertension, hip fracture, hyperlipidaemia, depression, pancreatic cyst	T2DM, hyperlipidaemia, IHD, gout
Other medicines	Allopurinol, amlodipine, aspirin, clopidogrel, epoetin alfa, folic acid, frusemide, insulin, isosorbide mononitrate, metoprolol, pantoprazole, sevelamer, simvastatin, thyroxine	Allopurinol, amlodipine, aspirin, atenolol, atorvastatin, calcitriol, calcium carbonate, citalopram, colchicine, fexofenadine, folic acid, insulin	Allopurinol, bisoprolol, calcitriol, esomeprazole, epoetin alfa, folic acid, insulin, perhexiline, sevelamer, simvastatin, warfarin	Aspirin, calcium carbonate, duloxetine, epoetin alfa, ezetimibe, fluticasone/salmeterol, folic acid, metoprolol, salbutamol, sevelamer	Allopurinol, amlodipine, atorvastatin, clopidogrel, epoetin alfa, folic acid, metoprolol, insulin, pantoprazole

BMI = body mass index; FFM = fat‐free mass; CLCR = creatinine clearance; HD = haemodialysis; T2DM = Type 2 diabetes mellitus; UTIs = urinary tract infections; IHD = ischemic heart disease; AF = atrial fibrillation; HBP = hypertension. Creatinine clearance was calculated using the Cockcroft Gault equation and fat free mass was calculated using the Janmahasatian et al 2005 fat free mass equation.

Table A2.

Clinical biochemistry results for the 5 haemodialysis subjects

	Session	Sample taken	Subject 1	Subject 2	Subject 3	Subject 4	Subject 5
Creatinine (μmol L −1 )	0	‐	680	1220	733	626	687
HbA1c (%)	0	‐	6.8	8.8	6.4	8.8	7.3
HbA1c (mmol mol −1 )	0	‐	51	73	46	66	56
Lactate (mmol L −1 )	0	‐	1.85	1.21	1.24	0.98	1.38
	1	Predialysis	1.32	0.95	‐	2.32	2.12
	1	Postdialysis 2 hours	2.72	1.0	3.74	2.39	2.03
	1	Postdialysis 4 h	2.08	1.1	1.40	2.07	3.75
	2	Predialysis	2.21	0.57	0.95	0.91	2.43
	3		2.19	0.63	1.96	1.29	1.68
	4		‐	‐	‐	‐	‐
	5		‐	‐	‐	‐	‐
	6		2.41	0.96	1.56	‐	1.82
	7		‐	‐	‐	‐	‐
	8		‐	‐	‐	‐	‐
	9		1.66	1.68	1.70	3.36	2.97
	9	Postdialysis 2 h	2.80	1.47	1.86	2.33	3.32
	9	Postdialysis 4 h	3.10	1.97	1.72	4.13	2.98
	10	Predialysis	‐	‐	1.99	1.41	‐
	11		‐	‐	‐	‐	‐
	12		1.42	0.5	2.17	2.38	2.74
Bicarbonate (mmol L −1 )	0	‐	16	22	20	19	21
	1	Predialysis	18	23	‐	20	23
	1	Postdialysis 2 h	23	30	26	26	26
	1	Postdialysis 4 h	26	32	30	28	23
	2	Predialysis	19	24	22	17	20
	3		18	24	20	19	24
	4		‐	‐	‐	‐	‐
	5		‐	‐	‐	‐	‐
	6		17	23	22	‐	20
	7		‐	‐	‐	‐	‐
	8		‐	‐	‐	‐	‐
	9		17	24	21	21	19
	9	Postdialysis 2 h	27	27	31	25	26
	9	Postdialysis 4 h	26	27	27	24	24
	10	Predialysis	‐	‐	26	20	‐
	11		‐	‐	‐	‐	‐
	12		20	23	21	24	20

Table A3.

