Handling Delayed or Missed Dose of Antiepileptic Drugs: A Model-Informed Individual Remedial Dosing

doi:10.21203/rs.3.rs-1501686/v1

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Research Article

Handling Delayed or Missed Dose of Antiepileptic Drugs: A Model-Informed Individual Remedial Dosing

https://doi.org/10.21203/rs.3.rs-1501686/v1

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Background and Objectives:

Antiepileptic drugs are the major treatment modality for patients with epilepsy. Delayed or missed doses are common during long-term or lifelong anti-epilepsy treatment. This study aims to explore optimal individualized remedial dosing regimens for delayed or missed doses of nine commonly used antiepileptic drugs.

Methods

Monte Carlo simulation based on previously published population pharmacokinetic models was employed to explore remedial regimens of carbamazepine, clobazam, eslicarbazepine acetate, lamotrigine, levetiracetam, oxcarbazepine, phenobarbital, topiramate, and valproic acid. Six remedial strategies for delayed or missed doses were investigated. The deviation time outside the individual therapeutic range was used to evaluate each remedial regimen. The influences of patients’ demographics, concomitant medication, and scheduled dosing intervals on remedial regimens were assessed. RxODE and Shiny in R were employed to perform Monte Carlo simulation and recommend individual remedial regimens.

Results

The recommended remedial regimens were highly correlated to delayed time, scheduled dosing interval, and half-life of the antiepileptic drug. Moreover, the recommended remedial regimens for pediatric and adult patients were different. The renal function, along with concomitant medication that affect the clearance of the antiepileptic drug, may also influence the remedial regimens. A web-based dashboard was developed to provide optimal individualized remedial regimens for nonadherent patients, and a user-defined module with all parameters that could be defined flexibly by the user was built.

Discussion

Monte Carlo simulation based on population pharmacokinetic models may provide a rational approach to propose remedial regimens for delayed or missed doses of antiepileptic drugs.

Pharmacokinetics

Antiepileptic drugs

Adherence

Monte Carlo simulation

Delayed or missed dose

Population pharmacokinetics

Epilepsy is a chronic disorder of the brain and affects around 50 million people worldwide.¹ Roughly half of the patients with epilepsy have coexisting physical or psychiatric comorbidities and the overall mortality rate is increased by two- to threefold compared to the general population.² Antiepileptic drugs (AEDs) are the initial treatment modality for the vast majority of patients with epilepsy.³ With the appropriate use of AEDs, up to 70% of patients could become seizure-free.⁴

Since patients with epilepsy often require long-term or lifelong AEDs treatment, poor medication adherence becomes a major problem.^{5, 6} The nonadherence was reported in approximately 30–50% of patients with epilepsy.^{7, 8} Among all patterns of nonadherence, missed doses were reported by 71% of responsive patients.⁹ Since nonadherence has been associated with poor seizure control, increased time of hospitalization, and increased morbidity and mortality,^10–12 handling a delayed or missed dose becomes a common concern for the patients and healthcare providers.¹³

Package inserts of most AEDs, such as valproic acid (Depakote®), lamotrigine (Lamictal®), and levetiracetam (Keppra®), approved by the US Food and Drug Administration (FDA) recommend that “If a dose is missed, it should be taken as soon as possible unless it is near the next scheduled dose. If a dose is skipped, the patient should not double the next dose”.^14− 16 Patient information leaflet approved by Medicines and Healthcare Products Regulatory Agency (MHRA) of United Kingdom and the European Medicines Agency (EMA) along with Medicines and Medical Devices Safety Authority (MEDSAFE) in New Zealand propose similar recommendations.^{17, 18} However, no convincing evidence was provided for those recommendations, and the appropriate remedial dosing regimens for delayed or missed doses remain unclear.

Too large a remedial dose may result in concentration-dependent adverse drug reactions such as dizziness, nausea, and emesis, while inadequate remedial dose may increase the risk of seizure recurrence.^{3, 19} Therefore, optimal remedial dosing instructions for the delayed or missed dose of AEDs are imperative.^{20, 21}

Due to the ethical considerations, it is hard to conduct prospective clinical studies to explore and evaluate remedial strategies for the delayed or missed dose. Population pharmacokinetic (PK) modeling and simulation are regarded to be effective and have been applied to develop remedial dosing regimens for AEDs including carbamazepine,²² valproic acid,²³ lamotrigine,²⁴ and eslicarbazepine acetate.²⁵ However, since the prediction and simulation by the golden standard population PK software (NONMEM) employed in previous studies is too time-consuming, only typical patients with commonly used regimens were investigated.^22–25 Optimal remedial regimens for various delayed or missed dose scenarios were incompletely explored.

