A Systematic Review of Multiple Linear Regression-Based Limited Sampling Strategies for Mycophenolic Acid Area Under the Concentration-Time Curve Estimation.

BACKGROUND AND
OBJECTIVE: One approach of therapeutic drug monitoring in the case of mycophenolic acid (MPA) is a limited sampling strategy (LSS), which allows the evaluation of the area under the concentration-time curve (AUC) based on few concentrations. The aim of this systematic review was to review the MPA LSSs and define the most frequent time points for MPA determination in patients with different indications for mycophenolate mofetil (MMF) administration.
METHODS: The literature was comprehensively searched in July 2021 using PubMed, Scopus, and Medline databases. Original articles determining multiple linear regression (MLR)-based LSSs for MPA and its free form (fMPA) were included. Studies on enteric-coated mycophenolic sodium, previously established LSS, Bayesian estimator, and different than twice a day dosing were excluded. Data were analyzed separately for (1) adult renal transplant recipients, (2) adults with other than renal transplantation indication, and (3) for pediatric patients.
RESULTS: A total of 27, 17, and 11 studies were found for groups 1, 2, and 3, respectively, and 126 MLR-based LSS formulae (n = 120 for MPA, n = 6 for fMPA) were included in the review. Three time-point equations were the most frequent. Four MPA LSSs: 2.8401 + 5.7435 × C0 + 0.2655 × C0.5 + 1.1546 × C1 + 2.8971 × C4 for adult renal transplant recipients, 1.783 + 1.248 × C1 + 0.888 × C2 + 8.027 × C4 for adults after islet transplantation, 0.10 + 11.15 × C0 + 0.42 × C1 + 2.80 × C2 for adults after heart transplantation, and 8.217 + 3.163 × C0 + 0.994 × C1 + 1.334 × C2 + 4.183 × C4 for pediatric renal transplant recipients, plus one fMPA LSS, 34.2 + 1.12 × C1 + 1.29 × C2 + 2.28 × C4 + 3.95 × C6 for adult liver transplant recipients, seemed to be the most promising and should be validated in independent patient groups before introduction into clinical practice. The LSSs for pediatric patients were few and not fully characterized. There were only a few fMPA LSSs although fMPA is a pharmacologically active form of the drug.
CONCLUSIONS: The review includes updated MPA LSSs, e.g., for different MPA formulations (suspension, dispersible tablets), generic form, and intravenous administration for adult and pediatric patients, and emphasizes the need of individual therapeutic approaches according to MMF indication. Five MLR-based MPA LSSs might be implemented into clinical practice after evaluation in independent groups of patients. Further studies are required, e.g., to establish fMPA LSS in pediatric patients.

Key Points

Introduction

Mycophenolate mofetil (MMF) is an immunosuppressive drug, whose active form is mycophenolic acid (MPA). MMF is administered after solid organ transplantation [1] as the prophylaxis against acute rejection, as well as being given in autoimmune diseases [2] and nephrotic syndrome [3, 4], as well as in atopic dermatitis [5]. MPA is highly protein bound (97–99%) with free MPA (fMPA) being pharmacologically active [6]. MPA pharmacokinetics are complex and highly variable, with numerous factors influencing the interindividual variability [2].

Due to the pharmacokinetic variability, therapeutic drug monitoring (TDM) in the case of MPA is recommended in clinical practice [2, 7]. TDM has been shown to be favorable not only in renal transplant recipients [8] but also in patients with lupus nephritis [9] and steroid-dependent nephrotic syndrome [10-12]. The most accurate approach to TDM is the determination of the full pharmacokinetic profile of the drug and calculation of the area under the concentration–time curve from 0 to 12 h (AUC0–12), as the concentration determined before the next dose (Ctrough) does not reflect the overall exposure to MPA [8]. Determining AUC0–12 is, however, time-consuming, expensive, and uncomfortable for patients; therefore, different approaches of TDM are being investigated.

One of the possibilities of TDM is establishing a limited sampling strategy (LSS) and predicting AUC0-12 on the basis of only a few blood samples [8]. LSS may be calculated using a Bayesian approach or multiple linear regression (MLR) analysis, which uses an equation derived from stepwise regression analysis based on concentrations measured at pre-defined times after dosing [7, 13]. Each MLR LSS constitutes an equation: AUC  = b  + M × C  + M × C  + M × C  + …  + M × C, where AUC indicates predicted AUC, b indicates the intercept, C, C, C, C indicate the concentrations obtained at t1 t2, t3 and tI time points, respectively, and M, M, M and M indicate the coefficients associated with each timed concentration [14]. Such strategies have been proposed for MPA in many groups of patients [15-19], with emphasis that each LSS should be applied to the same group of patients for whom it was established [20]. As it does not depend on the pharmacokinetic model of the drug and can be calculated with simple software or manually [14], MLR is easier to use in clinical practice than Bayesian analysis; however, the MLR approach has some limitations. First is the reliance of the equations' accuracy on exact times of blood sample collection [7, 14]. Second is the poor prediction of the exposure to the drug in patients with abnormal pharmacokinetics [14]. And third is its applicability limitation for the dosage regimen and the population from which MLR LSS was derived. The main disadvantage of the Bayesian approach is the requirement of advanced software and highly-qualified staff. However, as this methodology uses the population approach [14], it does not require strict adherence to sampling times and is characterized by better precision and accuracy [7, 14]. The aim of this systematic review was to summarize the MPA LSSs established with MLR for different groups of patients. The summary also aimed at defining the most frequently used sampling points for MPA determination.

Methods

Search Strategy

The literature databases PubMed, Scopus, and Medline were comprehensively searched in July 2021 with the combination of ‘mycophenolic acid’ or ‘mycophenolate mofetil’ and the terms, ‘limited sampling strategy’, ‘limited sampling strategies’, ‘limited sampling’, ‘optimal sampling’, ‘sparse sampling’, and ‘minimal sampling’. Additionally, the reference lists of studies found in the literature were searched to detect articles potentially eligible for inclusion. Only studies published in English were included.

Study Selection

The flow diagram of article selection is presented in Fig. 1.

Fig. 1.

The flow diagram of article selection. aSix records fulfilled more than one exclusion condition. bOne study included pediatric patients after renal transplantation as well as with autoimmune diseases

Inclusion Criteria

Original articles determining LSS based on MLR calculations for MPA and fMPA were included. The studies concerned adult and pediatric patients receiving MMF as a prophylaxis after transplantation (solid organ, hematopoietic stem cells) to treat autoimmune diseases or nephrotic syndrome.

Exclusion Criteria

The articles describing LSS for enteric-coated mycophenolic sodium (EC-MPS) were excluded, as there is an evident difference in MPA pharmacokinetics for these two formulations, MMF and EC-MPS [unpredictable absorption profile, delayed maximum concentration (Cmax), and higher pre-dose concentration (C0) after EC-MPS administration] [2, 21]. Therefore, in our opinion, EC-MPS LSSs should be analyzed separately. Also, the studies using previously established LSS, those with Bayesian estimator, with different than twice a day MMF dosing schedules and reviews were excluded. There are some studies establishing MPA LSSs with a Bayesian estimator, and although this approach has some advantages (e.g., better accuracy and precision, the lack of strict adherence to sampling times, and number of samples [7]), we decided to include only MLR-based MPA LSSs due to the excessive amount of data and the difficulty in analyzing MLR-based LSSs and Bayesian-approach LSSs.

Data Analysis

The data were analyzed according to the most frequently used time points in three groups of patients treated with MMF: (1) adult renal transplant recipients, (2) adults receiving MMF due to other indication than renal transplantation, and (3) pediatric patients. The most frequently used time points were calculated in relation to the number of LSSs equations in each group, and as the percentage of the sum of all time points used in all LSSs equations in each group of patients. Whenever possible, the predictive performance results of the LSSs (bias, precision, validation group) were included in the review, as was the information whether the validation was internal or external. If the LSS was validated with data which were at the same time used for LSS determination, then the validation was internal. If the data from a separate group of patients (or the patients were divided into two groups) were used for the validation, then the validation was external. The best MPA LSSs were chosen based on the following criteria of the predictive performance: r2 > 0.950, bias and precision < 10%.

