NextDose: A web-based Bayesian dose forecasting tool

Last updated 6 September 2024

Tacrolimus

Tacrolimus is widely used as an immunosuppressant after organ transplantation. It has been recommended that whole blood concentrations be interpreted by standardization to those expected with a haematocrit of 45% (Storset, Holford et al. 2014a, Storset, Holford et al. 2014b, Staatz, Størset et al. 2015).

Body size is best described using predicted fat free mass and theory based allometric scaling. Concomitant steroid dosing markedly decreases tacrolimus oral bioavailability (Storset, Holford et al. 2014b, Staatz, Størset et al. 2015).

Understanding Concentrations

Tacrolimus concentrations are measured in whole blood. It is measured in whole blood with concentrations approximately 8,000 times than unbound in plasma (Sikma, Van Maarseveen et al. 2020). Part of the reason for this is convenience for the laboratory because concentrations in whole blood are about 20 to 60 times higher than in plasma depending on the haematocrit (Figure 1).

The distribution and elimination of drugs is determined by unbound concentration, and it is the unbound concentration that determines both beneficial and adverse effects. These principles are fundamental in describing and understanding pharmacokinetics and pharmacodynamics. They apply equally to tacrolimus which then introduces challenges in interpreting whole blood concentrations.

The pharmacokinetics of tacrolimus have been described using a theory based approach to predict plasma concentration under the assumption that unbound concentration is proportional to plasma concentration (Storset, Holford et al. 2014b). An essentially linear relationship between unbound and plasma tacrolimus concentration supports this assumption (Sikma, Van Maarseveen et al. 2020). The plasma concentration is used to predict whole blood concentration (erythrocyte bound + plasma) using a saturable binding model (Jusko, Piekoszewski et al. 1995).

The distribution and elimination of tacrolimus is not affected by changes in erythrocyte binding or changes in haematocrit. Literature reports that claim changes in haematocrit are associated with changes in clearance are misleading because tacrolimus elimination is not affected by erythrocyte mass. The implementation of the theory-based PK model in NextDose uses standardization of whole blood tacrolimus concentrations to a standard value of 45% which means changes in PK parameters such as clearance and volume of distribution will be reflected in the standardized whole blood concentration without being confounded by changes in haematocrit (Figure 1).

Figure 1 Tacrolimus concentration as a function of haematocrit (HCT). Red line: Plasma concentration (Cp) (constant at 0.3 mcg/L). Green solid line: Whole blood concentration (Cwb) calculated from literature values of binding to red blood cells: [Cwb = Cp + Cp × HCT (fraction) × Bmax / (Cp + Kd)], where Bmax=418 mcg/L erythrocytes and Kd=3.8 mcg/L plasma [35]. Green dashed line: haematocrit-standardised concentration (Cstd) (Cstd = Cwb × 45% / HCT%).(Storset, Holford et al. 2014b).

Because of failure to understand these principles almost all research and clinical use of tacrolimus concentrations is distorted by not recognizing the misleading consequences of using un-standardized whole blood concentrations. This distortion continues today (2024) despite the theory and clinical application of standardized concentrations having been available since 2014.

Target Concentration

The use of a trough concentration target is based on tradition but without pharmacological support. The trough concentration is the lowest concentration during a steady state dosing interval, but the pharmacological effects are determined by the full time course of concentrations which are necessarily all higher than or equal to the trough concentration. A more pharmacologically rational target that captures exposure to all the concentrations causing the drug effect is the area under the concentration time curve (AUCssDI). Dividing AUCssDI by the dosing interval (DI) is the average steady state concentration (Cssavg). Cssavg is independent of the dosing interval and is thus a simple choice for a target concentration based on pharmacological principles. Nevertheless, this choice is still rather naïve because it does not account for the time course of concentration and the delays in the concentration response relationship but it clearly a step in the right direction away from the traditional trough concentration.

By default, NextDose suggests using Cssavg as the target concentration, rather than trough concentration. A CssAvg 15 mcg/L (HCT=45%) is approximately equivalent to a trough concentration of 7 mcg/L (HCT=33%) (Storset, Holford et al. 2014b).

There is no pharmacological reason to change the target depending on genotype. The CYP3A4 and CYP3A5 genotypes change exposure (AUCssDI) and thus the average concentration (Cssavg). They do not change the pharmacodynamics of tacrolimus.

NextDose will take care of the CL and F changes when estimating the Bayesian CL and F and use that to predict the dose needed to achieve the target.

A simulation based study compared covariate based dosing (fat free mass) with Bayesian target concentration adapted dosing. Bayesian dosing improved the day 5 Cssavg within an 80-125% acceptable range around the target concentration of 14.2 mcg/L from 37% to 65% (Storset, Holford et al. 2014b).

