A limited sampling strategy based on Maximum A Posteriori Bayesian estimation for a five-probe phenotyping cocktail
Supporting Information
Thu Thuy Nguyen1,*, Henri Bénech2, Alain Pruvost2, Natacha Lenuzza1
1 CEA, LIST, Data Analysis and Systems Intelligence Laboratory, Gif-sur-Yvette, France;
2 CEA, DSV, iBiTecS, Gif-sur-Yvette, France
* Corresponding author: Thu Thuy Nguyen
Address: CEA, LIST, Data Analysis and Systems Intelligence Laboratory
Gif-sur-Yvette, France
Tel: +33 1 69 08 66 98
Email:
Table S1Phenotyping indexes(PI) calculated from observed concentrations of “CIME1” study by noncompartmental analysis (NCA) and those obtained by maximum a posteriori Bayesian estimation (MAPBE) using population models
Probe / Subject / NCA / MAPBEPI / Rank / PI / Rank
Midazolam
PI= AUCMID
(ng h/ml) / 1 / 52.84 / 5 / 59.61 / 6
2 / 49.65 / 3 / 50.30 / 3
3 / 44.02 / 2 / 45.06 / 2
4 / 60.93 / 7 / 64.77 / 7
5 / 50.86 / 4 / 54.10 / 4
6 / 31.86 / 1 / 34.72 / 1
7 / 109.56 / 10 / 99.07 / 10
8 / 58.27 / 6 / 58.64 / 5
9 / 86.38 / 8 / 77.85 / 8
10 / 96.10 / 9 / 98.18 / 9
Tolbutamide
PI= AUCTOL
(ng h/ml) / 1 / 16801.07 / 7 / 16732.69 / 7
2 / 16770.21 / 6 / 16021.98 / 6
3 / 21017.21 / 10 / 20296.42 / 10
4 / 8976.29 / 1 / 9076.31 / 1
5 / 17527.03 / 8 / 17318.13 / 8
6 / 11927.95 / 4 / 11863.89 / 3
7 / 12293.14 / 5 / 12703.17 / 5
8 / 11880.28 / 3 / 12155.83 / 4
9 / 9780.36 / 2 / 9996.56 / 2
10 / 17924.37 / 9 / 17758.47 / 9
Caffeine
PI= AUCPAX/AUCCAF / 1 / 0.53 / 3 / 0.45 / 1
2 / 0.73 / 9 / 0.70 / 9
3 / 0.60 / 4 / 0.47 / 2
4 / 0.67 / 6 / 0.56 / 5
5 / 0.86 / 10 / 0.89 / 10
6 / 0.51 / 2 / 0.48 / 3
7 / 0.66 / 5 / 0.61 / 7
8 / 0.71 / 8 / 0.66 / 8
9 / 0.71 / 7 / 0.56 / 6
10 / 0.29 / 1 / 0.54 / 4
Dextromethorphan*
PI= AUCDEX/AUCDOR / 1 / 0.06 / 2 / 0.05 / 2
2 / 0.39 / 7 / 0.21 / 8
3 / 0.42 / 8 / 0.21 / 7
5 / 0.29 / 6 / 0.17 / 6
6 / 0.07 / 3 / 0.06 / 3
7 / 0.14 / 4 / 0.13 / 4
8 / 0.22 / 5 / 0.13 / 5
9 / 0.05 / 1 / 0.05 / 1
10 / 1.49 / 9 / 1.18 / 9
Omeprazole
PI= AUCOME/AUC5OH-OME / 1 / 1.14 / 8 / 1.24 / 9
2 / 0.76 / 6 / 0.82 / 5
3 / 0.52 / 2 / 0.57 / 1
4 / 0.85 / 7 / 0.89 / 7
5 / 0.56 / 3 / 0.76 / 4
6 / 0.66 / 4 / 0.72 / 3
7 / 0.48 / 1 / 0.58 / 2
8 / 0.73 / 5 / 0.89 / 6
9 / 1.33 / 10 / 1.50 / 10
10 / 1.26 / 9 / 1.18 / 8
*subject 4 not includedin modelling for dextromethorphan because the insufficient sample size prevented us from considering the genotype as a covariate of the model.
Close results were obtained between PI calculated from observed concentrations by NCA as described in a previous work (Lenuzza et al. 2014)and those obtained by MAPBE using population models.