Therefore, this study aims to comprehensively provide individual remedial dosing regimens for patients with epilepsy who had a delayed or a missed dose of one of the nine commonly used AEDs using a fast algorithm of RxODE in R. Moreover, the influence of patients’ demographics, concomitant medication, and dosing interval on remedial regimens was investigated.

Rationale

During successful AEDs treatment, the drug concentration fluctuates within the therapeutic range for patients with full adherence. However, if the patient delayed or missed a dose, the drug concentration would deviate from the patient’s therapeutic range. Therefore, remedial dosing aims to restore the drug concentration to the patient’s therapeutic range and reduce the time outside the patient’s therapeutic range as much as possible.

As the therapeutic window can vary significantly from patient to patient,²⁶ guidelines for therapeutic drug monitoring of AEDs recommend using the individual therapeutic range of the patient instead of the fixed reference range.²⁷ In our study, the patient with full adherence is assumed to obtain desired efficacy and safety. Therefore, the range between the 5th percentile trough concentration and the 95th percentile peak concentration at the steady-state of a given dose is set as the patient’s individual therapeutic range.^22–24

To evaluate the impact of non-adherence and remedial regimens, the total deviation time where concentrations are outside the individual therapeutic range was estimated. It was calculated by the sum of deviation time above and below the individual therapeutic range. The schematic diagram of the rationale for remedial dosing regimens selection is presented in Fig. 1. The remedial regimens with less total deviation time were regarded to be more appropriate.^{23, 24, 28}

Remedial dosing regimen

Population PK characteristics of AEDs

The population PK studies of nine commonly used AEDs including carbamazepine, clobazam, eslicarbazepine acetate, lamotrigine, levetiracetam, oxcarbazepine, phenobarbital, topiramate, and valproic acid were identified in the PubMed and Embase databases or retrieved from the systematic reviews.^29–32

Population PK studies were identified if they enrolled more than 30 participants and the concentration-time profiles of typical patients based on the established model showed no obvious deviation from the others. Additionally, preference was given to studies that prospectively investigated in multi-centers or studies that included intensive samplings.

The population PK model and the corresponding fixed effect parameter estimates for simulation were set as the values in each of the previous studies. Regarding the random effects, between-subject variability was set at the reported values and the residual unexplained variability of all models was set as additive error of 0.1 mg/L and proportional error of 1% to facilitate the Monte Carlo simulation.³³ The simulations were performed using RxODE (version 0.9.1-8)³⁴ in R (version 3.6.1).

Remedial dosing regimen design

For the clinical feasibility, when a dose is delayed or missed, the patients are recommended to take the remedial dose regimen at two time-points, including the time when they remembered the delayed dose and the time for the next scheduled dose.^{13, 35} Therefore, six remedial strategies were investigated. The graphic remedial strategies are shown in Fig. 2, and details are listed below:

Strategy A

skip the delayed dose, and resume the regular dosing regimen at the next scheduled dosing time;

Strategy B

take the delayed dose immediately, and resume the regular dosing regimen at the next scheduled dosing time;

Strategy C

take the remedial dose immediately, and then resume the regular dosing regimen at the next scheduled dosing time;

Strategy D

take the delayed dose immediately, followed by a remedial dose at the next scheduled dosing time, and then resume the regular dosing regimen;

Strategy E

take both the remedial dose and delayed dose immediately, skip the next scheduled dose, and then resume the regular dosing regimen;

Strategy F

do not take the remedial dose immediately, but take both the remedial dose and delayed dose at the next scheduled dosing time, and then resume the regular dosing regimen.

Impact of patients’ demographics, concomitant medication, and scheduled dosing interval

To explore the impact of patients’ demographics on remedial regimens, pediatric patients (10 years old, 30 kg and 140 cm) and adult patients (40 years old, 70 kg and 180 cm) taking tablets were employed as typical patients. Moreover, for patients taking syrup or oral solution, younger children (5 years old, 16 kg and 110 cm) were employed as typical patients. The demographic characteristics of virtual patients and corresponding dosing regimens are summarized in Table 1.