Figure 2 Simulation study showing improvement in day 5 Cssavg (from (Storset, Holford et al. 2014b)).

Tacrolimus trough target concentration attainment was subsequently shown to be improved using Bayesian forecasting and haematocrit based standardisation of whole blood concentrations (Storset, Asberg et al. 2015).

CYP3A4 and CYP3A5 Genotypes

In view of increased interest in genotype based initial dosing of tacrolimus (Khatri, Felmingham et al. 2024) two CYP3A4 genotypes are included in NextDose (Figure 3).

Figure 3 NextDose genotypes showing the CYP3A4 and CYP3A5 genotypes which are relevant to tacrolimus.

CYP3A4 normal metaboliser is *1/*1. CYP3A4 poor metaboliser is *22. CYP3a4 poor metabolisers have a clearance 26% lower than normal metabolisers.

“Because of the low number of CYP3A5 *1/*1 carriers in the dataset (n = 3), these subjects were grouped with CYP3A5*1/*3 carriers(n=33) during covariate analysis. CLp was estimated to be 30% higher (ΔOFV −46.0, P < 0.001) and F 18% lower (ΔOFV −2.9, P = 0.09) in this group compared with patients not expressing functional CYP3A5 enzyme (*3/*3 carriers). Although an independent effect on F in addition to the effect on CLp was not statistically supported at the significance level of 0.05 during covariate inclusion, effects on both parameters were retained because both CLp and F should theoretically be altered in patients with functional CYP3A5 enzyme in their liver and intestines.” (Storset, Holford et al. 2014b)

CYP3A5 normal expresser is *3/*3. CYP3A5 extensive expresser is *1/*1 or *1/*3. CYP3A5 expressers have a 30% increase of CL and 18% decrease in oral bioavailability. Overall, these two effects of CYP3A5 increased expression decrease tacrolimus exposure and are used predict the dose required to achieve the target concentration.

Parameter Estimates and Covariate Effects

The tacrolimus parameter estimates and covariate effects are illustrated using data from a child who was given tacrolimus before and after a kidney transplant. The transplant took place about 5 h after the first concentration measurement (Figure 4).

Figure 4 Time course of predicted and observed tacrolimus (HCTstd). Storset2024 model without early post-transplant effect on oral bioavailability. Note the first 3 concentrations observed after transplantation are higher than the population prediction consistent with an early post-transplant effect.

Figure 5 Parameter estimates and covariate effects. Storset2024 model without early transplant effect on oral bioavailability.

The fractional early transplant effect on bioavailability (fTx on F%) is zero because this effect is not included in the Storset2024 model.

The Storset2024 BTEL model is an extension of the original model for a post-transplant effect on bioavailability (Storset, Holford et al. 2014b). Bioavailability has a nominal value of 1 before transplant. The early post-transplant effect of an increase in bioavailability in the first two days after transplant is constant over that period. The post-transplant effect then declines exponentiality with a rapid half life (3 minutes) to reach the nominal value of 1. There is then a very small linear increase (0.5% /year) in bioavailability as a function of post-transplant day+2.

See Table 1 and Figure 7 for results using the Storset2024 BTEL model including time after transplant effects.

Table 1 Parameters and Covariate Effects. Interpretation comments refer to values in Figure 6.