Table S2Relative prediction errors (RE) and relative root mean square errors (RRMSE) of the phenotyping index (PI) for each probe
Probe andphenotyping index / Number of
samples/subject / Mean RE (%) / 95%CI of MRE / Range of RE / RRMSE (%) / 95%CI of RRMSE
Midazolam
PI= AUCMID / 15 / -0.36 / -1.38 / 0.66 / -15.85 / 17.67 / 7.15 / 6.42 / 7.80
10 / -0.89 / -2.03 / 0.25 / -22.36 / 26.92 / 8.32 / 7.31 / 9.21
9 / -1.30 / -2.47 / -0.13 / -19.80 / 24.19 / 8.78 / 7.78 / 9.67
8 / -1.26 / -2.47 / -0.05 / -20.47 / 25.07 / 9.15 / 8.05 / 10.13
7 / -1.26 / -2.47 / -0.05 / -20.47 / 25.07 / 9.15 / 8.05 / 10.13
6 / -1.52 / -2.88 / -0.16 / -27.11 / 29.71 / 10.33 / 9.08 / 11.43
5 / -2.19 / -3.63 / -0.75 / -32.76 / 27.20 / 11.28 / 9.90 / 12.51
4 / -1.86 / -3.53 / -0.20 / -34.07 / 31.33 / 12.65 / 11.15 / 13.99
3 / -1.93 / -3.97 / 0.12 / -36.89 / 45.33 / 15.24 / 13.17 / 17.06
2 / -2.21 / -4.25 / -0.17 / -36.68 / 37.02 / 15.53 / 13.38 / 17.41
1 / -5.54 / -7.99 / -3.09 / -54.06 / 43.90 / 21.44 / 17.35 / 24.86
Tolbutamide
PI= AUCTOL / 15 / -1.52 / -2.79 / -0.26 / -27.70 / 22.18 / 9.51 / 8.40 / 10.50
10 / -1.90 / -3.41 / -0.39 / -26.53 / 25.22 / 11.21 / 10.05 / 12.27
9 / -2.54 / -4.16 / -0.93 / -31.30 / 30.64 / 12.73 / 11.22 / 14.07
8 / -2.54 / -4.16 / -0.92 / -30.79 / 33.05 / 12.79 / 11.25 / 14.16
7 / -2.36 / -4.12 / -0.59 / -29.58 / 36.40 / 13.77 / 12.07 / 15.28
6 / -2.58 / -4.38 / -0.79 / -29.71 / 40.16 / 14.07 / 12.30 / 15.64
5 / -2.63 / -4.52 / -0.75 / -31.54 / 37.16 / 14.89 / 13.04 / 16.53
4 / -2.59 / -4.50 / -0.68 / -31.60 / 39.80 / 15.06 / 13.22 / 16.69
3 / -2.98 / -5.25 / -0.71 / -48.88 / 38.43 / 18.14 / 15.73 / 20.27
2 / -1.96 / -5.50 / 1.59 / -55.03 / 74.09 / 28.21 / 24.10 / 31.78
1 / -2.01 / -5.77 / 1.75 / -55.69 / 89.92 / 29.36 / 25.31 / 32.91
Caffeine
PI= AUCPAX/AUCCAF / 15 / -4.47 / -6.69 / -2.25 / -74.98 / 52.84 / 14.46 / 12.42 / 16.25
10 / -1.91 / -4.56 / 0.73 / -75.88 / 83.76 / 17.08 / 14.68 / 19.18
9 / -1.07 / -3.99 / 1.86 / -71.93 / 74.04 / 19.38 / 16.57 / 21.83
8 / -1.17 / -4.09 / 1.75 / -72.64 / 74.57 / 19.28 / 16.54 / 21.68
7 / 2.46 / -0.94 / 5.87 / -73.47 / 107.65 / 22.12 / 18.78 / 25.02
6 / 2.89 / -0.61 / 6.39 / -72.17 / 121.34 / 22.29 / 19.18 / 25.01
5 / 4.13 / 0.32 / 7.94 / -73.55 / 93.89 / 24.14 / 20.86 / 27.02
4 / 4.77 / 0.90 / 8.65 / -74.33 / 90.91 / 24.83 / 21.43 / 27.82
3 / 1.39 / -1.92 / 4.69 / -70.42 / 81.81 / 21.19 / 18.75 / 23.38
2 / 5.36 / 0.20 / 10.53 / -64.88 / 191.42 / 35.76 / 29.24 / 41.27
1 / 12.53 / 5.89 / 19.18 / -63.91 / 202.33 / 41.81 / 35.60 / 47.20
Dextromethorphan
PI= AUCDEX/AUCDOR / 15 / 2.85 / 0.19 / 5.50 / -36.99 / 91.31 / 17.10 / 14.26 / 19.53
10 / 2.30 / -0.80 / 5.39 / -42.71 / 108.71 / 20.24 / 16.46 / 23.42
9 / 2.09 / -1.26 / 5.44 / -40.44 / 117.04 / 21.64 / 16.54 / 25.75
8 / 3.32 / -0.27 / 6.91 / -43.66 / 129.67 / 21.63 / 16.76 / 25.59
7 / 3.56 / -0.03 / 7.14 / -42.48 / 130.33 / 21.68 / 16.35 / 25.95
6 / 3.10 / -0.76 / 6.97 / -42.31 / 151.22 / 24.97 / 16.15 / 31.41
5 / 2.70 / -1.40 / 6.80 / -51.50 / 128.42 / 28.11 / 21.16 / 33.65
4 / 5.63 / 0.78 / 10.48 / -62.48 / 162.98 / 36.71 / 10.75 / 50.79
3 / 8.32 / 1.92 / 14.72 / -73.63 / 173.92 / 40.98 / 29.65 / 49.79
2 / 7.47 / 1.09 / 13.86 / -73.77 / 176.27 / 44.33 / 27.70 / 56.24
1 / 5.43 / -2.64 / 13.50 / -82.54 / 279.37 / 61.54 / 45.84 / 73.99
Omeprazole
PI= AUCOME/AUC5OH-OME / 15 / 0.89 / -2.07 / 3.85 / -45.31 / 66.31 / 20.43 / 17.46 / 23.02
10 / 0.88 / -2.09 / 3.86 / -45.45 / 66.14 / 20.73 / 17.70 / 23.37
9 / 0.67 / -2.36 / 3.70 / -43.97 / 69.73 / 21.11 / 17.87 / 23.91