Results

Study Identification and Characteristics

The search of the literature returned 55 studies concerning MLR LSSs for MPA and fMPA. In this review, 126 MLR-based LSS formulae were included [16–20, 22–71], among which two studies included both MPA and fMPA LSS [40, 61] and one study concerned only fMPA LSS [51]. There was one study which considered patients receiving either MMF or EC-MPS as one group and established the MPA LSSs for them [30]. If the study included several LSSs, those which the authors described as the best or those with the best r2 were chosen. Most of the studies concerned adult patients, who were treated with MMF after renal transplantation (n = 27; Table 1) or due to other indications (n = 17; Table 2). A total of 11 studies with MLR-based LSSs were found for children (Table 3). The data are presented in the tables in chronological order (the newest first).

Table 1

The characteristics of MLR-based equations found in the literature for predicting MPA AUCpred in adult renal transplant recipients treated with MMF

No.	Equation	r2	CNI co-administered	Bland–Altman analysis	Biasa	Precisionb	RMSE	Validation method/type	Additional information	References
1	9.57 × C6  + 27.238	0.907	–	–	Not different from zero	–	7.91	Jackknife method	–	[22]c
2	14.04  + 10.43 × C8  + 1.58 × C2d	0.87	Tac	10% outside 95% CI	10.28%	12.99%	–	Validation group/external	SE of estimation: 8.2	[23]
3	11.95  + 8.9 × C8  + 1.41 × C2  + 1.48 × C4d	0.91	Tac	5% outside 95% CI	8.64%	12.93%	–		SE of estimation: 6.76	[23]
4	8.36  + 7.49 × C8  + 1.34 × C2  + 1.66 × C4  + 0.76 × C1d	0.948	Tac	5% outside 95% CI	5.26%	8.35%	–		SE of estimation: 5.34	[23]
5	3.542  + 3.332 × C0.5  + 1.117 × C1.5  + 3.946 × C4d	0.90e	Tac	5% outside 95% CI	1.67%	8.90%	12.20%	–	–	[24]
6	8.149  + 1.442 × C2  + 1.056 × C4  + 7.133 × C6f	0.88e	Tac	5% outside 95% CI	− 0.2%	9.20%	13.20%		–	[24]
7	0.414  + 1.210 × C0.5  + 2.256 × C1.5  + 4.134 × C4g	0.85	CsA/Tac	–	1.65%	–	5.81%	Validation group/external	–	[25]
8	7.4  + 2.3 × C0  + 1.2 × C1  + 2.3 × C3  + 4.4 × C6	0.85	Tac	–	–	–	5.5	Leave-one-out cross-validation/internal	–	[26]
9	10.6  + 1.1 × C1  + 1.1 × C2  + 2.0 × C4  + 3.9 × C6	0.86	Tac	–	–	–	5.5		< 31 postoperative day	[26]
10	3.8  + 3.5 × C0  + 1.2 × C1  + 1.9 × C3  + 5.4 × C6	0.92	Tac	–	–	–	3.9		≥ 31 of postoperative day	[26]
11	4.272  + 4.074 × C6  + 1.896 × C2  + 4.680 × C10  + 0.859 × C0.5	0.918	Tac	5.17% outside 95% CI	− 0.20%	8.70%	14.20%	–	–	[27]
12	7.951  + 4.040 × C6  + 1.893 × C2  + 4.542 × C10	0.863	Tac	6.9% outside 95% CI	− 0.30%	12.20%	17.30%		–	[27]
13	17.3  + 4.4 × C0  + 1.1 × C1  + 2.9 × C4	0.86	Tac	–	–	14.51%	16.04%	–	–	[28]
14	14.9  + 1.3 × C1  + 3 × C4  + 3.7 × C6	0.87	Tac	–	–	14.38%	14.86%		More accurate in patients with two MPA peaks	[28]
15	20.30  + 5.80 × C0  + 3.06 × C4	0.91	Tac	–	–	–	–	–	SD of residual error: 11.2 μg·h/mL; pre-Tx period	[29]
16	23.37  + 4.21 × C0  + 3.60 × C4	0.48	Tac	–	–	–	–		SD of residual error: 11.1 μg·h/mL; 1 month post-Tx	[29]
17	22.93  + 4.63 × C0  + 5.60 × C6	0.6	Tac	–	–	–	–		SD of residual error: 12.8 μg·h/mL; 3 months post-Tx	[29]
18	16.5  + 4.9 × C1.5  + 6.7 × C3.5h	0.82/0.66i; 0.71j	Tac	–	–	14%/17%i,k; 13%j	9%/24%i; 17%j	Bootstrap/external	–	[30]
19	0.81  + 1.07 × C0.5  + 2.20 × C2  + 3.48 × C4	0.79e	Tac	–	− 0.20%	13.60%	3.60%	Jackknife/internal	–	[31]
20	9.328  + 1.311 × C1  + 1.455 × C2  + 2.901 × C4	0.838	Tac	–	− 3.80%	14.90%	–	Jackknife/internal	–	[32]
21	–0.5754  + 1.0664 × C0.5  + 1.4692 × C1.5  + 4.7313 × C3g	0.901	Tac	–	1.74%	11.79%	–	Jackknife/internal	–	[33]
22	0.3546  + 0.9297 × C0.5  + 1.2872 × C1.5  + 3.6416 × C3  + 2.9424 × C4g	0.901	Tac	–	2.60%	9.39%	–		–	[33]
23	–0.2677  + 3.0326 × C0  + 0.7353 × C0.5  + 0.5545 × C1 + 0.7171 × C1.5  + 3.6757 × C3g	0.939	Tac	Minimal bias	0.67%	7.73%	–		–	[33]