Column	Description	Interpretation
Time h	Time of observed concentration	The first time (71.63 h) is relative to the first dose of tacrolimus
CL L/h	Empirical Bayes estimate of whole blood clearance with standard HCT of 45%	The value 11.7 L/h reflects this is a child (adult value around 17 L/h)
fCL%	Fractional difference from group* value for CL reflecting the random between subject effect	The difference is modest (29.3%) indicating the covariate effects are doing a reasonable job of predicting CL
V L	Empirical Bayes estimate of whole blood volume of distribution with standard HCT of 45%	The value 29.7 L reflects this is a child (adult value around 130 L)
fV%	Fractional difference from group value for V reflecting the random between subject effect	The difference is large (-52.1%) indicating the covariate effect (size) is doing a poor job of predicting V
F	Oral apparent bioavailability fraction	The values less than 1 reflect predictable effects of prednisolone and CYP3A5 expresser genotype as well as random between subject effects
fF%	Fractional difference from group value for F reflecting the random between subject effect	The differences are small to modest (-18% to -30.8%) indicating the covariate effects are doing a reasonable job at predicting F
FFM kg	Predicted fat free mass based on total body mass, height, sex and postnatal age	FFM is used as the allometric mass for scaling CL and V
RF	Renal function	Not used in the PK model but reflects improvement following transplant
HCT%	Observed haematocrit	HCT is used to standardize tacrolimus concentrations
Days Post Tx	Days following the time of transplant. The -1 value means the observed concentration was obtained prior to the transplant not days before transplant.	Value used to predict early transplant increase in bioavailability when days are greater than zero and less than 2
fTx on F%	Fractional difference from group value for early transplant effect on bioavailability reflecting the random between subject effect	The Storset2024 BTEL model group estimate is a 2.57 fold increase in oral bioavailability between 0 and 2 days post-transplant otherwise oral bioavailability has a nominal value of 1. This is consistent with (Storset, Holford et al. 2014b). The Ftx on F% value of minus 44.9% reflects the random between subject effect indicating in this subject the bioavailability appears only to have increased by about 15.4% (0.449 x 2.57-1) during the first 2 days post-transplant. After 2 days there are only very small differences in F relative to the group value of 1. fTx on F% value is always 0 for the Storset2024 model because a post-transplant effect is not included.
fPred on F%	Fractional difference from group value for steroid effect on bioavailability reflecting the random between subject effect	The difference is modest (24.4%) indicating the steroid effect is doing a reasonable job of predicting F
fCYP3A4 on CL%	Genotype prediction of effect on clearance	CL is decreased for subject with a poor metaboliser genotype
fCYP3A5 on CL%	Genotype prediction of effect on clearance	CL is increased for subject with an expresser genotype
fCYP3A5 on CL%	Genotype prediction of effect on bioavailability	F is decreased for subject with an expresser genotype
Cp mcg/L	Individual prediction of tacrolimus plasma concentration	The Storset model is based on predicted plasma concentrations. The Kd for binding to red cell mass is 3.8 mcg/L (Jusko, Piekoszewski et al. 1995).
fpu% at HCT 45%	Individual prediction of tacrolimus plasma unbound to red cell mass	The fraction of plasma unbound and observed HCT is used to predict whole blood concentrations for comparison with observed whole blood concentrations.

* The group value is the parameter value after incorporating the predictable covariate effects without any random effects. In older literature it might be called the “typical value”.

Figure 6 Time course of predicted and observed tacrolimus (HCTstd). Storset2024 BTEL model including early transplant effect on oral bioavailability.

The predicted increase in bioavailability in the 2 days following transplant is reflected in the 4 high peak population concentrations. The individual predictions are lower because of the estimated random effect for this subject.

Figure 7 Parameter estimates and covariate effects. Storset2024 B model including time after transplant effect on oral bioavailability.

References

Jusko, W. J., W. Piekoszewski, G. B. Klintmalm, M. S. Shaefer, M. F. Hebert, A. A. Piergies, C. C. Lee, P. Schechter and Q. A. Mekki (1995). "Pharmacokinetics of tacrolimus in liver transplant patients." Clin Pharmacol Ther 57(3): 281-290.

Khatri, D., B. Felmingham, C. Moore, S. Lazaraki, T. Stenta, L. Collier, D. A. Elliott, D. Metz and R. Conyers (2024). "Evaluating the evidence for genotype-informed Bayesian dosing of tacrolimus in children undergoing solid organ transplantation: A systematic literature review." British Journal of Clinical Pharmacology Early View(n/a).

Sikma, M. A., E. M. Van Maarseveen, C. C. Hunault, J. M. Moreno, E. A. Van de Graaf, J. H. Kirkels, M. C. Verhaar, J. C. Grutters, J. Kesecioglu, D. W. De Lange and A. D. R. Huitema (2020). "Unbound Plasma, Total Plasma, and Whole-Blood Tacrolimus Pharmacokinetics Early After Thoracic Organ Transplantation." Clinical Pharmacokinetics 59(6): 771-780.

Staatz, C. E., E. Størset, T. K. Bergmann, S. Hennig and N. Holford (2015). "Tacrolimus pharmacokinetics after kidney transplantation – Influence of changes in haematocrit and steroid dose." British Journal of Clinical Pharmacology: DOI: 10.1111/bcp.12729.

Storset, E., A. Asberg, M. Skauby, M. Neely, S. Bergan, S. Bremer and K. Midtvedt (2015). "Improved Tacrolimus Target Concentration Achievement Using Computerized Dosing in Renal Transplant Recipients--A Prospective, Randomized Study." Transplantation 99(10): 2158-2166.

Storset, E., N. Holford, S. Hennig, T. K. Bergmann, S. Bergan, S. Bremer, A. Asberg, K. Midtvedt and C. E. Staatz (2014b). "Improved prediction of tacrolimus concentrations early after kidney transplantation using theory-based pharmacokinetic modelling." Br J Clin Pharmacol 78(3): 509-523.

Storset, E., N. Holford, K. Midtvedt, S. Bremer, S. Bergan and A. Asberg (2014a). "Importance of hematocrit for a tacrolimus target concentration strategy." Eur J Clin Pharmacol 70(1): 65-77.

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