Details of the haemodialysis (HD) sessions for each subject

	Session	Subject 1	Subject 2	Subject 3	Subject 4	Subject 5
Duration of HD session (h:min)	1	4:01	4:58	5:02	4:05	4:00
	2	4:00	5:00	5:06	4:30	4:00
	3	4:04	5:00	5:02	4:30	4:00
	4	3:16	5:05	5:05	4:30	4:00
	5	4:18	5:00	5:03	4:30	4:11
	6	4:03	5:06	5:07	4:30	4:00
	7	4:05	5:00	5:05	4:30	4:00
	8	4:07	5:05	5:04	4:00	4:00
	9	4:00	5:06	5:05	4:30	4:00
	10	4:05	5:00	5:00	4:30	4:00
	11	4:06	5:03	5:12	4:30	4:00
	12	4:08	5:00	5:04	4:30	4:00
Ideal weight (kg) #	1–12	81	100	78	93	78
Weight before HD (kg)	1	83.1	103.7	83.4	94.1	79.6
	2	82.7	103.7	83.2	95.9	78.7
	3	83.0	105.1	83.7	95.4	80.4
	4	83.1	103.7	82.1	96.4	79.6
	5	82.8	102.1	81.8	98.6	79.7
	6	84.3	103.6	83.0	94.7	80.0
	7	83.5	102.6	80.3	95.9	79.6
	8	82.4	102.0	81.6	96.9	79.0
	9	83.1	104.0	81.7	96.1	79.5
	10	82.2	103.5	82.1	95.1	79.4
	11	83.4	102.2	81.1	96.5	79.1
	12	84.0	104.3	81.5	96.3	79.2
Weight after HD (kg)	1	80.4	102.7	81.1	92.3	77.7
	2	80.2	101.9	80.9	93.2	77.7
	3	80.1	102.1	80.7	93.0	78.1
	4	81.3	101.5	80.5	93.6	77.4
	5	80.4	101.1	80.5	96.0	77.5
	6	81.4	101.0	79.8	92.9	77.7
	7	80.8	100.6	80.2	93.3	77.3
	8	80.2	100.1	80.0	93.3	77.4
	9	80.7	100.5	79.8	93.3	77.3
	10	80.1	100.0	80.0	93.0	77.5
	11	80.6	100.0	79.5	93.8	77.8
	12	81.8	100.8	79.4	93.5	77.4
Blood flow rate (mL min −1 )	1–12	320	350	350	330	350
Dialysate flow rate (mL min −1 )	1–12	500	500	500	500	500
Dialysate	1–12	Potassium	Potassium	Potassium	Potassium	Potassium
Dialyser model *	1–12	FX80	FX100	FX80	FX100	FX80

^# Ideal weight is the average weight at the end of each HD session.

^* Dialyser FX80 and 100 are high flux dialyser (Fresenius Medical Care, Bad Homburg, Germany). Both use a Helixone membrane with a surface area of 1.8 and 2.2 m² respectively. They have a reported ultrafiltration coefficient of 59 and 73 mL h⁻¹ *mmhg respectively.

Table A4.

Key model building steps. Runs are described in the footer. Run 11 is the final model. The final model decision was driven mainly by the diagnostic plots (see Figures 1 and A4)

