NextDose: A web-based Bayesian dose forecasting tool

Last updated 14 August 2020

Individual Parameters and Covariate Effects

NextDose estimates pharmacokinetic (PK) and pharmacodynamic (PD) parameters using a Bayesian method. These individual parameters are known as empirical Bayes estimates (EBEs). The EBEs are used to individualize dose predictions and to predict the time course of concentrations and biomarkers such as INR.

The EBEs are determined in part by population parameters and in part by any observations that are available. The population parameters describe a standard individual based on patient factors such as weight and renal function (e.g. weight=70 kg, renal function=1). These patient factors are known as covariates. Covariates are used to predict a group parameter value using covariate effects. For example, group clearance can be predicted from weight (WTKG) and renal function (RF0 and population clearance by assuming clearance is linearly proportional to RF and a theory based allometric function of WTKG (Equation 1):

Equation 1

RF is calculated from the ratio of the creatinine clearance (CLcr) calculated from serum creatinine to the glomerular filtration rate (GFR) predicted for an individual of the same size and maturation. Note that CLcr is the value for that individual without any standardization based on for size, maturation or sex. NextDose calculates CLcr based on the ratio of creatinine production rate (CPR) to steady state Scr. CPR is predicted using a model developed from data in (Rhodin, Anderson et al. 2009). This model uses fat free mass, post-menstrual age and sex to calculate CPR relative to a 70 kg, 176 cm, 20 y old adult male. When a series of Scr measurements are available the Scr time course is used to predict CLcr without assuming steady state.

Note that Equation 1 is usually an over-simplification by assuming that clearance is entirely proportional to RF. Even for drugs that are thought to be almost completely renally eliminated (such as gentamicin) a substantial part of the observable clearance is not predictable from RF (Matthews, Kirkpatrick et al. 2004). In that case the clearance can be split into a component not predictable from renal function () and a component predictable from renal function (). The component may actually be due to renal elimination but it cannot linked to RF based on CLcr. An example is shown in Equation 2.

Equation 2

Individual estimates (EBEs) of the parameter are then predicted from the group parameter value and an individual specific random effect. This random effect is made up of a between subject variability component (BSV) and a within subject variability component (WSV). The within subject variability is usually estimated with reference to an interval known as an occasion and WSV is therefore commonly described as between occasion variability (BOV). The definition of an occasion in NextDose is a dosing interval which includes one or more observations.

Random effects are commonly assumed to be log-normally distributed so that the individual clearance is predicted using Equation 3:

Equation 3

 


 

NextDose Predictions of Doses and Individual Parameters and Covariate Effects

Figure 1 shows the concentration predictions in a patient treated with vancomycin who had three pre-dose vancomycin concentration observations.

Figure 1

 

The Bayesian dose predictions for these 3 observation occasions are shown in Figure 2

Figure 2

NextDose TCI vancomycin NNNN:2020-06-17-131151_conc_holfordGAV2020_AVG

 

Target: AUC  300 mg/L*h per 12 hours at steady state
 

Bayesian

Route

Predicted Dose

Actual Dose

       

 

1

IV

1008 mg every 12 hours

1250 mg

10/06/2020 03:55

                               

2

IV

 863 mg every 12 hours

1250 mg

12/06/2020 03:50

                               

3

IV

 863 mg every 12 hours

 900 mg

14/06/2020 04:05

                               

 

Proposed IV maintenance dose  911 mg every 12 hours (Bayesian Average)


 

 

CL 

L/h

fCL%

L

fV%

F

fF%

FFM 

kg

RF%

3.36

-20

24.9

0.2

1

0

38.9

100

2.87

-20.1

24.9

0.2

1

0

38.9

85.4

2.88

-20

24.9

0.2

1

0

38.9

85.4

Following the dose predictions is a table of individual parameters (EBEs) and covariate effects. NextDose shows 8 values which are displayed for all medicines.

