NextDose: A web-based Bayesian dose forecasting tool
Last updated 29 July 2021
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% |
V 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 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 |
|
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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