24	8.64  + 5.13 × C0  + 0.62 × C0.66  + 2.84 × C2	0.79	CsA/Sir	–	0.90%	–	14%	Validation group/external	–	[34]
25	8.32  + 0.904 × C1.5  + 1.955 × C4  + 10.206 × C10	0.965	CsA	–	MPE: 0.71 mg·h/L	–	5.41 mg·h/L	Jackknife/internal	–	[35]
26	11.629  + 1.286 × C1.5  + 14.418 × C4	0.919	CsA	–	MPE: 0.34 mg·h/L	–	6.38 mg·h/L		–	[35]
27	15.547  + 14.46 × C10	0.882	CsA	–	MPE: 0.17 mg·h/L	–	8.06 mg·h/L		–	[35]
28	10.43  + 1.47 × C0  + 1.06 × C0.66  + 1.65 × C2	0.862	CsA	–	–	–	4.1	Dataset-splitting method similar to a bootstrap/external	83% (±20%)m	[36]
29	3.13  + 2.44 × C0  + 1.31 × C1.25  + 6.12 × C4	0.828	CsA	–	–	–	4.6		81% (±20%)m	[36]
30	7.77  + 1.99 × C0  + 1.05 × C0.66  + 3.88 × C3	0.809	CsA	–	–	–	4.9		83% (±20%)m	[36]
31	8.31  + 5.91 × C0  + 0.79 × C0.66  + 5.86 × C4	0.822	Sir	–	–	–	10		78% (±20%)m	[36]
32	7.05  + 5.57 × C0  + 1.24 × C1.25  + 5.66 × C4	0.818	Sir	–	–	–	10.1		70% (±20%)m	[36]
33	10.19  + 7.15 × C0  + 0.80 × C0.66  + 2.05 × C2	0.774	Sir	–	–	–	11.3		69% (±20%)m	[36]
34	15.94  + 1.77 × C2  + 2.34 × C4  + 4.76 × C9	0.877	Tac	–	2.90%	10.90%	14.80%	Validation group/external	–	[37]
35	20.38  + 0.26 × C0  + 2.06 × C2  + 3.82 × C4	0.693	Tac	–	2.90%	17.10%	21.50%		–	[37]
36	4.24  + 2.05 × C2  + 8.51 × C7  + 2.29 × C12	0.94	Tac	No value beyond ±2 SD	1.15 ± 3.08	–	–	–	–	[38]
37	14.81  + 0.80 × C0.5  + 1.56 × C2  + 4.80 × C4	0.70	CsA	Mean error: 10.1 mg·h/L	1.3 ± 12.8%	10.2 ± 7.6%	–	Validation group/external	76% (±15%)m	[39]
38	11.29  + 0.51 × C0.5  + 2.13 × C2  + 8.15 × C8	0.88	CsA	Mean error: 6.9 mg·h/L	–0.6 ± 8.6%	6.9 ± 5.0%	–		92% (±15%)m	[39]
39	10.403  + 0.841 × C2  + 1.105 × C3  + 0.447 × C4	0.901	CsA	Good agreement; a few values beyond 95% CI; average bias of < 1%	0.56 ± 28.21%	11.22 ± 0.94%	–	Jackknife/internal	–	[40]
40	3.504  + 1.098 × C1  + 0.670 × C2  + 5.659 × C4	0.937	CsA		1.48 ± 11.76%	14.70 ± 0.58%	–		–	[40]
41	178.167  + 0.954 × C2  + 4.001 × C4	0.975	CsA		2.96 ± 4.95%	12.14 ± 0.66%	–		LSS for fMPA	[40]
42	180.543  + 0.956 × C2 − 0.223 × C3  + 4.342 × C4	0.975	CsA		4.34 ± 3.56%	12.67 ± 0.72%	–		LSS for fMPA	[40]
43	136.826  + 0.76 × C1  + 0.84 × C2  + 3.914 × C4	0.982	CsA		2.38 ± 7.18%	14.35 ± 0.60%	–		LSS for fMPA	[40]
44	3.0410  + 9.8588 × C0  + 0.5963 × C0.5  + 2.5612 × C3	0.893	CsA	–	MPE: 0.17	–	3.85	–	–	[41]
45	2.8401  + 5.7435 × C0  + 0.2655 × C0.5  + 1.1546 × C1  + 2.8971 × C4	0.956	CsA	–	MPE: 0.00	–	2.45		–	[41]
46	12.61  + 0.37 × C0.5  + 0.49 × C1  + 3.22 × C4  + 8.17 × C10	0.92	CsA	–	–	–	–	–	–	[42]
47	7.182  + 4.607 × C0  + 0.998 × C0.67  + 2.149 × C2	0.73	CsA	–	Mean bias: 0.0 mg·h/L (−1.5/0.2)j	19.3 mg·h/L (6.9/8.1)j		Validation-nondiabetics; usefulness-diabetics/external	62%/62%l; (±25%)m	[43]
48	15.3  + 7.06 × C4  + 6.77 × C8 − 3.76 × C12	0.97	Tac	–	–	–	–	–	–	[44]
49	–0.247  + 11.73 × C6  + 2.92 × C2	0.99	CsA	–	–	–	–		–	[44]
50	3.48  + 0.58 × C20min  + 0.97 × C1  + 6.64 × C3	0.946	CsA	–	–	–	13.6%	Jackknife/internal	–	[45]
51	4.38  + 2.14 × C1  + 7.19 × C9	0.906	CsA	–	–	–	13.8%		–	[45]
52	4.42  + 1.74 × C1  + 2.99 × C4  + 5.43 × C9	0.944	CsA	–	–	–	11.3%		–	[45]
53	10.2  + 0.72 × C20min  + 8.65 × C3	0.903	CsA	–	–	–	17.9%		–	[45]
54	7.75  + 6.49 × C0  + 0.76 × C0.5  + 2.43 × C2	0.862	Tac	–	Prediction error: 6.1 ± 19.0%	–	–	Validation group (cross-validation)/external	82% (±15%)m	[46]
55	15.93  + 0.73 × C1.25  + 0.8 × C2  + 7.32 × C10	0.861	CsA	Good agreement	–	–	–	–	–	[47]
56	15.19  + 6.92 × C0  + 1.08 × C1  + 0.72 × C2	0.756	CsA	–	–	–	–		–	[47]
57	10.72  + 0.94 × C1.25  + 0.84 × C2  + 1.46 × C4  + 6.5 × C10	0.901	CsA	Good agreement	–	–	–		–	[47]
58	6.02  + 5.61 × C0  + 1.28 × C1  + 0.9 × C2  + 2.54 × C4	0.89	CsA	Good agreement	–	–	–		–	[47]
59	9.02  + 3.77 × C0  + 1.33 × C1  + 1.68 × C3  + 2.96 × C6	0.841	CsA	–	–	–	–	–	–	[48]