The first 6 describe the parameters clearance (CL), central volume of distribution (V) and bioavailability (F). Following the EBE for each parameter is the fractional change (f) from the group parameter value expressed as a percentage. When a medicine is given parenterally then F is 1 and there is no random effect.

The EBE for CL appears to decrease from 3.36 l/h to 2.87 L/h. This is explained by the change in RF% from 100% to 85.4%. The first prediction of renal function was made before a serum creatinine observation was provided so renal function is assumed to be normal (100%). The second two occasion were associated with a serum creatinine measurement and a 15% change in RF. The random effect difference for this patient is 20% lower than the group prediction. For vancomycin this is primarily due to between subject variability (BSV) because the between occasion variability (BOV) in this model is small.

The last 2 standard values are the covariate effects, predicted fat free mass (FFM) and renal function (RF). RF is expressed as a percentage where 100% means normal renal function relative to predicted normal glomerular filtration rate.

FFM is used to predict the effect of body size and composition on clearance, volume of distribution and glomerular filtration rate. RF is used to predict a component of clearance that is related to RF. The remaining component is not linked to RF (non-renal function clearance).

Gentamicin, amikacin and vancomycin

Medicine specific values are shown with gentamicin, amikacin and vancomycin predictions. This example is for vancomycin.

CLcr

 L/h

Normal 

GFR L/h

CPR 

uM/h

RFss%

CLcrss

 L/h

CPRss

 uM/h

.

5.33

.

.

.

.

4.55

5.33

 150

 128

6.55

 216

4.55

5.33

 150

 128

6.55

 216

The first (CLcr) is the predicted creatinine clearance which takes into account the time course of change in serum creatinine (Scr) in order to predict the steady state Scr. The next value is the predicted normal glomerular filtration rate (GFR). GFR is predicted from size and maturation (Rhodin, Anderson et al. 2009). Renal function is calculated from the ratio of CLcr to normal GFR. CLcr is calculated from the ratio of creatinine production rate (CPR) to Scr. The NextDose method for calculating CPR is based on a model derived from combined GFR and SCr data (Rhodin, Anderson et al. 2009)

The last 3 values are predictions of RF, CLcr and CPR using methods for CLcr that assume the measured SCr is at steady state (Schwartz 1992, Matthews, Kirkpatrick et al. 2004)

Busulfan

There are no medicine specific values shown for busulfan.

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

10.8

36.7

7.94

-8.7

1

0

36.5

.

 

Methotrexate

Methotrexate has additional specific values for observed urine pH and predicted CLcr

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

Urine pH

CLcr L/h

7.77

-68.1

41.2

-73.6

1

0

55.9

73.2

7.00

5.60

9.25

-62.1

48.4

-69

1

0

55.9

73.2

7.00

5.60

Tacrolimus

There are 6 specific values for tacrolimus. Oral bioavailability is high during the first 2 days after transplant and fall to normal after day 2 (day of transplant is day 0). There is a BSV random effect on bioavailability upto day 2 which is 63% lower than expected. The daily dose of prednisolone (Pred) affects oral bioavailability and in this case F is 75.6% of F without a steroid effect. The CYP3A5 genotype can affect both F and CL. In this case there is no genotype effect. The haematocrit influences the measured whole blood value of tacrolimus so its value (HCT) is shown here. Finally the predicted plasma to blood fraction (fu) expressed as a percentage 2.09% at a standardized blood concentration (HCT=45%) is shown.

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

9.09

-52.3

43.3

-71.9

0.720

-4.8

70.4

.

9.09

-52.3

43.3

-71.9

0.841

11.2

70.4

.

 

Day Tx 

on F

diffDTx

F%

Pred 

on F %

GT CYP3A5 

on

 F %

GT CYP3A5 

on CL %

HCT %

fu%

at HCT 45%

1

-62.687

75.6

 100

 100

29.0

2.09

1

-62.687

75.6

 100

 100

29.0

2.09

Linezolid

Linezolid has 2 specific values. The first is the minimum inhibitory concentration (MIC, 2 mg/L). The second is the baseline platelet count (PLT0, cells/microL).

