Handling interoccasion variability in model‐based dose individualization using therapeutic drug monitoring data

Abstract

Aims

This study aims to assess approaches to handle interoccasion variability (IOV) in a model‐based therapeutic drug monitoring (TDM) context, using a population pharmacokinetic model of coagulation factor VIII as example.

Methods

We assessed 5 model‐based TDM approaches: empirical Bayes estimates (EBEs) from a model including IOV, with individualized doses calculated based on individual parameters either (i) including or (ii) excluding variability related to IOV; and EBEs from a model excluding IOV by (iii) setting IOV to zero, (iv) summing variances of interindividual variability (IIV) and IOV into a single IIV term, or (v) re‐estimating the model without IOV. The impact of varying IOV magnitudes (0–50%) and number of occasions/observations was explored. The approaches were compared with conventional weight‐based dosing. Predictive performance was assessed with the prediction error percentiles.

Results

When IOV was lower than IIV, the accuracy was good for all approaches (50^th percentile of the prediction error [P50] <7.4%), but the precision varied substantially between IOV magnitudes (P97.5 61–528%). Approach (ii) was the most precise forecasting method across a wide range of scenarios, particularly in case of sparse sampling or high magnitudes of IOV. Weight‐based dosing led to less precise predictions than the model‐based TDM approaches in most scenarios.

Conclusions

Based on the studied scenarios and theoretical expectations, the best approach to handle IOV in model‐based dose individualization is to include IOV in the generation of the EBEs but exclude the portion of unexplained variability related to IOV in the individual parameters used to calculate the future dose.

What is already known about this subject

• Interoccasion variability (IOV) is commonly included in population pharmacokinetic models.

• The potential of model‐based dose individualization using therapeutic drug monitoring data is known to be challenged by high magnitudes of IOV.

• The impact of different methods to handle IOV in Bayesian forecasting has not been studied.

What this study adds

• The accuracy of the forecast dose is good for commonly used approaches to handle IOV in model‐based therapeutic drug monitoring, but the precision may vary substantially.

• The preferred approach to handle IOV in Bayesian forecasting is to include IOV in the generation of the empirical Bayes estimates but exclude the portion of unexplained variability related to IOV in the calculation of the individualized dose.

1. INTRODUCTION

Model‐based therapeutic drug monitoring (TDM) is a procedure for individualization of dosing regimens. Its main goal is to decrease the risk of under‐ or over‐dosing and consequently achieve the desired therapeutic effect and avoid the appearance of unwanted side effects by adjusting the dosing regimen according to the pharmacokinetic (PK) and in some cases also pharmacodynamic (PD) characteristics of the individual patient.1, 2, 3 To be eligible for monitoring, a drug should be easy to measure, include a well characterized concentration–effect relationship, have a narrow or intermediate therapeutic margin, and have a high unexplained interindividual variability (IIV) that is larger than other types of variability.3 Model‐based TDM has been used with drugs belonging to multiple therapeutic areas,4, 5, 6, 7, 8 with positive outcomes including not only better efficacy and safety of drug therapy, but also improved cost‐effectiveness.9, 10

Model‐based TDM uses established population PK or PK/PD models as Bayesian priors, an observed individual response (for instance, a drug concentration), dosing history and covariate information (optional) to estimate individual model parameters, which will be used to forecast and adjust the future treatment.11 In population models, unexplained random variability can be identified as: variability at a parameter level, including IIV and variability between occasions within the same individual (interoccasion variability, IOV); and variability at an observation level, comprising residual error variability which includes, for instance, errors of measurement (analytical assay error or uncertain dosing/sampling times) and model misspecification. The estimation of IOV allows separating changes in parameters on different occasions from the residual error or IIV and should be tested during model development,12, 13 as ignoring this level of variability has previously been shown to lead to bias in parameter estimates.12 When a drug exhibits high IIV compared to residual and/or IOV variability, the PK or PD observations may differ substantially and constantly between individuals but not between occasions, making model‐based TDM a valuable tool. However, if the magnitude of residual variability and/or IOV is moderate to high, the use of model‐based TDM is challenged,12, 14, 15 given the lack of predictive ability of these types of variabilities. Wallin et al. assessed the impact of different variability levels (IIV and IOV on PK and PD parameters) to predict a target nadir neutrophil count using a model‐based TDM setting, and concluded that the precision in target achievement was constant with varying IIV, but decreased with increasing IOV.14 The usefulness of model‐based TDM depends also on the magnitude of the therapeutic margin of the drug and it is only helpful if the overall IOV and residual variability are lower than the safe and effective variability of the drug.16, 17 Even though IOV in the model challenges the prediction of the individual response on the next occasion, many models developed currently include IOV and it is not clear what is the most accurate and precise way to individualize dosing regimens in its presence. In fact, even though a wide range of TDM software packages is available for dose individualization,18 these do generally not support the inclusion of IOV, which leads healthcare professionals to neglect IOV, or sum it with other sources of variability, with unknown consequences.