AUC predicted area under the concentration-time (0–12 h) curve, CI confidence interval, CNI calcineurin inhibitor, CsA cyclosporine, fMPA free mycophenolic acid, MLR multiple linear regression, MMF mycophenolate mofetil, MPA mycophenolic acid, MPE mean prediction error, RMSE root mean square prediction error, SD standard deviation, SE standard error, Sir sirolimus, Tac tacrolimus, Tx transplantation, Cx concentration at x h

aMean or median percentage prediction error

bMean or median absolute percentage prediction error

cOnly abstract available

dDispersible tablet

eAdjusted r2

fCapsule

gGeneric MMF

hMost of the pharmacokinetic data simulated based on the literature data; C3.5 calculated as the arithmetic mean of C3 and C4

iSimulated data/observed data from MMF- and EC-MPS-treated patients

jOnly for data from MMF-treated patients

kMean relative prediction error

lPatients with diabetes/patients without diabetes

mGood guess (number of AUCpred within ± 15% or ± 20% or ± 25% of AUCtotal)

Table 2

The characteristics of MLR-based equations found in the literature for predicting MPA AUCpred in adult patients treated with MMF due to other indication than renal transplantation

No.	MMF indication	Equation	r2	CNI co-administered	Bland–Altman analysis	Biasa	Precisionb	RSME	Validation method	Additional information	References
1	Heart transplantation	8.424  + 0.781 × C0.5  + 1.263 × C2  + 1.660 × C4  + 3.022 × C6c	0.844	Tac	One case exceed 95% confidence interval	2.09 ± 14.05%	11.17 ± 8.52%	–	Bootstrap (internal)/validation group (external)	87%d	[70]
2	Hematopoietic cell transplantation	1.2039 × AUC1–4  + 8.9727e	0.65	CsA	–	–	–	–	Validation group/external	92.31%f	[49]
3	Lung transplantation	4.04  + 1.64 × C1  + 3.08 × C4  + 5.17 × C8	0.852	Tac	–	2.00%	11.66%	–	Validation group/external	77.27%d	[50]
4	Anti-neutrophil cytoplasmic antibody-associated vasculitis	8.5  + 0.77 × C0.5  + 4.0 × C2  + 1.7 × C4	0.928	–	–	–	–	–	–	–	[71]
5	Liver transplantation	34.2  + 1.12 × C1  + 1.29 × C2  + 2.28 × C4  + 3.95 × C6	0.976	Tac	Mean error 9.02 mg·h/L	2.33 ± 13.0%	9.74 ± 8.81%	–	Bootstrap/internal	74.5%d; LSS for fMPA	[51]
6	Islet transplantation	1.783  + 1.248 × C1  + 0.888 × C2  + 8.027 × C4	0.98	Tac	–	− 3.09%	9.53%	–	Jackknife/internal	75%d	[20]
7		2.778  + 1.413 × C1  + 0.963 × C3  + 7.511 × C4	0.973	Tac	–	− 3.22%	11.02%	–		81.25%d	[20]
8		1.448  + 1.239 × C1  + 0.271 × C1.5  + 9.108 × C4	0.96	Tac	–	− 1.90%	11.46%	–		75%d	[20]
9		1.410 − 0.259 × C0  + 1.443 × C1  + 9.622 × C4	0.957	Tac	–	− 2.68%	11.53%	–		75%d	[20]
10		1.547  + 1.417 × C1  + 9.448 × C4	0.957	Tac	–	− 2.46%	11.14%	–		75%d	[20]
11	Heart transplantation	9.693  + 0.626 × C0.5  + 0.606 × C1  + 2.197 × C2	0.841	CsA	Good agreement	3.2 ± 16.73%	–	–	Validation group/external	70%d	[52]
12	Autoimmune disease (antineutrophil cytoplasmic antibody-associated systemic vasculitis; systemic lupus erythematosus)	38.3  + 11.7 × C0	0.48	–/CsAg	–	3.4%	–	26.8%	Validation group/internal	–	[53]
13		30.8  + 10.1 × C0  + 0.7 × C0.67	0.53	–/CsAg	–	4.8%	–	25.1%		–	[53]
14		17.5  + 7.1 × C0  + 1.0 × C1  + 2.6 × C3	0.61	–/CsAg	–	0.8%	–	22.6%		–	[53]
15		12.3  + 4.7 × C0  + 1.2 × C1  + 2.7 × C3  + 1.8 × C6	0.7	–/CsAg	–	20.4%	–	17.3%		–	[53]
16	Liver transplantation	4.46  + 0.81 × C1  + 1.78 × C2  + 2.51 × C4  + 4.94 × C8	0.95	Tac	The best agreement; mean error 9.02 mg·h/L	0.27 ± 1.79%	8.83 ± 1.24%	–	Bootstrap/internal	83.3%d	[54]
17		5.92  + 1.10 × C1  + 1.01 × C2  + 1.77 × C4  + 4.80 × C6	0.927	Tac	–	0.36 ± 1.86%	9.71 ± 1.21%	–		83.3%d	[54]
18		9.37  + 2.18 × C2  + 2.10 × C4  + 4.71 × C8	0.901	Tac	–	0.81 ± 2.70%	12.64 ± 11.97%	–		75%d	[54]
19		10.56  + 1.55 × C1.5  + 6.44 × C6	0.859	Tac	–	1.78 ± 2.64%	14.41 ± 1.61%	–		58.3%d	[54]
20	Heart transplantation	1.25 × C1  + 5.29 × C4  + 2.90 × C8  + 3.61 × C10	0.95	Tac	–	MPE: − 0.007 ± 0.123	–	–	Crossvalidation/internal	79%d	[55]
21		3.37 × C0  + 0.97 × C0.5  + 1.20 × C1  + 2.70 × C2	0.87	Tac	–	MPE: − 0.006 ± 0.189	–	–		46%d	[55]
22		1.53 × C1  + 5.51 × C4  + 4.62 × C8	0.91	Tac	–	MPE: − 0.017 ± 0.180	–	–		68%d	[55]
23		1.09 × C0.5  + 1.19 × C1  + 3.60 × C2	0.84	Tac	–	MPE: − 0.017 ± 0.208	–	–		50%d	[55]
24		1.65 × C0.5  + 4.74 × C2	0.75	Tac	–	MPE: − 0.032 ± 0.253	–	–		36%d	[55]
25	Heart transplantation	0.10  + 11.15 × C0  + 0.42 × C1  + 2.80 × C2	0.96	CsA	–	0.15 ± 7.85%	–	–	–	100%d	[56]
26		–0.51  + 11.47 × C0  + 3.24 × C2	0.94	CsA	–	0.495 ± 10.35%	–	–		90.9%d	[56]
27	Liver transplantation	6.03  + 0.89 × C1  + 1.94 × C2  + 2.24 × C6  + 4.64 × C8	0.911	Tac	Good agreement	1.18 ± 11.84%	–	–	Validation group/external	90.3%d	[57]
28	Liver transplantation	5.503  + 0.919 × C1  + 1.871 × C2  + 3.176 × C6  + 3.664 × C8	0.921	Tac	Good agreement; mean error ± 9.89 mg·h/mL	1.24 ± 11.19%	8.24 ± 7.61%	–	–	88%d	[58]
29		10.229  + 0.925 × C1  + 1.750 × C2  + 4.586 × C6	0.855	Tac	–	2.42 ± 15.73%	11.47 ± 10.95%	–		70.8%d	[58]
30		17.930  + 1.992 × C2  + 4.136 × C6	0.751	Tac	–	4.33 ± 21.74%	16.35 ± 14.84%	–		62.5%d	[58]
31	Lung transplantation	1.14  + 0.241 × logC0  + 0.406 × logC2	0.828	CsA/Tac	–	− 5.82%	–	5.97%h	Validation group/external	89%d; LSS for logAUC	[59]
32		1.09  + 0.202 × logC0  + 0.411 × logC1.5	0.791	CsA/Tac	–	− 5.71%	–	6.94%h		89%d; LSS for logAUC	[59]
33		1.000  + 0.153 × logC0  + 0.327 × logC0.6  + 0.354 × logC2	0.873	CsA/Tac	–	− 3.70%	–	5.81%h		89%d; LSS for logAUC	[59]
34		1.024  + 0.192 × logC0  + 0.213 × logC1  + 0.355 × logC2	0.827	CsA/Tac	–	− 6.88%	–	6.88%h		100%d; LSS for logAUC	[59]
35		1.154  + 0.253 × logC0 − 0.070 × logC1.5  + 0.460 × logC2	0.8	CsA/Tac	–	− 5.90%	–	6.03%h		100%d; LSS for logAUC	[59]
36	Liver transplantation	8.144  + 2.880 × C3	0.575	CsA/Tac	–	12.6%	–	–	–	–	[60]
37	Hematopoietic cell transplantation	4.43  + 2.76 × C0  + 0.51 × C1  + 1.97 × C2  + 4.27 × C6	0.85	CsA	–	0.8 μg·h/mL/7.1 ± 16.6%i	MAE: 2.3 μg·h/mL	–	Validation group/external	Oral	[61]
38		63.92  + 2.01 × C0  + 0.67 × C1  + 2.05 × C2  + 4.26 × C6	0.9	CsA	–	21.7 ng·h/mL/10.4 ± 17.0%i	MAE: 39.0 ng·h/mL	–		Oral; LSS for fMPA	[61]
39		–0.49  + 1.58 × C2  + 0.41 × C4  + 13.88 × C6	> 0.99	CsA	–	1.7 μg·h/mL/7.6 ± 17.5%i	MAE: 2.3 μg·h/mL	–		Intravenous	[61]
40		7.99  + 1.40 × C2  + 2.47 × C4  + + 9.54 × C6	> 0.99	CsA	–	0.3 ng·h/mL/1.1 ± 13.1%i	MAE: 22.7 ng·h/mL	–		Intravenous; LSS for fMPA	[61]
41	Heart transplantation	5.568  + 0.902 × C1.25  + 2.022 × C2  + 4.594 × C6	0.926	CsA	Good agreement	–	–	–	–	–	[62]
42		3.800  + 1.015 × C1.25  + 1.819 × C2  + 1.566 × C4  + 3.479 × C6	0.948	CsA	–	–	–	–		–	[62]

AUCpred predicted area under the concentration-time (0–12 h) curve, CNI calcineurin inhibitor, CsA cyclosporine, fMPA free mycophenolic acid, MAE mean absolute error, MLR multiple linear regression, MMF mycophenolate mofetil, MPA mycophenolic acid, MPE mean prediction error, RMSE root mean square prediction error, Tac tacrolimus, Cx concentration at x h

aMean or median percentage prediction error

bMean or median absolute percentage prediction error

cDispersible tablets

dGood guess (number of AUCpred within ±15% of AUCtotal)

eSampling time 1, 2 and 4 for AUC1-4

fPredictive accuracy

gOnly 3 patients (8%) received CsA

hPrecision

iBias/mean prediction error %

Table 3

The characteristics of MLR-based equations found in the literature for predicting MPA AUCpred in children treated with MMF