There is a marked decrease in RF with a decrease in CL. Nephrotoxicity is a well known adverse effect of linezolid.

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

MIC

PLT0

1.31

-47.6

10.2

-45.4

1

0

46.7

23.4

2.00

212000

1.31

-47.6

10.2

-45.4

1

0

46.7

23.4

2.00

212000

1.29

-47.6

10.2

-45.4

1

0

46.7

20.7

2.00

212000

1.29

-47.6

10.2

-45.4

1

0

46.7

20.7

2.00

212000

1.26

-47.6

10.2

-45.4

1

0

46.7

15.3

2.00

212000

1.25

-47.6

10.2

-45.4

1

0

46.7

13.3

2.00

212000

1.24

-47.6

10.2

-45.4

1

0

46.7

13

2.00

212000

1.24

-47.6

10.2

-45.4

1

0

46.7

12.3

2.00

212000

 

Voriconazole

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

2.19

-33.3

66.9

-5

1

0

42.5

.

There are many covariates that affect voriconazole PK. Ritonavir (RTV), St Johnís Wort (SJW), prednisolone (or prednisone) (Pred), methyl prednisolone (MePRed), dexamethasone (DEX). Phenytoin (PHE) and rifampicin (RIF) are both inducing agents. The CYP2C19 genotype may be associated with a reduced F (87.7% of normal) and CL (56.3% of normal). The minimum inhibitory concentration (MIC, mg/L) is also shown.

RTV

SJW

Pred

MePred

DEX

PHE or RIF

GT CYP2C19

on F %

GT CYP2C19

on CL %

MIC mg/L

0

0

0

0

0

0

87.8

56.3

1

 

Warfarin

The warfarin model estimates both PK and PD parameters.

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

0.141

-4.8

29.8

-0.9

1

0

66.0

.

 

The predicted baseline prothrombin complex activity (PCA0) is shown here as 97.9% of normal. The PCA half life (T2PCA) EBE is 11.5 h which is just under 0.5% higher than the group value (fT2PC%). The potency of the S-enantiomer of warfarin for inhibition of PCA synthesis is 0.211 mg/L (C50 S) and is -6.39% of the group value (fC50%). The exponent for the warfarin inhibition model is 2.75 (Hill) and this is 1.52% higher than the group value. The potency of the R-enantiomer of warfarin as an inhibitor of S-warfarin is 2.4 mg/L. The VKORC1 genotype affects the S-warfarin C50 so that it is 0.766 of normal. The CYP2C9 genotype effect on S-warfarin clearance is negligible with a fractional increase of 0.01.

 

PCA0 %

T2PCA h

fT2PC%

C50S

 mg/L

fC50%

Hill

fHill%

C50R

 mg/L

FGT VKOR

 on C50

FGT CYP2C9

 on CLs

97.9

11.5

0.469

0.211

-6.393

2.75

1.52

2.40

0.766

1.01

 

 

Mycophenolate

Mycophenlate unbound clearance increases substantially after a renal transplant (from 757 L/h to 1229 L/h over 1 month).

 

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

ALB g/L

fu MPA %

 757

-27.4

3263

7.7

0.950

0

66.1

14.7

32.0

1.66

 750

-28.1

3078

1.6

0.950

0

66.1

14.7

32.0

1.66

1449

-33.3

3264

7.8

0.950

0

66.1

14.7

31.0

1.71

1576

-27.4

3995

31.9

0.950

0

66.1

14.7

31.0

1.76

1229

-43.4

2947

-2.7

0.950

0

66.1

14.7

33.0

1.38

 

Both albumin and renal function influence mycophenolate plasma protein binding. The serum albumin (ALB, g/L) is shown along with RF. The unbound fraction of mycophenolate (unbound/total plasma) decreased from 1.66% to 1.38% in the month after transplant.