Table 1

Demographic characteristics of simulated patients and corresponding dosing regimens.
Antiepileptic Drugs	Age group	Formulation	EGFR (ml/min)	Concomitant medication	Dose Interval (h)	Dose Regimen (mg)
Carbamazepine	Children	Tablet	90	Neutral, PB, PHT, VPA	12	100
	Adults	Tablet	90	Neutral, PB, PHT, VPA	12	400
Clobazam	Children	Tablet	90	Neutral, PB, PHT, ZNS	12	5
	Adults	Tablet	90	Neutral, PB, PHT, ZNS	12	10
Eslicarbazepine	Children	Tablet	90	LEV, Neutral, PB	24	400
	Children ^a	Oral suspension	90	LEV, Neutral, PB	24	400^a
	Adults	Tablet	90	Neutral	24	800
Lamotrigine	Children	Tablet	90	CBZ, Neutral, PB, PHT, VPA	12	50
	Adults	Tablet	90	CBZ, Neutral, PB, PHT, VPA	12	100
Levetiracetam	Children	Tablet	30,60,90	Neutral	12	250
	Adults	Tablet	30,60,90	Neutral	12	500
Oxcarbazepine	Children	Tablet	30	Neutral	12	150
			60, 90	Neutral	12	300
	Adults	Tablet	30	Neutral	12	300
			60, 90	Neutral	12	600
Phenobarbital	Children	Tablet	90	Neutral, PHT, VPA	12	60
	Adults	Tablet	90	Neutral, PHT, VPA	12	60
Topiramate	Children	Tablet	90	CBZ, Neutral, PB, PHT	12	100
	Adults	Tablet	90	CBZ, Neutral, PB, PHT	12	200
Valproic acid	Children	Tablet	90	CBZ, Neutral	12	250
	Children ^b	Syrup	90	CBZ, Neutral	12	200^b
	Adults	Tablet	90	CBZ, Neutral, PB, PHT	12	500
					24	500
Children: 10 years old with 30 kg and 140 cm;
Adults: 40 years old with 70 kg and 180 cm;
Neutral: concomitant with a noninduced or noninhibited AED or as a monotherapy;
^a 8 mL oral solution for children with 5 years old with 16 kg and 110 cm;
^b 5 mL syrup for children with 5 years old with 16 kg and 110 cm;

Previous studies showed renal functions could influence the PK of levetiracetam and oxcarbazepine.^{36, 37} Therefore, remedial regimens were investigated for patients on levetiracetam and oxcarbazepine regimens with altered renal function (eGFR of 30, 60, and 90 mL/min).

Additionally, when monotherapy is unsuccessful, combination with other AEDs is often necessary for anti-epilepsy treatment. Since the concomitant AEDs may be inducers or inhibitors, their effect was also investigated.

As the formulation of most AEDs is rapid release tablet, a half-dose is applicable as the minimum remedial dose unit besides a regular tablet. As for children taking oral suspension or syrup, a dose of 1 mL is applied as the minimum remedial dose unit. Moreover, different dosing intervals (12 h and 24 h) and various delayed dose scenarios were investigated, in which doses were delayed from 1 to 12 h or 1 to 24 h with the step of 1 h after the scheduled time according to the dosing interval.

Under each non-adherence scenario, 1000 virtual patients were simulated to depict the PK profiles of each AEDs. Moreover, all virtual patients were simulated to have been administered multiple doses of AEDs and reached a steady-state before they delay or miss the dose. Meanwhile, if the differences of total deviation time between two remedial regimens were less than 1 h, these two remedial regimens were assumed to be equivalent.

Web-based dashboard

To provide individual remedial regimens, a web-based dashboard was established using RxODE and Shiny (version 1.5.0) in R. The concentration-time curves of each remedial strategy could be plotted by ggplot2 (version 3.2.1). In addition, the detailed deviation time above and below the individual therapeutic range would be estimated for each remedial regimen to help the selection of the most appropriate one for the individual patients. Moreover, to apply the dashboard for various clinical settings, a user-defined module was also developed, in which all parameters could be defined flexibly by the user.

Population PK characteristics of AEDs

A total of 14 population PK models for nine AEDs were identified.^36–49 The enrolled patients ranged from 44 in the study of levetiracetam for children⁴⁸ to 902 in the study of valproic acid for children.⁴³ In all 14 population PK studies, 10 were prospective clinical studies.^{37, 39–41, 43, 44, 46–49} In addition, studies for carbamazepine, eslicarbazepine, levetiracetam, topiramate, and valproic acid were conducted in multi-centers,^{37, 39, 40, 43, 44, 47, 48} in which studies for eslicarbazepine and levetiracetam contained intensive sampling data.^{39, 47, 48}

For population PK models of AEDs described by a one-compartment model with first-order absorption and elimination, the concentration at time t (C_t; mg/L) could be estimated according to Eq. 1 (Eq. 1).