No.	MMF indication	Equation	r2	CNI co-administered	Bland–Altman analysis	Biasa	Precisionb	Validation method	Additional information	References
1	Nephrotic syndrome	1.62  + 2.22 × C0  + 1.27 × C1  + 2.32 × C3  + 1.32 × C4  + 3.07 × C6	0.9477	–	–	− 0.39%	2.87%	Validation group/external	94%c	[19]
2		7.10  + 1.21 × C1  + 3.75 × C3  + 3.08 × C6	0.8388	–	–	− 2.69%	12.92%	Bootstrap	92%c	[19]
3	Nephrotic syndrome	8.7  + 4.63 × C0  + 1.90 × C1  + 1.52 × C2	0.9	–	Good agreement; corresponding residuals mean − 0.03 ± 0.17	3.88 ± 3.72%	–	Validation group/external	–	[63]
4		6.9  + 3.69 × C0  + 1.84 × C1  + 1.09 × C2  + 2.32 × C4	0.92	–	–	2.71 ± 3.13%	–		–	[63]
5		6.27  + 0.93 × C1  + 5.36 × C4  + 6.56 × C8	0.96	–	–	1.12 ± 3.36%	–		–	[63]
6	Idiopathic nephrotic syndrome	21.971  + 2.6059 × C2	0.6405	CsA	–		–		–	[64]
7	Systemic lupus erythematosus	12.82  + 4.86 × C0  + 0.66 × C1  + 0.15 × C1.5  + 0.95 × C2  + 2.25 × C3	0.88	–	Minimal bias	1.96%	11.28%d	Bootstrap/internal	–	[18]
8		13.81  + 0.68 × C1  + 1.08 × C2  + 2.21 × C3 + 4.62 × C0	0.87	–	Minimal bias	1.92%	11.24%d		–	[18]
9	Renal transplantation	18.6  + 4.3 × C0  + 0.54 × C0.5  + 2.15 × C2e	0.72	CsA	Mean difference 0.14 mg·h/L; prediction variation ±24.4 mg·h/L	–	–	Validation group/external	–	[65]
10		10.6  + 3.18 × C0  + 1.39 × C0.5  + 2.08 × C2f	0.67	CsA	Mean difference − 1.26 mg·h/L; prediction variation ±26.9 mg·h/L	–	–		–	[65]
11		9.55  + 4.50 × C0  + 0.88 × C0.5  + 2.67 × C2	0.77	CsA	–	6.48 ± 2.53%	–		–	[65]
12		9.87  + 0.90 × C1  + 1.73 × C2  + 6.86 × C8	0.91	CsA	–	3.56 ± 1.54%	–		–	[65]
13	Renal transplantation	8.217  + 3.163 × C0  + 0.994 × C1  + 1.334 × C2  + 4.183 × C4	0.9456	Tac	Good agreement (better than 3 points LSS)	–	–	–	–	[16]
14		10.01391  + 3.94791 × C0  + 3.24253 × C0.5  + 1.0108 × C2	0.8996	Tac	Good agreement; mean error of 2.9%	–	–	–	–	[16]
15	Renal transplantation	12.62  + 7.78 × C0  + 0.90 × C1  + 1.30 × C2	0.75	CsA/Tac	Prediction variation of ±12.2 μg·h/mL	–	–	–	–	[17]
16		13.73  + 9.024 × C0  + 1.779 × C2	0.67	CsA/Tac	Prediction deviation ±14 μg·h/mL	–	–	–	–	[17]
17		15.1  + 9.68 × C0  + 1.28 × C1	0.67	CsA/Tac	Prediction deviation ±14 μg·h/mL	–	–	–	–	[17]
18	Renal transplantation	7.73  + 0.94 × C1  + 2.55 × C2  + 5.48 × C6	0.845	CsA/Tac/–	Mean deviation 0.0 ± 10.6 mg·h/mL	–	–	–	–	[66]
19		8.22  + 3.16 × C0  + 0.99 × C1  + 1.33 × C2  + 4.18 × C4	0.867	CsA/Tac/–	Mean deviation 0.0 ± 9.8 mg·h/mL	–	–	–	–	[66]
20	Renal transplantation and autoimmune diseases	10.75 + 0.98 × C1 + 2.38 × C2 + 4.86 × C6	0.87	CsA/Tac	Good agreement, mean error ± 9.5 μg·h/mL	–	–	–	–	[67]
21		15.79  + 2.05 × C0  + 0.95 × C0.5  + 3.73 × C2	0.74	CsA/Tac	–	–	–	–	–	[67]
22		14.57  + 1.62 × C0  + 1.5 × C1  + 5.15 × C6	0.76	CsA/Tac	–	–	–	–	–	[67]
23	Renal transplantation	12.9  + 5.99 × C0  + 0.528 × C40min  + 2.4 × C2	0.7396	–	–	–	–	–	–	[68]
24	Renal transplantation	5.2  + 7.1 × C0  + 1.0 × C1.25  + 5.4 × C6	0.88	CsA	–	–	–	–	–	[69]
25		9.13  + 5.7 × C0  + 1.1 × C40min  + 2.1 × C2	0.74	CsA	–	–	–	–	–	[69]

AUC predicted area under the concentration-time (0–12 h) curve, CNI calcineurin inhibitor, CsA cyclosporine, MLR multiple linear regression, MMF mycophenolate mofetil, MPA mycophenolic acid, Tac tacrolimus, Cx concentration at x h

aMean or median percentage prediction error

bMean or median absolute percentage prediction error

cGood guess (number of AUCpred within ± 15% of AUCtotal)

dGiven as imprecision

eFor MPA concentrations determined with HPLC

fFor MPA concentrations determined with EMIT

Based on all LSSs found in the literature, blood samples for MPA determination were collected before the administration of the next dose and subsequently at 20 min, 0.5 h, 40 min, 1 h, 1.25 h, 1.5 h, 2 h, 3 h, 3.5 h, 4 h, 6 h, 7 h, 8 h, 9 h, 10 h, and 12 h afterwards. These time points were included in LSSs as C20min, C0.5, C40min, C1, C1.25, C1.5, C2, C3, C3.5, C4, C6, C7, C8, C9, C10 and C12, where ‘C’ is the concentration. In the LSS equations, MPA concentration determined before the next MMF dose is named as C0; however, it must be emphasized that, due to administration of MMF every 12 h, this concentration is the pre-dose trough concentration and should be named as Ctrough or Cmin. In the MLR-based LSSs, it is more convenient to write C0 instead of Ctrough.

For most of the studies, the predictive performance results were found. Bias was expressed as mean or median percentage prediction error; however, in some studies, bias was expressed as mean prediction error (MPE) or mean bias with units of the concentration multiplied by time. Precision was expressed as mean or median absolute percentage prediction error, however, in some studies, precision was expressed as mean absolute error with units of the concentration multiplied by time. Root square mean prediction error (RMSE) was also calculated in some studies as precision. Validation methods, if performed, included the bootstrap method, jackknife method, validation group, or cross-validation. Some LSSs were characterized by the good guess which is the percentage of the predicted AUC (AUCpred) within ± 15%, ± 20%, or ± 25% of the calculated AUC (AUCtotal).

The MLR-Based LSSs for Adult Renal Transplant Recipients

As MMF was primarily administered in prophylaxis of acute rejection in solid organ transplantation, most of the studies concerning MLR LSSs included renal transplant recipients [22-48] (Table 1). Three fMPA LSSs were included in the results as the occurrence of Cmax and Cmax2 should be the same for MPA and fMPA.

The equations included up to five time points with three time-point LSSs being the most frequent (59%). Of all the time points, those collected within 0–2 h after MMF administration constituted 58% of the total, whereas sampling between 3–5 h and 6–12 h after drug administration constituted 26% and 16%, respectively.

Of 59 MLR equations, the most frequently used time points were C4 and C2, which were included in 32 (54%) and 29 (49%) equations, respectively, and constituted 18% and 16% of the sum of all time points from 59 equations, respectively. The 22 (37%) equations including C0 and C0 constituted 13% of all time points. The most frequently included time point within 6–12 h after MMF administration was C6 (19% of equations). Two LSSs included C12 which is equal to C0 if blood samples are collected in steady-state; however, C12 was not analyzed with C0 when calculating the percentage.

If analyzed according to the calcineurin inhibitor co-administered, among all equations established for MMF and cyclosporine (CsA) treatment (n = 28), the most frequent time points in LSSs were C2 (18% of all time points, 54% of the equations), and C4 (17% of all time points, 50% of the equations). For tacrolimus (Tac) co-administration (30 LSSs), the time points most often included were C4 (19% of all time points, 57% of the equations), and C2 (15% of all time points, 47% of the equations). LSS established by Gaies et al. [25] was not included as the authors did not separately analyze patients receiving CsA and Tac.

With respect to the post-transplant period, the LSSs were divided into two groups: established for patients less than 1 month after transplantation, and longer than 3 months after transplantation. The LSSs established in the early post-transplant period (n = 22) most frequently included C2 (25% of all time points, 73% of the equations), and C4 (22% of all time points, 64% of the equations). For LSSs established in the stable post-transplant period (n = 16), the concentrations most often used included C1 (20% of all time points, 63% of the equations) and C3 (14% of all time points, 44% of the equations). In several studies, MPA concentrations and MPA LSSs were determined in patients in the early post-transplant period together with those in the stable post-transplant period. Therefore, those LSSs were not included in this analysis.

The worse r2 was for LSS established 1 month after transplantation and included two time points (C0 and C4; r2 < 0.5) [29]. Interestingly, the LSS with the same time points (C0 and C4), established in the same study but before transplantation, was characterized by much better r2 (0.91) [29]. The value of r2 above 0.98 was obtained for three LSSs, among which one included five time points [33], one included two time points [44], and one concerned fMPA [40]. The bias was within the range of − 3.80 to 10.28%. MPA LSS in one study was characterized by mean bias equal 0 mg h/L [41]. In other study, bias of one LSS was expressed as MPE and equal to 0.00 [43]. The precision defined as mean or median absolute percentage prediction error or RMSE ranged from 6.9 to 17.10% and 3.60 to 24%, respectively. Some studies calculated the good guess. The best results amounted to 92% [39], 83% [36], and 62% [43] for good guesses of AUCpred within ± 15%, ± 20%, or ± 25% of AUCtotal, respectively.