The PK of exogenous coagulation factor VIII (FVIII) is characterized by a large unexplained IIV (30 percent coefficient of variation [%CV] on CL, and 0–20%CV on volumes) and a small to large IOV (0–25%CV on CL, and 0–40%CV on volumes), thus requiring higher doses for some patients to achieve the targeted trough FVIII activity.19, 20, 21 During prophylactic treatment, FVIII activity in plasma is typically maintained above an empirical threshold of 0.01 IU/mL.22 Even though FVIII has a wide therapeutic margin, in recent years the use of model‐based TDM has been encouraged to optimize dosing regimens and reduce the high costs associated with therapy.23, 24, 25, 26 This analysis aims at comparing different approaches to handle IOV in a wide range of model‐based TDM settings, using a population PK model for exogenous coagulation FVIII as example.

2. METHODS

This simulation‐based study consisted of a series of steps, which were repeated for a range of settings. The workflow is represented in Figure 1 and is described in detail in the following methods sections. An example of the model code used, datasets and outputs is available in the Supplemental text S1. Briefly, in the first step, data (individual PK parameters and FVIII activity) were simulated from models with varying magnitudes of variability; these simulated data were considered to be the observed real‐world data and the simulated PK parameters were used to calculate the true individual dose that would be required to reach a given FVIII activity target. Secondly, individual parameters (empirical Bayes PK parameter estimates [EBEs]) were estimated using Bayesian forecasting employing the model used for simulation and using different amount of observations (occasions). Thirdly, the EBEs were used to calculate the individualized doses required to achieve a given target in the next occasion for each simulated patient. Finally, the target attainment on the subsequent occasion was calculated and evaluated assuming the individualized dose calculated in the previous step and the true parameters at the next occasion. Data management and statistical summaries were carried out using R (www.r‐project.org, version 3.3.1) and model estimations and simulations were conducted using NONMEM 7.3,27 assisted by Perl‐Speaks‐NONMEM (PsN, version 4.6.16).28

Figure 1.

Workflow of the simulation‐based study. EBEs: empirical Bayes estimates; FVIII: coagulation factor VIII; PK: pharmacokinetic; TDM: therapeutic drug monitoring

2.1. Model used in simulations

A previously published population PK model for FVIII in haemophilia A20 was used as an example. The model was developed using data from 4 PK studies including patients aged 7–74 years receiving prophylactic intravenous FVIII. In total, 31 severe and 3 moderate haemophilia A patients contributed with 714 FVIII activity samples. An occasion was defined as a visit with PK assessment and the dataset included a median of 3 study occasions per individual (range 1–7), with variable time between occasions (from 1 week to several months). Seven samples (median) were collected per occasion (range 1–16). The structural model comprised a 2‐compartment model with allometrically scaled disposition parameters using total body weight and a decrease in clearance (CL) with age. IOV was implemented according to the procedure described by Karlsson and Sheiner.12 IIV was included on CL (28%) and central volume of distribution (V, 17%; correlation CL‐V 0.64); IOV was included on CL (13%) and V (10%), and the residual error model consisted of a combined additive (SD 0.012 IU/mL) and proportional (8.5%) component.

2.2. Simulation scenarios

To study different magnitudes of IOV in relation to IIV, alternative scenarios were constructed based on the original model, changing only the magnitude of IOV. Nine different IOV magnitudes, varying from 0% to 50% on CL or V (Table 1), were used to simulate individual parameters and steady‐state FVIII activity values at 4, 24 and 48 h post‐dose29 on 4 occasions, spaced 3 months apart, for 1000 hypothetical patients following FVIII administration of 30 IU/kg every other day. This set of individual parameters was considered as true, and the FVIII activity values as the observed TDM data. In all simulations, the hypothetical population comprised patients with severe haemophilia A and accordingly the endogenous FVIII activity and the respective IIV were set to zero. The age distribution in the simulated data set was generated using a truncated log‐normal distribution based on the characteristics of the original data. Body weight values were derived from a piecewise linear model describing the relationship between body weight and age including a random error component, estimated from the observed data. The mean age ± standard deviation in the simulation dataset was 25.1 ± 12.6 years (range 7.0–68.7), and body weight 67.0 ± 18.0 kg (range 16.6–113.2).