\({C}_{t}=\frac{{k}_{a}\bullet DOSE}{V/F\bullet ({k}_{a}-\frac{0.693}{{t}_{1/2}})}\bullet \left[\left(\frac{1-{e}^{-\frac{0.693}{{t}_{1/2}}\bullet n\bullet \tau }}{1-{e}^{-\frac{0.693}{{t}_{1/2}}\bullet \tau }}\bullet {e}^{-\frac{0.693}{{t}_{1/2}}\bullet t}\right)-(\frac{1-{e}^{-{k}_{a}\bullet n\bullet \tau }}{1-{e}^{-{k}_{a}\bullet \tau }}\bullet {e}^{{k}_{a}\bullet t})\right]\) (Eq. 1)

where DOSE (mg) represents the administered dose; \({k}_{a}\) (h^− 1) represents absorption rate constant; \(n\) represents the number of doses administered;\({t}_{1/2}\)(h) represents the half-life; t (h) represents the time after the last dose;\(V/F\) (L) represents the apparent volume of distribution, and τ (h) represents the dosing interval. The characteristics and parameter estimates of each identified model are summarized in Supplementary Table 1.

Remedial dosing regimens

The Monte Carlo simulation showed that the recommended remedial regimens were mostly dependent on the delayed time. For typical patients with normal renal function (eGFR of 90 mL/min) taking monotherapy of AEDs every 12 h (q12 h), the recommended remedial regimens for various delayed times are summarized in Table 2.

Table 2

The recommended remedial regimens for typical patients.
Patient type	AEDs	Dosage (mg)	Delayed time (h)
Patient type	AEDs	Dosage (mg)	1	2	3	4	5	6	7	8	9	10	11	12
Children	CBZ	100	100(B)	100(B)	100(B)	100(B)	100(B) 50(D)	50(D)	50(D)	50(D)	50(D) 150(E/F)	50(C/D) 150(E/F)	50(C/D) 150(E/F)	150(F)
Adults	CBZ	400	400(B)	400(B)	400(B) 200(C)	200(C/D)	200(C)	200(C)	200(C)	200(C/D)	200(C/D)	200(C/D)	200(D) 600(E)	600(F)
Children	CLB	5	2.5(C/D)	2.5(D)	2.5(D)	2.5(D)	2.5(D)	2.5(D) 7.5(F)	2.5(D) 7.5(F)	2.5(D) 7.5(F)	2.5(C/D) 7.5(F)	2.5(C/D) 7.5(E/F)	2.5(C/D) 7.5(E/F)	7.5(F)
Adults	CLB	10	5(C/D)	5(C/D)	5(C/D)	5(D)	5(D)	5(D) 15(F)	5(D) 15(F)	5(D) 15(F)	5(C/D) 15(E/F)	5(C/D) 15(E/F)	5(C/D) 15(E/F)	15(F)
Children	LTG	50	50(B)	50 (B)	50 (B) 25(C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D) 75(E)	25 (C/D) 75(E/F)	75 (F)
Adults	LTG	100	100(B)	100(B)	100(B) 50(D)	100(B) 50(C/D)	50(D)	50(D)	50(D)	50(D) 150(F)	50(D) 150(E/F)	50(C/D) 150(E/F)	50(C/D) 150(E/F)	150(F)
Children	LEV	250	250(B)	250(B) 125(C)	250(B) 125(C)	125(C)	125(C)	125(C)	125(C)	125(C/D)	125(D)	125(D)	125(D) 375(E)	375(F)
Adults	LEV	500	500(B) 250(C)	250(C/D)	250(C)	250(C)	250(C)	250(C)	250(C)	250(C/D)	250(C/D)	250(C/D) 750(E)	250(C/D) 750(E/F)	750(F)
Children	OXC	300	300(B)	300(B) 150(C/D)	150(C/D)	150(C/D)	150(C/D)	150(C)	150(C)	150(C/D)	150(C/D)	150(D)	150(D) 450(E)	450(F)
Adults	OXC	600	600(B)	600(B) 300(D)	300(D)	300(D)	300(D)	300(D)	300(D) 900(F)	300(D) 900(F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	900(F)
Children	PB	60	60(B)	60(B)	60(B) 30(D)	60(B) 30(D)	60(B) 30(D)	30(D)	30(D)	30(D) 90(E)	30(D) 90(E)	30(C/D) 90(E/F)	30(C/D) 90(E/F)	90(F)
Adults	PB	60	60(B)	60(B)	60(B)	60(B)	60(B)	60(B)	60(B) 30(D)	60(B) 30(D)	30(D) 90(F)	30(C/D) 90(E/F)	30(C/D) 90(E/F)	90(F)
Table 2 (continue)
Patient type	AEDs	Dosage (mg)	Delayed time (h)
Patient type	AEDs	Dosage (mg)	1	2	3	4	5	6	7	8	9	10	11	12
Children	TPM	100	100(B)	100(B) 50(C/D)	50(C/D)	50(C)	50(C)	50(C)	50(C/D)	50(D)	50(D)	100(A)	100(A)	100(A)
Adults	TPM	200	200(B) 100(C/D)	100(C/D)	100(C/D)	100(C/D)	100(C)	100(C/D)	100(C/D)	100(D)	100(D)	100(D) 300(E)	100(A)	100(A)
Children	VPA	250	250(B)	250(B)	250(B) 125(C/D)	250(B) 125(C/D)	125(C/D)	125(C)	125(C)	125(C)	125(C/D)	125(C/D) 375(E)	125(C/D) 375(E)	375(F)
	VPA	200^a	200(B) 160(C/D)	160(C/D)	160(C/D)	120(C) 160(C/D)	120(C) 160(D)	120(C) 160(D)	120(C/D)	80(C) 120(C/D)	80(C) 120(C/D)	80(C/D) 120(D)	80(C/D) 280(E/F)	240(F) 280(F)
Adults	VPA	500	500(B)	500(B)	500(B)	500(B)	250(C/D) 500(B)	250(C/D)	250(C/D) 750(F)	250(C/D) 750(F)	250(D) 750(F)	250(C/D) 750(E/F)	250(C/D) 750(E/F)	750(F)
CBZ carbamazepine; CLB clobazam; LTG lamotrigine; LEV levetiracetam; OXC oxcarbazepine; PB phenobarbital; TPM topiramate; VPA valproate acid;
Children 10 years, 30 kg, 140 cm, 90 ml/min;
Adults 40 years, 70 kg, 180 cm, 90 ml/min;
^a Syrup of 5 mL for children with 5 years old with 16 kg and 110 cm;