Based on the results of the predictive performance, the most promising MPA LSSs for renal transplant recipients were: MPA AUCpred  = 2.8401  + 5.7435 × C0  + 0.2655 × C0.5  + 1.1546 × C1  + 2.8971 × C4 if CsA was co-administered [41] and MPA AUCpred  = 8.36  + 7.49 × C8  + 1.34 × C2  + 1.66 × C4  + 0.76 × C1 if Tac was co-administered [23]. The latter equation had the advantage of being validated in an external group of patients. The LSSs which was characterized by very good bias and precision was MPA AUCpred  = 0.414  + 1.210 × C0.5  + 2.256 × C1.5  + 4.134 × C4 [25], which had the advantages of being validated in a validation group and applied to patients receiving either CsA or Tac; however, the r2 was < 0.950. High r2 was observed for the following equations: AUCpred  = 8.32  + 0.904 × C1.5  + 1.955 × C4  + 10.206 × C10 [35], AUCpred  = 15.3  + 7.06 × C4  + 6.77 × C8 − 3.76 × C12, and AUCpred  = – 0.247  + 11.73 × C6  + 2.92 × C2 [44]; however, the bias and precision were given in AUC units [35] or not given at all [44], so it is therefore difficult to compare these results with those expressed as percentages. For CsA co-treated patients, fMPA LSSs were characterized by high r2 (> 0.950); however, precision was > 10% for all three equations and the validation was internal [40].

The MLR-Based LSSs for Adult Patients Treated with MMF with Different Indication than Renal Transplantation

Among other MMF indications in adults than rejection prophylaxis after renal transplantation, studies aiming at establishing LSS for liver transplant recipients (n = 5) [51, 54, 57, 58, 60], heart transplant recipients (n = 5) [52, 55, 56, 62, 70], lung transplant recipients (n = 2) [50, 59], and hematopoietic stem cell transplant recipients (n = 2) [49, 61] were found. There were single studies including patients after islet transplantation [20], patients with autoimmune diseases (antineutrophil cytoplasmic antibody-associated systemic vasculitis and systemic lupus erythematosus) [53] and patients with anti-neutrophil cytoplasmic antibody-associated vasculitis [71] (Table 2). In one study, separate LSSs were established after oral and intravenous MMF administration for both total and fMPA [61]. One LSS consisted of AUC1-4 instead of particular time points [49].

The equations included up to four time points with three time-point LSSs being the most frequent (48%). Of all time points, those collected within 0–2 h after MMF administration constituted 64% of the sum of all time points, whereas sampling between 3–5 h and 6–12 h after drug administration constituted 18% and 19%, respectively.

Of 42 MLR equations, the most frequently used time points were C2 and C1. C2 was included in 28 (67%) equations and constituted 22% of the sum of all time points from 42 equations, while C1 was included in 24 (57%) equations and constituted 19% of all the time points from 42 equations. The number of 15 (36%) equations including C0 and C0 constituted 12% of all time points. The most frequently included time point within 6–12 h after MMF administration was C6 (36% of equations).

For other indications than renal transplantation, most MPA LSSs (n = 21) were established when Tac was co-administered. For these LSSs, the most frequent time points were C1 (24% of all time points, 76% of the equations), C2, and C4 (19% of all time points, 62% of the equations). Interestingly, for MMF and Tac co-administration, C0 was used in only two LSSs (10%). For CsA co-administration (10 LSSs), the time points most often included were C2 (31% of all time points, 100% of the equations), C6 (19% of all time points, 60% of the equations), and C1 (16% of all time points, 50% of the equations). C0 was used in four LSSs (40%) and constituted 13% of all time points. Four LSSs established for patients among whom only 8% received CsA [53] were not included in this analysis. Additionally, there were six LSSs established for the group of patients treated with two agents, either MMF and CsA or MMF and Tac [59, 60]. Five of them included logarithmic concentrations and sampling up to 2 h after drug administration [59]. The sixth LSS which was established for patients receiving concomitantly with MMF CsA or Tac included only one time point, and its r2 was low (0.575) [60].

For LSSs established for patients treated with MMF less than 1 month, the most frequently included time points were C2 (27% of all time points, 87% of the equations) and C6 (23% of all time points, 73% of the equations). LSSs established for patients treated with MMF longer than 3 months most frequently consisted of C2 (24% of all time points, 69% of the equations), and C0 (22% of all time points, 62% of the equations).

The r2 value of 0.98 was reached for four LSSs [20, 51, 61]. The bias was within − 1.1% to 20.4%. No LSS was characterized by bias equal to 0. The closest to zero bias was 0.15% [56] and − 0.006 expressed as MPE [55]. The precision defined as mean or median absolute percentage prediction error or RMSE ranged from 8.24 to 16.35% and 5.81 to 26.8%, respectively. The best results of AUCpred within ± 15% of AUCtotal amounted to 100% [56, 59].

Based on the results of the predictive performance, the most promising MPA LSS were: AUCpred  = 1.783  + 1.248 × C1  + 0.888 × C2  + 8.027 × C4 [20] established for patients after islet transplantation and AUCpred  = 4.46  + 0.81 × C1  + 1.78 × C2  + 2.51 × C4  + 4.94 × C8 for liver transplant recipients [54]. Both equations were established for patients co-treated with Tac. For CsA co-treated patients after heart transplantation, the best LSS was AUCpred  = 0.10  + 11.15 × C0  + 0.42 × C1  + 2.80 × C2; however, precision was not shown [56]. The LSSs for Tac co-treated liver transplant recipients were characterized by very good bias and precision (AUCpred  = 5.92  + 1.10 × C1  + 1.01 × C2  + 1.77 × C4  + 4.80 × C6 [54] and AUCpred  = 5.503  + 0.919 × C1  + 1.871 × C2  + 3.176 × C6  + 3.664 × C8 [58]); however, r2 was < 0.950 in both cases. High r2 was observed for externally validated LSS for CsA co-treated patients after hematopoietic stem cell transplantation (AUCpred  = − 0.49  + 1.58 × C2  + 0.41 × C4  + 13.88 × C6 [61]); however, the bias and precision were given in AUC units. The best LSS for fMPA, characterized by high r2 and good bias and precision, was AUCpred  = 34.2  + 1.12 × C1  + 1.29 × C2  + 2.28 × C4  + 3.95 × C6, and was established for liver transplant recipients [51]. All five LSSs with log-transformed concentrations, established for lung transplant recipients, were characterized by good bias and precision; however, r2 was < 0.90 for all of them [59]. Another fMPA LSS, which was characterized by high r2 (AUCpred  = 7.99  + 1.40 × C2  + 2.47 × C4  + 9.54 × C6), was established for intravenous MMF administration and validated externally; however, the results of bias and precision were expressed in ngh/mL [61].

The MLR-Based LSS for Pediatric Patients Treated with MMF

A total of 25 LSSs established for pediatric patients were included. These LSSs were found in 11 studies [16–19, 63–69]. Most of these concerned children after renal transplantation [16, 17, 65, 66, 68, 69]. There were three studies concerning nephrotic syndrome [19, 63, 64], one concerning systemic lupus erythematosus [18], and one which included both children after renal transplantation and with autoimmune diseases [67].

The equations included up to five time points. Three time-point LSSs were the most frequent (64%). Of all the time points, those collected within 0–2 h after MMF administration constituted 78% of all the time points, whereas sampling between 3–5 h and 6–12 h after drug administration constituted 11% and 10%, respectively.

Of 25 MLR equations, the most frequently used time points were C0 and C2. Each of these concentrations was included in 19 (76%) equations and constituted 24% of the sum of all time points from 25 equations. The most frequently included time point within 6–12 h after MMF administration was C6 (24% of equations). Among 14 LSSs established for children after renal transplantation, the most frequently included time points were the same as for all the pediatric studies. C0 and C2 were included in 12 LSSs (86%) and each constituted 29% of the sum of all time points from 14 equations.

Pediatric patients for whom MPA LSSs were established received concomitantly CsA (seven LSSs), Tac (two LSSs) or either CsA or Tac, but were analyzed together (eight LSSs). For eight LSSs, solely MMF was administered. The most frequently included time points only for LSSs established for children co-administered with CsA were analyzed. For these LSSs, the most frequent time points were C2 (32% of all time points, 88% of the equations), C0 (26% of all time points, 71% of the equations), and C0.5 (16% of all time points, 43% of the equations).

The best r2 was for three time points LSSs (C1, C4, C8) and was established for children with nephrotic syndrome. The best LSSs for renal transplant recipients (r2  = 0.91) also included three time points (C1, C2, C8). None of the equations reached r2 above 0.98. Only four studies included the bias (− 2.69% to 6.48% with − 0.39% being the closest to zero) and precision (2.87–12.92%). In one study [19], the results of a good guess were shown (the percentage of AUCpred within ± 15% of AUCtotal).