Table 1.

Simulation scenarios, approaches used in Bayesian forecasting and dose calculation and number of samples and occasions included in the scenarios used in the simulations

Simulation scenario					Bayesian forecasting and dose calculation
Model	IOV (%CV)		IIV (%CV)		Approach	Model to generate EBEs	Model to generate dose	Information used
	CL	V	CL	V		exemplified for CL		No. samples	Occasion number
Original	13	10	28	17	IIV + IOV	Original TVCL = 222 × ${\left(\frac{\mathit{WT}}{68}\right)}^{0.75}$× (1–0.00696 × (age ‐ 24)) CLij = TVCL × $e^{{\mathrm{\eta }}_i+{\mathrm{\kappa }}_{\mathit{ij}}}$	CLij TDM = TVCL × $e^{{\mathrm{\eta }}_i+{\mathrm{\kappa }}_{\mathit{ij}}}$	4, 24 and 48 h	1, 2 or 3 1 + 2 or 2 + 3 1 + 2 + 3
					IIV + IOV – IIV EBE for dose	Original CLij = TVCL × $e^{{\mathrm{\eta }}_i+{\mathrm{\kappa }}_{\mathit{ij}}}$		4 or 48 h 4 and 24 h 4, 24 and 48 h
					IIV – IOV ignored	Original but IOV variance (πCL 2) fixed to 0 CLij = TVCL × $e^{{\mathrm{\eta }}_i}$		4, 24 and 48 h
					IIV – IOV & IIV summed	Original but IIV variance set to sum of IIV & IOV variances (ωCL 2 + πCL 2) and IOV variance fixed to 0 (πCL 2 = 0) CLij = TVCL × $e^{{\mathrm{\eta }}_i}$	CLij TDM = TVCL × $e^{{\mathrm{\eta }}_i}$	4, 24 and 48 h
					IIV – re‐estimated	Model re‐estimated to include only IIV CLij = TVCL × $e^{{\mathrm{\eta }}_i}$		4 or 48 h 4 and 24 h 4, 24 and 48 h
Alternative models varying magnitude of IOV
IOV CL	0, 20, 30, 50	10	28	17	IIV + IOV IIV + IOV – IIV EBE for dose IIV – IOV ignored IIV – IOV and IIV summed IIV – re‐estimated	As above	As above	4, 24 and 48 h	1 + 2 + 3
IOV V	13	0, 20, 30, 50

Abbreviations: CL, clearance; CL_ij, empirical Bayes estimate of clearance for the ith subject at the jth occasion; CL_ijTDM, individual parameter used to calculate the individualized dose; %CV, percent coefficient of variation; EBEs, empirical Bayes estimates; IIV, interindividual variability; IOV, interoccasion variability; TVCL, typical value of clearance (mL/h); V, volume of distribution; WT, body weight (kg); η_i and κ_ij, individual IIV and IOV terms, independently estimated and normally distributed with mean zero and variances ω_CL ² and π_CL ², respectively.

2.3. Approaches for dose individualization

2.3.1. Model‐based TDM approaches using Bayesian forecasting

The EBEs were obtained using maximum a posteriori Bayesian estimation in NONMEM. The approaches used to calculate the individualized30, 31 doses are described below and summarized in Table 1:

• IIV + IOV: individualized doses were calculated based on the EBEs which were estimated by the model used for each simulation scenario, including all sources of variability (covariates, IIV, IOV and residual error).

• IIV + IOV – IIV EBE for dose: EBEs were estimated by the model used for each simulation scenario, including all sources of variability (covariates, IIV, IOV and residual error); however, individualized doses were calculated based on individual pharmacokinetic parameters, which resulted from removing the random effect related to IOV (κ_ij) from the EBEs.

• IIV – IOV ignored: individualized doses were calculated based on the EBEs which were estimated by the model used for each simulation scenario, including covariates, IIV and residual error, but setting the IOV variance (π²) to 0.

