NextDose: A web-based Bayesian dose forecasting tool

Last updated 16 June 2024

Individual Parameters and Covariates

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 total body mass (TBM) and renal function (e.g. TBM=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 TBM and renal function (RF and population clearance by assuming clearance is linearly proportional to RF and a theory based allometric function of TBM (Equation 1):

Equation 1

RF is calculated from the ratio of the estimated glomerular filtration rate (eGFR) calculated from serum creatinine to the normal GFR (nGFR) predicted for an individual of the same size and maturation with normal renal function. Note that eGFR is the value for that individual without any scaling by body size or body surface area. NextDose calculates eGFR based on the ratio of creatinine production rate (CPR) to steady state Scr. CPR is predicted using a model developed from observed GFR data (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. Further details can be found in (O'Hanlon, Holford et al. 2023, Holford, O'Hanlon et al. 2024)

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 creatinine clearance (Matthews, Kirkpatrick et al. 2004). This observation has been extended to identify two components of renal clearance – one component limited by GFR, Both components are linked to RF as shown in Equation 2 and Equation 3 (Holford, O'Hanlon et al. 2024).

Equation 2

An asymmetrical sigmoid function was used to describe the relationship between RF and CLGFR using drug specific parameters, CLGFR_RF50, Hill_LT and Hill_GE. The sigmoidicity parameter in Equation 2 has a different value depending on whether RF is less than (Hill_LT) or greater than or equal (Hill_GE) to CLGFR_RF50.

The second component of clearance. CLNGFR, is not linked to GFR (Equation 3).

Equation 3

CLNGFRpop is a drug specific population parameter estimate for CLNGFR which is directly proportional to RF. Additional factors include allometric scaling for size (FsizeNGFR, using normal fat mass, and maturation based on post-menstrual age, Fmat,PMANGFR, and on postnatal transition, Fmat,PNANGFR.

The group clearance for extensively renally eliminated drugs such as gentamicin, tobramycin, amikacin and vancomycin is calculated using Equation 4

Equation 4

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 5:

Equation 5

NextDose Predictions of Doses, Individual Parameters and Calculated Covariates

Figure 1 shows the concentration predictions in a patient treated with vancomycin who had four concentration observations after the first dose and a pre-dose concentration observation after 6 doses.

Figure 1

The Bayesian dose predictions for these 2 dosing occasions with vancomycin observations are shown in Figure 2

Figure 2

NextDose TCI vancomycin holfordGAV2023_AVG

Target: AUC 400 mg/L*h per 24 hours ( Css avg 16.7 mg/L )

Trapezoid	AUC	Units	Interval	Dose Pred
1	139	mg/L*h	0-infinity	maintenance dose 2878 mg

Bayesian	Route	Predicted Dose	Actual Dose	Latest Obs
1	IV	1614 mg every 1 day	1000 mg	2019/02/24 15:59
2	IV	1614 mg every 1 day	1000 mg	2019/02/27 07:59

Proposed IV maintenance dose 807 mg every 12 hours (Average)

Following the dose predictions is a table of individual parameters (EBEs) and calculated covariates (Table 1). NextDose shows 8 values which are displayed for all medicines.

Table 1 Empirical Bayes Parameters and % difference from group values for this patient

Time h	CL L/h	fCL%	V L	fV%	F	fF%	FFM kg	RF%
1: 7.98	4.04	78.3	31.9	0	1	0	54.5	43.1
2: 71.98	4.03	77.8	31.9	0	1	0	54.5	43.1

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 difference (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 last 2 standard values are calculated 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 components of clearance that are related to RF.

Gentamicin, amikacin and vancomycin

Some additional medicine specific values relating to renal function are shown with gentamicin, tobramycin, amikacin and vancomycin predictions. Table 2 shows an example for vancomycin.

Table 2

CLcr L/h	Normal GFR L/h	CPR uM/h	RFss%	CLcrss L/h	CPRss uM/h
2.94	6.81	312	55.9	3.52	373
2.94	6.81	312	55.9	3.52	373

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 2 values are the predicted normal glomerular filtration rate (normal GFR) and creatinine production rate (CPR) (O'Hanlon, Holford et al. 2023).

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 medicine 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

Pred

on F %

GT CYP3A5

F %

GT CYP3A5

on CL %

HCT %

fu%

at HCT 45%

-62.687

75.6

100

29.0

2.09

-62.687

75.6

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 John’s 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

87.8

56.3

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

40.0

0.050

0.025

0.171

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

Holford, N., C. J. O'Hanlon, K. Allegaert, B. Anderson, A. Falcão, N. Simon, Y.-L. Lo, A. H. Thomson, C. M. Sherwin, E. Jacqz-Aigrain, C. Llanos-Paez, S. Hennig, L. Mockus and C. Kirkpatrick (2024). "A physiological approach to renal clearance: From premature neonates to adults." British Journal of Clinical Pharmacology 90(4): 1066-1080.

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.

O'Hanlon, C. J., N. Holford, A. Sumpter and H. S. Al-Sallami (2023). "Consistent Methods for Fat Free Mass, Creatinine Clearance and Glomerular Filtration Rate to describe Renal Function from Neonates to Adults." CPT Pharmacometrics Syst Pharmacol 12: 401-412.

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.