The best LSSs were AUCpred  = 6.27  + 0.93 × C0  + 5.36 × C4  + 6.56 × C8 [63], and AUCpred  = 1.62  + 2.22 × C0  + 1.27 × C1  + 2.32 × C3  + 1.32 × C4  + 3.07 × C6 [19], both for children with nephrotic syndrome treated solely with MMF. For pediatric renal transplant recipients co-treated with Tac, the best LSS was AUCpred  = 8.217  + 3.163 × C0  + 0.994 × C1  + 1.334 × C2  + 4.183 × C4; however, no bias and precision was included in the study [16]. Bias < 5% was observed for the following equation, AUCpred  = 9.87  + 0.90 × C1  + 1.73 × C2  + 6.86 × C8, developed for pediatric renal transplant recipients, co-treated with CsA; however, r2 was equal 0.91 in this case [65].

Additional Information Concerning MPA LSSs Studies

The detailed information on the patients’ age, drugs co-administered with MMF, method used for MPA determination, and the duration of MMF treatment or time elapsed from the transplantation are presented in Table 4.

Table 4

Additional information on MLR-based equations found in the literature for predicting MPA AUCpred for patients treated with MMF

Additional data	References
Demographic data, age, years
0–5	–
6–11	[17, 19, 63–65]
≥ 12	[16, 18, 66–68]
18–29	[35]
30–49	[23–29, 31, 32, 36–40, 42–45, 48–52, 56–59, 70]
≥ 50	[20, 34, 41, 53–55, 60, 62, 71]
Drugs co-administered
CsA	[34, 41, 45, 49, 53]a, [61, 64, 66, 67]
CsA, corticosteroids	[17, 25, 35, 36, 39, 40, 42–45, 47, 48, 52, 56, 59, 60, 62, 64, 65, 69]
Tac	[16, 20, 29, 32, 46, 55, 57, 66, 67]
Tac, corticosteroids	[17, 23–28, 30, 31, 33, 37, 38, 44, 50, 51, 54, 58–60, 70]
Steroids	[19, 53, 71]
Sirolimus, daclizumab, corticosteroids	[34, 36]
None	[18, 63, 66, 67]
No information	[22]b, [68]b
Analytical method
HPLC	[18–20, 22, 25, 32–44, 46–49, 51, 52, 55–59, 61, 62, 65, 68, 69]
UPLC-UV	[23]
UPLC with photodiode array detection	[30]
LC-MS/MS	[31, 70]
LC/ESI-MS/MS	[50]
EMIT	[16, 17, 24, 27–29, 45, 53, 54, 60, 63, 65–67, 71]
PETINIA technique	[26, 64]
Post-transplant time or the duration of MMF treatment
Pre-transplantation	[29]
Within 7 days	[20, 23, 24, 27, 31, 36, 48, 49, 51, 60, 61, 63]
Within 7 days and 1 month	[16, 30, 35, 37, 39, 40, 43, 46–48, 54, 57, 58, 60, 65, 66]c, [67]c, [68–70]d, [71]e
1–3 months	[16, 20, 29, 36, 41, 42, 44, 46, 52, 53, 62]
3 months	[18, 46, 47]
≥ 3 months	[16, 31, 32]
< 6 months	[25]
3–6 months	[33, 36, 44, 65, 68, 69]
6–12 months	[25, 44, 45, 47, 52, 56, 65]
< 1 year	[19, 20, 26, 28, 34, 52]
> 1 year	[17, 19, 20, 25, 26, 28, 44, 50, 52, 55, 59, 64, 65]
Stable post-transplant period, stable trough concentrations	[22]b, [38]

AUC predicted area under the concentration-time (0–12 h) curve, CsA cyclosporine, EMIT enzyme multiplied immunoassay technique, HPLC high-performance liquid chromatography, LC/ESI-MS/MS liquid chromatography positive ion electrospray ionization tandem mass spectrometry, LC-MS/MS liquid chromatography–tandem mass spectrometry, MLR multiple linear regression, MMF mycophenolate mofetil, MPA mycophenolic acid, PETINIA homogeneous particle-enhanced turbidimetric inhibition immunoassay technique, Tac tacrolimus, UPLC-UV ultra-performance liquid chromatography with ultraviolet detection

aOnly 3 patients (8%) received CsA

bAll information provided are based on the article abstract

cMedian 21 days after transplantation

dAt least 7 days, the upper time limit was not defined

eAt least 2 weeks, the upper time limit was not defined

To characterize the patients, we extracted six age groups based on the mean age described in each study. In four articles [30, 46, 47, 61], the mean age of the patients was not defined. In two articles, only the range of patients’ age was given (19–53 years [33] and 5–17 years [69]), not the mean. These studies are not included in Table 4. In the majority of studies [18–20, 22, 25, 32–44, 46–49, 51, 52, 55–59, 61, 62, 65, 68, 69], the high-performance liquid chromatography (HPLC) method was used for MPA determination. In 15 studies, MPA concentrations were determined based on enzyme multiplied immunoassay technique (EMIT) [16, 17, 24, 27–29, 45, 53, 54, 60, 63, 65–67, 71] (in one study both methods were applied [65]).

MMF was administered as dispersible tablets [23, 24, 70], suspension [65], or generic formulation [25, 33] apart from the standard formulation used in the majority of studies. In one study [61], LSSs were separately established for intravenous and oral MMF administration.

In Musuamba et al.'s study [30], the LSS included C3.5, which was calculated based on C3 and C4, as C3.5 was not collected. Moreover, although this study included both MMF- and EC-MPS-treated patients, most of the data were simulated.

Limitations of the MPA LSSs Studies

In the majority of the studies included in this review, the limitations concerned patients’ characteristics. The most frequent limitation was a relatively small sample size [20, 26, 31, 32, 36, 41, 43, 45, 48, 49, 56, 70, 71]. The duration of MMF treatment was a limitation and concerned the substantial difference in the duration of treatment and regimens among patients [49, 64], late post-transplant period (approximately 4 years) [50] or narrow time range to the first two post-transplant weeks [70]. Some of the studies included patients of only one race in the evaluation [19, 50] or with trace proteinuria during the day of blood collection [19], others did not fully supervise the contribution of concomitant drugs [16, 19, 26, 64, 71]. Several studies excluded patients with gastrointestinal disease or diarrheal illness [32] or those with rejection or notable adverse effects [20, 41]. Few limitations concerned the pharmacokinetics, such as MPA LSS overprediction of AUC by 30% [61], low frequency of the sample collection at time intervals [19, 50], and the exclusion from the dataset of profiles with either extraordinarily high MPA C0 or delayed absorption (tmax > 2 h) [36]. In one study, the lack of control patients was emphasized [64]. Other limitations included the limited universality of the LSS method [26, 48, 52].

Discussion

Estimating LSS is the approach of TDM applied for many drugs, e.g., MPA, levofloxacin, etoposide, moxifloxacin, ganciclovir, Tac, and CsA [72-78] in many diseases. Due to numerous factors influencing MPA pharmacokinetics, it is extremely difficult to establish a universal MPA LSS which might be applied in all MMF-treated patients. In our opinion, the review of MPA LSSs may be useful, as summaries of MLR LSSs for MPA which included the years up to 2009 [14] and up to 2013 [7] were found, and, therefore, this study contains the actual literature review. Moreover, some studies in which the LSS developed for one population was used to predict MPA exposition in an other population [15, 79, 80] were found in the literature. The authors [15] observed that the application of LSS established for lung transplant recipients to predict MPA AUC in patients after heart transplant yielded satisfactory prediction results (bias and precision within ± 15%); however, they concluded that the LSSs seem to be center-specific. Moreover, in Gellermann et al.'s study [81], the authors applied the LSSs established for children after renal transplantation and adult heart transplant recipients to evaluate AUC in children with nephrotic syndrome. In Katsuno et al.'s study [9], the LSS established for renal transplant recipients was used to predict AUC in patients with lupus nephritis. Additionally, Tong et al. [80] applied the LSS established with the HPLC method to evaluate AUC for patients for whom EMIT was used for MPA determination, while Neuberger et al. [79] applied MPA LSS established after EC-MPS administration in MMF-treated patients.

This review has included LSSs for total MPA generated with MLR mostly after oral MMF administration; however, there was one study [61] which included MPA LSS developed after separate oral and intravenous administration. Three studies established LSSs for fMPA [40, 51, 61]. There were also a few LSSs which included particular formulations, such as suspension [65], dispersible tablets [23, 24, 70], or a generic form of the drug [25, 33].

Most of the studies established LSSs with the intercept included, except those established by Kaczmarek et al. [55]. According to these authors [55], the equation without an intercept distributes relative prediction errors fairly evenly throughout the measuring range, whereas non-homogeneous models tend to yield larger relative prediction errors for lower values. However, the approach of not including the intercept was not found in other studies.