• IIV – IOV & IIV summed: individualized doses were calculated based on the EBEs which were estimated by the model used for each simulation scenario, including covariates, IIV and residual error, but summing the IIV and IOV variances (ω² and π², respectively) into a single IIV term (ω² + π²) and setting the IOV variance (π²) to 0. The original model included a covariance element between IIV on CL and V, which was re‐calculated in the alternative simulated scenarios to correspond to the original correlation magnitude.

• IIV – re‐estimated: individualized doses were calculated based on the EBEs which were estimated by an alternative model re‐estimated without IOV, which included covariates, IIV and residual error. This model was estimated based on the original data from which the original model was developed (simulation scenario original model) or based on rich simulated data (simulated time points: 0.25, 0.5, 1, 3, 6, 9, 24, 28, 32, 48 h post‐dose) from the alternative IOV models (simulation scenarios IOV CL and V 0–50%).

For all approaches except IIV – re‐estimated, the population parameters were not re‐estimated, but only the variances of IIV or IOV were changed as described. The EBEs used to produce the individual parameters to calculate the individualized doses were obtained for each simulated dataset using the previously mentioned approaches while varying the amount of data included: only 1 occasion (occasion number 1, 2 or 3), 2 occasions (1 + 2 or 2 + 3) and 3 occasions (1 + 2 + 3). The individual doses resulting in a FVIII trough activity target of 0.01 IU/mL at 48 h post‐dose were calculated from each set of EBEs.

2.3.2. Body weight‐based dosing

A (body) weight‐based dosing regimen (IU/kg) was added as a comparison between a conventional approach and model‐based TDM. For weight‐based dosing, the dose of 30 IU/kg was reduced applying a scaling factor of 0.3 (9 IU/kg), which was found to generate median FVIII activities close to the defined target of 0.01 IU/mL across simulated scenarios and therefore facilitates the comparison with the results obtained by model‐based TDM individualized dosing schemes.

2.4. Influence of the number of samples at each occasion

The influence of the number of samples within an occasion when calculating the forecast dose was assessed for the simulation scenario original model. One (4 or 48 h post‐dose), 2 (4 and 24 h), and 3 samples (4, 24 and 48 h), were used to generate the EBEs and calculate the dose following the approaches IIV + IOV – IIV EBE for dose and IIV – re‐estimated.

2.5. Evaluation of predictive performance

The performance of each model‐based TDM approach to forecast the individualized dose for the different simulated scenarios was assessed with the relative prediction error, calculated as:

$${\mathrm{PE}}_{\mathrm{i}}\%=\frac{\left({\text{dose}}_{\mathrm{TDM}}–{\text{dose}}_{\text{true}}\right)}{{\text{dose}}_{\text{true}}}\times 100$$

where PE_i is the prediction error in the i^th simulated subject, dose_TDM is the TDM individualized dose on the next occasion based on a given approach for a certain information content and dose_true is the true dose on the next occasion. Similarly, the PE for weight‐based dosing was calculated based on the individual weight‐based dose (same across occasions) and the true dose on the next occasion. The accuracy of each approach was quantified by the 50^th percentile of the PE (P50), and precision by a range of percentiles of the PE (P2.5, P10, P25, P75, P90, P97.5). The prediction of FVIII activity was assessed through the model‐based TDM dose and the calculation of the FVIII activity for the subsequent occasion using the true individual parameters. For example, the estimation of the EBEs from data on occasions 1 and 2 led to the calculation of the individual dose to achieve the FVIII activity target on occasion 3, which along with the true parameters on occasion 3 enabled the calculation of the expected FVIII activity (obtained in a real‐world TDM setting).

2.6. Nomenclature of targets and ligands

Key protein targets and ligands in the article are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS guide to PHARMACOLOGY32 and are permanently archieved in the Concise Guide to PHARMACOLOGY2017/18.33