Model	Run 1	Run 4	Run 5	Run 6	Run 8	Run 9	Run10	Run11	Run12	Run13	Run14	Run15	Run21
OFV	−86.1	−187.9	−187.9	−198.1	−196.5	−156.5	−151.8	−152.2	−155.5	−151.5	−152.6	−153.3	−68.86
CLR (L h −1 )	0	0	0	0	0	0	0	0	0	0	0	0	0
CLNR (L h −1 )	0.535	0.547	0.548	0.474	0.485	0.824	0.575	0.486	0.487	0.484	0.442	0.521	0.494
V2 (L)	18.038	17.290	17.294	13.892	13.981	4.498	15.922	17.492	17.880	17.346	16.141	20.445	23.73
V3 (L)	35.945	41.703	41.711	32.698	32.560	8.102	44.203	48.627	48.464	48.129	44.414	47.253	48.23
Q (L h −1 )	5.811	4.590	4.594	3.559	3.607	0.708	4.761	5.250	5.423	5.129	4.555	6.650	4.59
k a (h −1 )	0.156	0.074	0.074	0.073	0.073	0.020	0.077	0.077	0.079	0.077	0.068	0.092	0.096
F1	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55
Prop	0.313	0.224	0.224	0.225	0.225	0.254	0.248	0.248	0.245	0.248	0.248	0.248	0.31
Add	0.004	0.010	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
CLHD (L h −1 )	10.598	10.202	10.206	8.004	8.041	2.984	10.320	11.396	10.260	‐	11.597	10.779	10.5
FID56 F1	‐	‐	‐	0.334	0.351	0.388	0.633
FID56CL	‐	‐	‐					3.183	3.123	3.178	3.273	2.871	3.28
VDIAL											1.907	1.278
FDT									1.25
KOA (Lh −1 )										21.01
BSV CL	29.661	2.3602	2.3616	1.9069	1.8770	0.206	0.476	0.476	0.476	0.476	0.476	0.476	0.476
OMEGA (2,1)	−4.935	−0.280	−0.280	−0.278	−0.249	0.155	‐	‐	‐	‐	‐	‐
BSV V2	0.873	0.070	0.070	0.040	0.033	0.135	0.13	0.13	0.13	0.13	0.13	0.13	0.13
OMEGA (3,1)	7.290	0.612	0.612	0.654	0.636	‐	‐	‐	‐	‐	‐	‐
OMEGA (3,2)	−1.026	0.0012	0.0014	−0.095	−0.084	‐	‐	‐	‐	‐	‐	‐
BSV F1	2.495	0.331	0.332	0.225	0.216	‐	0.084	0.084	0.084	0.084	0.084	0.084	0.084
OMEGA (4,1)	−13.35	−0.552	−0.552	−0.515	‐	‐	‐	‐	‐	‐	‐	‐
OMEGA (4,2)	1.919	0.055	0.055	0.073	‐	‐	‐	‐	‐	‐	‐	‐
OMEGA (4,3)	−4.471	−0.262	−0.262	−0.150	‐	‐	‐	‐	‐	‐	‐	‐
BSV k a	8.475	0.527	0.527	0.602	0.644	0.314	‐	‐	‐	‐	‐	‐
SE CLNR	‐	‐	‐	‐	‐	0.054	0.151	0.182	0.186	0.182	0.199	0.180	0.189
SE V2	‐	‐	‐	‐	‐	0.898	3.047	2.891	2.718	2.795	4.063	4.687	3.24
SE V3	‐	‐	‐	‐	‐	3.403	14.111	13.553	13.549	13.120	16.752	12.542	19.4
SE Q	‐	‐	‐	‐	‐	1.268	1.493	1.416	1.556	1.344	2.104	2.972	1.78
SE k a	‐	‐	‐	‐	‐	0.005	0.011	0.011	0.011	0.011	0.029	0.023	0.02
SE prop	‐	‐	‐	‐	‐	0.0086	0.0180	0.0181	0.0190	0.0182	0.0175	0.0187	0.034
SE CLHD	‐	‐	‐	‐	‐	1.552	2.009	1.865	1.522	‐	2.052	1.574	0.886
SE FID56	‐	‐	‐	‐	‐	0.0397	0.1783	1.9011	1.8503	1.9045	2.0405	1.5678	2.42
SE BSVCL	‐	‐	‐	‐	‐	0.5027	‐	‐	‐	‐	‐	‐
SE OMEGA (2,1)	‐	‐	‐	‐	‐	0.440	‐	‐	‐	‐	‐	‐
SE BSV V2	‐	‐	‐	‐	‐	0.392	‐	‐	‐	‐	‐	‐
SE BSV F1	‐	‐	‐	‐	‐	0.140	‐	‐	‐	‐	‐	‐
SE VDIAL											0.25	0.29
SE FDT									0.165
SE KOA											6.10

OFV = objective function value; CLR = renal clearance; CLNR = nonrenal clearance; V2 = central volume; V3 = peripheral volume; Q = intercompartmental clearance; k_a = absorption rate constant; F1 = bioavailability; Prop = proportional error; Add = additive error; CLHD = haemodialysis clearance; FID56F1 = fractional effect for subject 1 on bioavailability; FID56CL = fractional effect of subject 1 on clearance, VDIAL = fractional effect of dialysis on volume, FDT = fractional effect of dialyser type on CLHD, KOA = mass transfer area coefficient, BSV = between subject variability; SE = standard error.

Run 1 = Duong et al model + CLHD (haemodialysis clearance) + omega block 4 (CL,V2,ka, F1) + F1 fixed to 0.55;

Run 4 = Run 1 excluding 4 data points (deemed outliers);

Run 5 = Run 4 + additive error fixed to 0.01;

Run 6 = Run 4 + additive error fixed to 0.01 + FID56F1;

Run 8 = Run 4 + additive error fixed to 0.01 + FID56F1 + omega block 3 (CL,V2;F1)

Run 9 = Run 4 + additive error fixed to 0.01 + FID56F1 + omega block 2 (CL, F1);

Run 10 = Run 4 + additive error fixed to 0.01 + FID56F1 + BSV fixed;

Run 11 = Run 4 + additive error fixed to 0.01 + FID56CL + BSV fixed;

Run 12 = Run 4 + additive error fixed to 0.01 + FID56CL + BSV fixed+ fractional effect of dialyser type on CLHD

Run 13 = Run 4 + additive error fixed to 0.01 + FID56CL + BSV fixed + Michaels model for CLHD;

Run 14 = Run 4 + additive error fixed to 0.01 + FID56CL + BSV fixed + fractional effect of dialysis on V2

Run 15 = Run 4 + additive error fixed to 0.01 + FID56CL + BSV fixed + fractional effect of dialysis on V3

Run21 = Run11 with all outliers included in the data file

Sinnappah KA, Kuan IHS, Thynne TRJ, Doogue MP, Wright DFB. The pharmacokinetics of metformin in patients receiving intermittent haemodialysis. Br J Clin Pharmacol. 2020;86:1430–1443. 10.1111/bcp.14244