Among all MPA LSSs included in this review, the most often used time points were 2 h after MMF administration, that is near MPA tmax [1], and 6 h after MMF administration. Surprisingly, in adult renal transplant recipients, the most often used time point was C4, which is between tmax and tmax2 [82]. C0 was the most frequently included only in LSSs for pediatric patients. As MPA undergoes enterohepatic recirculation [2], it seems reasonable that, to describe MPA exposition accurately, the LSS should contain sampling over 6 h after MMF administration. Time points within 6–12 h after drug administration constituted less than 20% of all time points in each analyzed group. For adult transplant recipients, sampling within 3–5 h after MMF administration constituted a quarter of all time points.

Particular attention must be paid to the kind of calcineurin inhibitor co-administered. According to the literature, Tac does not influence MPA clearance [4]; however, in the case of CsA, MPA concentrations are lower if MMF and CsA are administered concomitantly [1]. CsA inhibits MPA enterohepatic recirculation [2] which causes the decrease in MPA exposition, and, therefore, in the case of CsA co-administration, the blood sampling does not require including time points around the second MPA maximum concentration (Cmax2) [7]. Comparing LSSs between patients treated concomitantly with CsA or Tac, the time points beyond 6 h were more frequently included in LSS when Tac was co-administered. For adult renal transplant recipients, the most frequently used time points were C2 and C4, and C4 and C2 if treated with MMF and CsA or MMF and Tac, respectively. When the indication for MMF treatment was different for renal transplantation, the most frequently used time points were C2, C1, and C6 and C1, C2, and C4 if CsA and Tac were co-administered, respectively. For pediatric patients, only a subgroup treated with MMF and CsA was evaluated as Tac co-treatment referred to only two LSSs. For MMF and CsA administration, in MPA LSSs, the most frequently included time points were C2, C0, and C0.5.

Constantly improving renal function after transplantation affects MPA pharmacokinetics [1]; therefore, some differences in time points included in LSSs which were established for patients treated with MMF less than 1 month after renal transplantation and longer than 3 months after renal transplantation were expected. Surprisingly, the most frequently used time points were within 4 h after drug administration irrespective of the post-transplant period (C2 and C4 and C1 and C3, for less than 1 month and longer than 3 months post-transplant, respectively). In MPA LSSs developed for patients with other than renal transplantation indication for MMF treatment, different sets of time points were used more frequently. These time points were C2 and C6 versus C2 and C0 for patients treated with MMF less than 1 month and longer than 3 months, respectively. For pediatric patients, the comparison of the results in relation to duration of MMF treatment were impossible to be found, as in most studies MPA LSSs were developed for children in the early as well as in stable post-transplant period or treated with MMF less than 1 month and longer than 3 months.

Some LSSs were used in numerous studies or applied in clinical practice to estimate MPA AUC and improve MPA TDM. Van Hest et al. [43] checked the utility of MPA LSS established for patients without diabetes in patients with diabetes and showed LSS suitability in the latter group. The LSS developed by Weber et al. [65] was applied to calculate MPA AUC0–12 and to obtain the optimal MMF dose in children after allogeneic hematopoietic cell transplantation [83]. The authors [83] proved that pharmacological monitoring of MPA AUC0–12 allowed a reduction in the incidence of acute and chronic graft-versus-host disease in patients who were undergoing prophylactic treatment with Tac and MMF. The MPA AUC0–12 was calculated using the LSS developed by Yamaguchi et al. [29] to evaluate the effects of UDP-glucuronosyltransferases polymorphisms on the pharmacokinetics of MMF in Chinese renal transplant recipients [84]. MPA AUC0-12 estimated based on the LSS from the Musuamba et al. study [30] was used to check the influence of omeprazole on MMF pharmacokinetics in kidney transplant recipients [85]. Poulin et al. [32] used LSS to perform population pharmacokinetic analysis of Tac and MMF concomitant administration in adult kidney recipients [86] as well as to determine associations between the absolute neutrophil count, MPA exposure, and the polymorphisms in metabolism or transporter genes responsible for MPA disposition [87]. The LSS of Miura et al. [37] was applied in renal transplant recipients to check the utility of plasma level monitoring of MPA and to correlate it with clinical outcomes [88]. The LSS developed for autoimmune disease [53] was used to investigate MPA exposure in patients with systemic sclerosis treated with MMF [89].

We found a few LSSs with satisfactory bias and precision; however, the usefulness of some of them is limited by the inclusion of time points beyond 4 h after MMF administration. Some of the LSSs were characterized by good bias and precision, but the r2 was < 0.90. Nevertheless, several MLR-based LSSs might help in establishing MPA AUCtotal for efficient TDM. With respect to the MMF indications, the following LSSs seems to be the most promising:

MPA AUCpred  = 2.8401  + 5.7435 × C0  + 0.2655 × C0.5  + 1.1546 × C1  + 2.8971 × C4 for adult renal transplant recipients co-treated with CsA [41];

MPA AUCpred  = 1.783  + 1.248 × C1  + 0.888 × C2  + 8.027 × C4 for adult patients after islet transplantation co-treated with Tac [20];

MPA AUCpred  = 0.10  + 11.15 × C0  + 0.42 × C1  + 2.80 × C2 for adult patients after heart transplantation co-treated with CsA [56];

fMPA AUCpred  = 34.2  + 1.12 × C1  + 1.29 × C2  + 2.28 × C4  + 3.95 × C6 for adult liver transplant recipients [51];

MPA AUCpred  = 8.217  + 3.163 × C0  + 0.994 × C1  + 1.334 × C2  + 4.183 × C4 for pediatric renal transplant recipients co-treated with Tac [16].

These LSSs require further evaluation in independent groups of patients before introducing them into clinical practice. The above LSS for fMPA might be difficult to implement as it included one time point 6 h after MMF administration. For MMF indications other than those listed above, we did not find any LSS which would fulfill the criteria of r2 > 0.95 and precision and bias < 10%. The usefulness of other LSSs with satisfactory results of predictive performance is limited by the inclusion of time points more than 4 h after drug administration. MPA LSSs established in pediatric populations were less numerous and rarely included the bias and precision. Moreover, we did not find any fMPA LSS established in a pediatric population. Those found for adult renal transplant recipients were not characterized by sufficient bias and precision, although, for these patients, fMPA monitoring should be of particular interest as it reflects the pharmacologically active form of the drug.

The limitation of our study is the lack of EMBASE search. Another limitation is that several articles did not fully characterize patient groups or did not show the results of predictive performance.

Conclusions

We found five MLR-based MPA LSSs which might be considered as useful in clinical practice; however, they require further evaluation in independent groups of patients. The LSSs for pediatric patients were less numerous and not fully characterized. There were only a few fMPA LSSs, although fMPA is a pharmacologically active form of the drug. For adult patients, MPA LSSs most frequently included C2 and C4, while, for pediatric patients, C0 and C2 were the most often used. The fact that the time points of MPA concentrations most frequently included in LSSs were different for adult renal transplant recipients, adults after other than renal transplantation, and in children treated with MMF, emphasizes the need of individual therapeutic approaches for each group of MMF-treated patients. Whereas the methodology of developing MPA LSS is rather a simple method enabling TDM, establishing the most accurate MPA LSSs require numerous factors to be considered, such as the drugs co-administered with MMF (particularly calcineurin inhibitors), the time elapsed from the transplantation or the duration of treatment with MMF, and the indication for MMF treatment. LSS is a useful tool in MPA therapeutic monitoring; however, if sampling beyond few hours after MMF administration is required, optimizing drug dosage by the LSS approach appears to be less convenient.

This review summarizes mycophenolic acid (MPA) and its free form (fMPA) limited sampling strategies (LSSs), calculated with multiple linear regression for adult and pediatric patients with different mycophenolate mofetil (MMF) indications, and includes detailed information on each LSS (type of calcineurin inhibitor co-administered, duration of MMF treatment, predictive performance of LSS).

The review includes LSSs not only for renal transplant recipients, which is the most frequent MMF indication, but also for patients after lung, heart, islet, liver, or hematopoietic stem cell transplantation, as well as patients with autoimmune diseases and children with nephrotic syndrome for whom therapeutic drug monitoring is of importance.

Four MPA LSSs (for adult patients after renal, islet, and heart transplantation and pediatric renal transplant recipients) and one fMPA LSS (for adult liver transplant recipients) were the most promising and should be validated in independent groups before introduction into clinical practice.