3. RESULTS

The performance of the explored approaches to predict individualized doses for the original model scenario is depicted in Figure 2 and summarized in Table 2. On a population level, the individually predicted doses resulted in low bias (P50 < 3.7%), regardless of the information content or the approach used to handle IOV. As expected, with increasing information content, imprecision decreases for all approaches. When information from 1 occasion was included, the P97.5 ranged from 178 to 268% across approaches, i.e. the TDM individualized doses were 178–268% or larger than the true dose on the next occasion for 2.5% of the population (for a median patient receiving 603 IU, these numbers correspond to doses of 1673 IU–2218 IU). For 3 occasions, the P97.5 range was lower, 139–225% (for a median patient, 1441–1959 IU). IIV + IOV – IIV EBE for dose showed the most precise results, most evident when information available was sparse (one occasion P97.5 = 178%). The approach IIV – re‐estimated performed slightly better than IIV – IOV ignored and IIV – IOV & IIV summed, particularly when data from just 1 occasion were used. When data from 3 occasions were used, all approaches had a similar predictive ability (P97.5 = 139–144%), except the IIV + IOV approach, which performed worst overall (P97.5 = 225%). The weight‐based dosing resulted in substantially higher imprecision than the model‐based approaches (P97.5 = 345%), suggesting an added value of performing model‐based TDM. The consequence of using the individualized doses assessed by calculating the FVIII activity for the next occasion shows identical results in terms of predictive performance, and the percentiles can be found in Supplemental text S2 (Figure S1).

Figure 2.

Percentiles of the prediction error for the alternative model‐based therapeutic drug monitoring approaches when forecasting the dose leading to a coagulation factor VIII activity of 0.01 IU/mL at 48 hours postdose, using information from 1, 2 or 3 occasions, or weight‐based dosing. EBEs: empirical Bayes estimates; IIV: interindividual variability; IOV: interoccasion variability

Table 2.

Summary statistics of individualized dose forecasting prediction errors (PE) for the original model scenario and varying IOV magnitudes on the clearance of factor VIII

	Percentile	Information content	PE for each dose individualization approach (%)
			IIV + IOV	IIV + IOV – IIV EBE for dose	IIV – IOV ignored	IIV – IOV & IIV summed	IIV – re–estimated	Weight
Original model	P50	1	−1.0	−1.2	−1.2	−1.4	−1.2	−1.9
		3	3.7	1.8	−1.0	−0.8	−0.5
	P75	1	55.9	44.3	50.7	53.5	50.2	74.7
		3	55.5	42.8	36.8	36.0	38.1
	P97.5	1	267.8	177.5	237.8	249.6	229.6	345.0
		3	224.9	139.0	144.1	143.8	140.4
IOV CL 0%	P50	1	0.2	0.4	0.3	0.1	0.8	−1.9
		3	1.3	2.0	1.5	1.2	2.0
	P75	1	24.2	22.1	23.2	23.4	23.6	66.0
		3	21.7	18.7	19.2	19.6	19.6
	P97.5	1	98.4	78.3	88.6	92.2	86.7	279.4
		3	75.9	60.5	67.5	67.6	65.0
IOV CL 20%	P50	1	−1.1	−2.5	−2.4	−1.5	−7.4	−1.3
		3	3.0	2.4	−5.2	−5.3	−2.8
	P75	1	84.0	62.7	74.5	79.6	59.2	82.5
		3	81.9	59.8	49.2	48.7	53.6
	P97.5	1	528.2	272.8	413.7	471.1	287.1	407.8
		3	448.2	211.8	232.9	238.6	223.2
IOV CL 30%	P50	1	−0.4	−3.7	−5.1	−1.0	−15.7	0.0
		3	6.4	0.3	−15.4	−15.4	−10.0
	P75	1	140.1	88.3	119.5	135.5	81.0	111.5
		3	146.0	92.5	62.9	62.5	69.6
	P97.5	1	1420.7	453.8	913.8	1229.8	463.7	505.2
		3	1328.8	375.5	432.9	451.6	382.7
IOV CL 50%	P50	1	−2.1	−6.2	−9.7	−3.6	−30.1	−4.2
		3	6.1	−5.1	−40.0	−40.2	−30.0
	P75	1	336.2	150.7	243.8	305.8	112.4	161.6
		3	360.4	152.9	77.8	78.4	92.6
	P97.5	1	11925.2	903.8	2959.3	7654.0	1065.1	859.1
		3	13616.6	787.3	936.5	1086.7	880.5

CL: clearance; IOV: interoccasion variability; PE: prediction error; P50: 50^th percentile; P75: 75^th percentile; P97.5: 97.5^th percentile.