 

 

Caffeine

Caffeine is used in premature neonates to reduce the risk of apnea of prematurity

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

0.008

-0.9

1.71

19.7

1

0

1.22

.

 

The number of days after birth (post-natal age, PNA) for this neonate is 0. Height (HT) is 40 cm. The allometric fraction of size affecting CL relative to a 70 kg adult is 0.05. The fractional maturation of non-renal function CL is 0.025 while the fractional maturation of renal clearance is 0.171 (relative to adult). The birth method was vaginal (0) rather than Caesarian (1).

PNA days

HT cm

FSIZCL

FMAT CLnrf

FMAT CLrf

BIRTH 

V=0 C=1

0

40.0

0.050

0.025

0.171

0

 

 

Hydroxychloroquine

Hydroxychloroquine is used for the treatment of lupus erythematosus and rheumatoid arthritis. Whole blood pharmacokinetics are described based on a standard hematocrit (HCT) of 45%.

 

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

BMI kg/m^2

ALB g/L

HCT %

VENT

11.6

25.2

 777

5.7

0.746

0

63.2

52.7

26.8

35.0

45.0

1

11.6

25.2

 777

5.7

0.746

0

63.2

52.7

26.8

35.0

45.0

1

11.6

25.2

 777

5.7

0.746

0

63.2

52.7

26.8

35.0

45.0

1

 

Body mass index (BMI), serum albumin (ALB), haematocrit (HCT) and use of artificial ventilation (0=no ventilator, 1=ventilator) are the medicine specific factors.

 

Dabigatran

The RE-LY 2011 PK model (Liesenfeld, T. et al. 2011) has random effects on V and F but not on CL so fCL % is always zero.

CL L/h

fCL%

V L

fV%

F

fF%

FFM kg

RF%

66.0

0

698

-0.8

1.08

8.1

62.8

43.8

 

CLcr, Normal GFR, CPR, RFss%, CLcrss, CPRss have the same meaning as described for gentamicin, amikacin and vancomycin.

 

The RE-LY 2011 PK model predicts CL with a sigmoid Emax model using CLcrss. The fractional effect of CLcrss (F CLcrss CL) is relative to the size scaled asymptotic CL (infinite CLcrss). The combined effects of three concomitant medications (proton pump inhibitors, amiodarone, verapamil) on bioavailability (F) is expressed as the % difference from no concomitant medication effect.

 

CLcr L/h

Normal GFR L/h

CPR uM/h

RFss%

CLcrss L/h

CPRss uM/h

F CLcrss CL

F ConMed F1 %

3.32

7.57

308

50.5

3.56

331

0.514

0

 

Liesenfeld, K.-H., L. T., C. Dansirikul, P. A. Reilly, S. J. Connolly, M. D. Ezekowitz, S. Yusuf, L. Wallentin, S. Haertter and A. Staab (2011). "Population pharmacokinetic analysis of the oral thrombin inhibitor dabigatran etexilate in patients with non-valvular atrial fibrillation from the RE-LY trial." Journal of Thrombosis and Haemostasis 9(11): 2168-2175.

Matthews, I., C. Kirkpatrick and N. Holford (2004). "Quantitative justification for target concentration intervention--parameter variability and predictive performance using population pharmacokinetic models for aminoglycosides." Br J Clin Pharmacol 58(1): 8-19.

Rhodin, M. M., B. J. Anderson, A. M. Peters, M. G. Coulthard, B. Wilkins, M. Cole, E. Chatelut, A. Grubb, G. J. Veal, M. J. Keir and N. H. Holford (2009). "Human renal function maturation: a quantitative description using weight and postmenstrual age." Pediatr Nephrol 24(1): 67-76.

Schwartz, G. J. (1992). "Does kL/PCr estimate GFR, or does GFR determine k?" Pediatr Nephrol 6(6): 512-515.

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