8 / 0.66 / -2.37 / 3.69 / -45.16 / 69.74 / 21.15 / 17.88 / 23.97
7 / 0.69 / -2.34 / 3.73 / -45.21 / 71.20 / 21.14 / 17.87 / 23.96
6 / 2.11 / -1.22 / 5.43 / -45.71 / 80.09 / 22.46 / 18.93 / 25.51
5 / 1.78 / -1.72 / 5.27 / -45.35 / 111.45 / 23.14 / 19.06 / 26.60
4 / 1.77 / -1.73 / 5.26 / -45.35 / 111.47 / 23.14 / 19.06 / 26.60
3 / 3.98 / -0.82 / 8.77 / -48.78 / 158.35 / 30.63 / 26.04 / 34.63
2 / 3.96 / -0.84 / 8.76 / -48.78 / 158.37 / 30.63 / 26.04 / 34.63
1 / 12.94 / 5.85 / 20.03 / -73.20 / 223.75 / 43.93 / 34.43 / 51.72
The results are obtained with the designs optimized within [0-24h] for maximum a posteriori Bayesian estimation of individual parameters for the five-probe cocktail CIME, the number of sampling times decreasing from 15 to 1. Ranges of RE as well as 90% confidences intervals of the mean RE and RRMSE are reported.
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Table S3Performance of different sampling designs in predicting individual phenotyping indexes for three probes common to the CIME and the Basel cocktail
Probe / (2, 8h) /Phenotyping index / MRE
(%) / RRMSE
(%) / P
(%) / ρ / SP metrics / MRE
(%) / RRMSE
(%) / P
(%) / ρ
MID / AUCMID/AUC1OH-MID / -0.33
[-4.74,4.09] / 85.59
[30.15,117.22] / 25.50
[19.46,31.54] / 0.97
[0.95,0.98] / CMID/C1OH-MID 2h / 134.65
[102.19,167.11] / 119.59
[56.52,159.40] / 76.00
[70.08,81.92] / 0.81
[0.75,0.86]
CAF / AUCPAX/AUCCAF / 0.18
[-3.26,3.62] / 24.11
[20.69,27.10] / 22.00
[16.26,27.74] / 0.89
[0.85,0.92] / CPAX/CCAF 8h / 10.87
[5.66,16.07] / 30.24
[25.37,34.42] / 29.00
[22.71,35.29] / 0.83
[0.78,0.87]
OME / AUCOME/AUC5OH-OME / 3.92
[-0.87,8.72] / 30.63
[26.03,34.61] / 33.50
[26.96,40.04] / 0.65
[0.55,0.72] / COME/C5OH-OME 2h / 11.35
[5.76,16.94] / 32.26
[27.44,36.44] / 35.50
[28.87,42.13] / 0.60
[0.51,0.68]
is the design used for MAPBE composed of 2 times from the single point (SP) design (: 2 or 8h)published for the Basel cocktail. The compounds common to the CIME and the Basel cocktail are midazolam (MID), caffeine (MID) and paraxanthine (PAX), omeprazole (OME) and 5-hydroxy-omeprazole (5-OH-OME). The mean relative prediction errors (MRE), the relative root mean square errors (RRMSE) and the proportion (P) of individuals with prediction errors of phenotyping indexes (PI) above 30% are reported as percentages, ρ is the Spearman correlation coefficient between the predicted and the true PI. AUC is the area under the curves of predicted individual concentration (C).95% confidences intervals of all measures are given in brackets.
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Fig.S1Structural models characterizing the pharmacokinetics of the five-probe cocktail CIME: one-compartment substrate/one-compartment metabolite (left) for caffeine/paraxanthine and omeprazole/5-OH-omeprazole; two-compartment substrate/one-compartment metabolite (right) for midazolam/1-OH-midazolam, tolbutamide/4-OH-tolbutamide and dextromethorphan/dextrorphan. X the central compartment, Xp the peripheral compartment with k12 and k21 the distribution rate constants between central compartment and peripheral compartment (in case of two compartments), ka the rate constant for oral absorption, V the volume of distribution of the central compartment, ke the elimination rate constant; Xm central compartment, Vm the volume of distribution, kem the elimination rate constant, kmthe metabolisation rate from the substrate into the metabolite
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