The impact of IOV magnitude on the predictive performance of the approaches assessed is depicted in Figure 3, and it is summarized in Table 2 for varying magnitudes of IOV on CL and in Supplemental Table S1 for varying magnitudes of IOV on V. As seen before, on a population level most of the studied approaches showed good accuracy, regardless of the information content used or the PK parameter associated with increased IOV. However, the approaches involving only IIV showed a tendency to under‐predict the target in the case of high magnitudes of IOV on CL (≥30%), in particular when using data from more than 1 occasion to calculate the forecast dose (P50 = –40.2 to –10%). As expected, the imprecision of the dose predictions increased with increasing magnitude of IOV, an effect more pronounced for CL than for V. As for the original model scenario, the IIV + IOV – IIV EBE for dose approach resulted in the most precise dose predictions, especially when using sparse data. For most magnitudes of IOV, the IIV – re‐estimated approach performed almost as well, but was worse in terms of the outer percentiles of the PE when IOV exceeded IIV on CL. Of all IIV approaches, IIV – re‐estimated was the one performing best, followed by IIV – IOV ignored and IIV – IOV & IIV summed. The corresponding plot with predicted FVIII activities can be found in Supplemental text S2 (Figure S2 ). The proportion of patients with low FVIII trough values tended to be lower for the IIV + IOV – IIV EBE for dose approach than for the IIV – re‐estimated approach. For instance, when the magnitude of IOV on CL was 30% and data from 3 occasions were used, the percent of patients with FVIII trough values <0.005 IU/mL was 26.3% for the IIV + IOV – IIV EBE for dose and 30.8% for the IIV – re‐estimated approach. The IIV + IOV approach lead to the most imprecise predictions and was even worse than weight‐based dosing, while Bayesian forecasting using the IIV + IOV – IIV EBE for dose or IIV – re‐estimated showed an advantage over weight‐based dosing also in the presence of high magnitudes of IOV.

Figure 3.

Median, 2.5^th percentile (P2.5) and P97.5 of the prediction error for the alternative model‐based therapeutic drug monitoring approaches when forecasting the dose leading to a coagulation factor VIII activity of 0.01 IU/mL at 48 hours postdose, using information from 1, 2 or 3 occasions, or weight‐based dosing, for different magnitudes of interoccasion variability (IOV; 0–50%) on clearance (CL) and on volume of distribution (V). EBEs: empirical Bayes estimates; IIV: interindividual variability; IOV: interoccasion variability

The impact of using a reduced number of samples within an occasion to predict the individualised dose with the best performing approaches for the original model scenario, i.e. IIV + IOV – IIV EBE for dose and IIV – re‐estimated, is depicted in Figure 4 (numerical summaries available in Table S2, and FVIII activities in Figure S3). When only 1 early sample (4 h after dose) was used to predict the next dose, no major differences were found between the approaches, and the imprecision was only slightly improved when information from more occasions was used. In addition, for the remaining sampling schedules, the IIV + IOV – IIV EBE for dose approach was better or similar than IIV – re‐estimated, regardless of the number of samples or occasions used. Weight‐based dosing performed worse than the remaining approaches tested, even when just 1 sample was considered.

Figure 4.

Median, 2.5^th percentile (P2.5) and P97.5 of the prediction error for the 2 best performing model‐based therapeutic drug monitoring approaches when forecasting the dose leading to a coagulation factor VIII activity of 0.01 IU/mL at 48 hours post‐dose, using information from 1, 2 or 3 occasions while varying the number of sampling points used, or weight‐based dosing. EBEs: empirical Bayes estimates; IIV: interindividual variability; IOV: interoccasion variability

4. DISCUSSION

In this study, we evaluated several approaches to handle IOV when predicting individualized doses using Bayesian forecasting, across varying magnitudes of IOV and varying amount of observations. In addition, these model‐based TDM approaches were compared with a conventional weight‐based dosing regimen. At a population level, most approaches led to the true dose and targeted FVIII activity value, regardless of the magnitude of IOV in the data. However, the imprecision of the predictions varied substantially between the scenarios and approaches assessed. The IIV + IOV – IIV EBE for dose approach was found to be the most accurate and precise approach to forecast doses, regardless of the magnitude of IOV in the data, number of occasions used in Bayesian forecasting or sampling times. The superiority of this approach was particularly evident when data from just 1 occasion were obtained. As data from more occasions became available, the predictive performance of IIV – re‐estimated became closer to IIV + IOV – IIV EBE for dose, and was followed by the approach IIV – IOV ignored. IIV + IOV was found to predict doses with considerable imprecision, and while it might seem an attractive option, since it makes use of the original model with IOV, it is not recommended to be applied in model‐based TDM.

We evaluated 5 commonly used Bayesian forecasting approaches to generate the EBEs and calculate the individualized doses. Of these, 2 included IOV in the generation of the EBEs, the IIV + IOV and IIV + IOV – IIV EBE for dose. Whereas the IIV + IOV approach included the random effects related to IIV and IOV in the parameters used to calculate the individualized doses, the approach IIV + IOV – IIV EBE for dose included only the random effect related to IIV. As IOV lacks predictive ability, including its random effect in the individual parameter used to generate the dose will increase the imprecision of the individualized doses. Since IIV + IOV – IIV EBE for dose used the unperturbed model during Bayesian forecasting and only the random effect related to IIV for dose calculation, it is in principle the most appropriate approach to be used in model‐based TDM. The remaining 3 approaches did not include IOV in the generation of the EBEs and thus the model used for Bayesian forecasting deviates from the true model. As a result, the EBE parameters used to calculate the doses are somewhat biased. In the approach IIV – IOV ignored, the random effect related to IOV is not considered while the remaining components of the model are kept unchanged, thus resulting in an underestimation of the variability in the parameter in question. In the approach IIV – IOV & IIV summed, IOV is combined with IIV, which instead results in an inflated IIV. The approach IIV – re‐estimated assumes that the data used to estimate the prior Bayesian model are available, and that the model can be re‐estimated without IOV. This approach implies that IOV may be assigned into biased structural parameters, IIV and/or residual variability terms. For all approaches, the higher the magnitude of IOV, the larger the bias included in the EBEs. In this simulation study, the consequences of the assumptions made by each approach were investigated across multiple magnitudes of IOV and information contents.

Concerning the IIV approaches applied to the original model scenario, the differences observed between these approaches were small because the magnitude of IIV in the models used for Bayesian forecasting was relatively similar in all cases. For the varying IOV scenarios, the IIV – re‐estimated approach performed considerably better than the remaining IIV approaches and was the preferred method when only including IIV. Even though IIV + IOV – IIV EBE for dose was the best approach overall, IIV – re‐estimated performed almost as well for most scenarios. The differences between these approaches were more evident for the original model scenario than for the simulated varying IOV scenarios. This is probably because the re‐estimated models without IOV, used in the IIV – re‐estimated approach, were based on a combination of sparse and rich real data from 34 patients for the original model, while the simulated IOV scenarios included rich data from 1000 hypothetical patients, which led to a biased Bayesian prior model in the former case. For this reason, the results of the IIV – re‐estimated approach in the simulated scenarios might be slightly overoptimistic, since rich patient data are not always available when estimating the prior Bayesian model to be used in model‐based TDM. In case the re‐estimation of the Bayesian prior model is not possible (e.g. if the data used to develop the model are not available), the approach IIV – IOV ignored should be preferred to the approach IIV – IOV & IIV summed, especially if the magnitude of IOV is moderate to high (>20%) and lower information contents are used. Consequently, if IIV + IOV – IIV EBE for dose cannot be used, e.g. due to limitations of the current model‐based TDM software packages, IIV – re‐estimated can be considered. However, the influence of neglecting IOV during model building should be evaluated carefully, since it can result in parameter estimates substantially biased, or in case IOV lumps with IIV, give a false sense of confidence on the benefits of model‐based TDM.12

In this study, we also evaluated the consequence of alternative sampling schedules within an occasion for the choice of the approach to handle IOV. If the time of sampling within an occasion did not carry relevant information about the target, e.g. when an early sample was used to predict a trough, the approaches tested performed similarly. However, if at least 1 sample was informative about the target, IIV + IOV – IIV EBE for dose produced more precise forecast doses than IIV – re‐estimated. In addition to investigating the effect of varying IOV on CL or V separately while maintaining the remaining components of the model constant, we explored varying IOV on both PK parameters simultaneously, which led to similar conclusions in terms of which approach performed best (results not shown).

In addition, we evaluated the impact of an individualized model‐based TDM approach comparing with dosing based on body weight. As expected, with exception of extreme magnitudes of IOV, individualized weight‐based dosing led to more variable dose and FVIII trough predictions than most of the individualized model‐based TDM dosing regimens. Notably, model‐based TDM using a single early sample performed better than weight‐based dosing, probably a consequence of a better use of patient covariate information, namely, weight and age as compared to the conventional approach, which relied solely on scaling the dose linearly with weight. This highlights the benefits of model‐based TDM treatment compared to weight‐based dosing, which is in agreement with current clinical recommendations.23

When evaluating the influence of IOV in model‐based TDM, there are factors to be considered other than just the magnitude of IOV. First, the influence of the parameter carrying IOV on the prediction of the target may be more important than the magnitude of the respective IOV. As expected, the imprecision of the dose predictions was greater for high magnitudes of IOV on CL than on V, since the selected target was a trough activity value observed during the post‐distribution phase. Therefore, even when the magnitude of IOV on V was 3 times the IIV on V, model‐based TDM was still found to have better predictive ability than weight‐based dosing. Second, model‐based TDM cannot be excluded in scenarios where IOV is approximately the same or greater than IIV in influential parameters, but its value is dependent on the magnitude of IIV and the therapeutic margin of the drug. Finally, and as expected, the amount of information available should be considered when comparing a conventional approach with model‐based TDM, since more occasions and richer data are usually linked to better predictions of doses, given that the Bayesian prior model is not biased. Our results obtained using NONMEM are expected to be comparable across TDM software tools, provided that Bayesian maximum a posteriori estimation is used and uncertainty is handled in a similar way.4, 5, 6, 34

In this study, we considered the IOV to represent random changes in individual PK parameters (CL and V1) between study occasions, as assumed in the widely applied IOV modelling implementation suggested by Karlsson and Sheiner.12 Assuming that IOV changes occur truly at random, this part of the variability lacks predictive ability for the next occasion and therefore should not be included when predicting the dose for the next occasion. With the approach recommended in this study to handle IOV, IOV should be included in the estimation of the individual PK parameters (i.e. EBEs), and these parameters can be used to identify time‐related changes and its sources (e.g. as physiological changes due to aging or the concomitant administration of a drug leading to a PK interaction). When a given individual parameter changes systematically over time, the sources of variability should be properly characterized in the model used as prior in the Bayesian estimation, for instance, through the assessment of time‐varying covariates (e.g. longitudinal age information or yes/no information of an interacting drug). If the individual parameters change systematically over time due to unknown reasons, such trends can be modelled using alternative approaches such as the dynamic IOV or stochastic differential equations.35, 36, 37

One limitation of this study is that we used only 1 drug as example, for which a trough FVIII activity below the target carries a higher risk of spontaneous bleeding and above leads to an unnecessary consumption of FVIII product. The use of a widely applied 2‐compartment model with first‐order elimination in this study may allow the applicability of the present findings to other drugs. If other model structures or therapeutic targets, for instance, a peak value, the area under the plasma drug concentration‐time curve, or the average concentration at steady‐state, are used we expect the IIV + IOV – IIV EBE for dose approach to still perform better than the other approaches. Moreover, although the information content available will be reflected in the shrinkage of the EBEs toward the population parameter, thus potentially influencing the magnitude of the differences in performance between approaches, the conclusion on the preferred approach would not be affected by the level of shrinkage. However, the degree of the improvement in predictive ability compared to, for instance, the approach IIV – re‐estimated, may vary on a case‐by‐case basis, and deserves to be studied further. Another limitation of this study is that we did not explore what were the consequences of varying variability at the observation level for model‐based TDM. It is expected that with higher magnitudes of residual error variability, the estimation of the EBEs rely more on the Bayesian prior model, and less on the observed data, but the implications of varying this source of error with respect to the magnitudes of IIV and IOV in model‐based TDM should be studied further.

5. CONCLUSION

When performing model‐based TDM in the presence of IOV, the portion of unexplained variability related to IOV should be included in the generation of the empirical Bayes estimates, but this portion of unexplained variability should not be included in the individual parameter used to calculate the forecast dose. This suggestion is in agreement with the theoretical expectations, and such approach was shown to be the best to handle IOV based on the selected model and simulated scenarios, in particular when sparse sampling from 1 occasion was used, or the magnitude of IOV was high.

COMPETING INTERESTS

There are no competing interests to declare.

Supporting information

Table S1

Summary statistics of individualized dose forecasting prediction errors (PE) for varying IOV magnitudes on the central volume of distribution of factor VIII

Table S2

Summary statistics of individualized dose forecasting prediction errors (PE) for the 2 best performing model‐based therapeutic drug monitoring approaches while varying the number of sampling points used, or weight‐based dosing.

Data S1.

Supporting information

Data S2.

Supporting information

Abrantes JA, Jönsson S, Karlsson MO, Nielsen EI. Handling interoccasion variability in model‐based dose individualization using therapeutic drug monitoring data. Br J Clin Pharmacol. 2019;85:1326–1336. 10.1111/bcp.13901