When the dose was delayed within 2 h, the whole delayed dose was recommended to be taken immediately, followed by resuming the regular regimens (Strategy B) for most AEDs except clobazam. For patients taking clobazam, they were recommended to take half of the missed dose immediately and resume the regular regimens (Strategy C) or to take the missed dose immediately and half of the missed dose at the next scheduled time (Strategy D) even if the dose was delayed within 2 h. For adults taking levetiracetam or topiramate, Strategy B was only recommended when the dose was delayed within 1 h. Moreover, for children taking oxcarbazepine or topiramate, all Strategies B, C, and D were recommended when the dose was delayed within 2 h.

When the delay time was more than 2 h and up to 2 h to the next scheduled time, patients were recommended to take Strategy C or D, depending on the AEDs and patient’s demographics. For example, when the delayed time was 4 h, Strategy C was recommended for adults taking levetiracetam, while Strategy D was recommended for adults taking oxcarbazepine, and both Strategy C and D were recommended for children taking oxcarbazepine.

When the dose was delayed within 2 h to the next dose, one-and-a-half of the missed doses were recommended to be taken immediately (Strategy E) for most AEDs. Especially, when the dose was missed (delayed 12 h for q12 h dosing), one-and-a-half of the missed doses were recommended to be taken at the scheduled time (Strategy F). Except for topiramate, when the dose was missed (delayed 12 h for q12 h dosing), taking only the scheduled dose (Strategy A) was recommended.

For children taking valproate acid syrup, the minimum remedial dose unit was smaller. Therefore, the recommended remedial regimens could be more precisely restored to the individual therapeutic range. When the dose was delayed within 4 h, either Strategy C or D with a remedial dose of 160 mg (4 mL of syrup) was recommended. When the dose was missed (delayed 12 h for q12 h dosing), Strategy F with a remedial dose of either 240 mg (6 mL of syrup) or 280 mg (7 mL of syrup) was recommended.

Impact of patient’s demographics, concomitant medication, and scheduled dosing regimen

For most AEDs, the recommended remedial regimens for pediatric (10 years old, 30 kg and 140 cm) and adult (40 years old, 70 kg and 180 cm) patients were different. For example, regarding topiramate, when the dose was delayed within 2 h, Strategy B was recommended for children while only Strategy C or D was recommended for adults.

Renal function only influences the CL/F of levetiracetam and oxcarbazepine, and the impact on remedial regimens was not the same for those two AEDs. For adults taking levetiracetam, the same remedial regimens were recommended for those with eGFR values between 30 and 60 mL/min. As for adults taking oxcarbazepine, the remedial regimens were the same for these with eGFR values between 60 and 90 mL/min. The recommended remedial regimens for adults with various eGFR levels taking levetiracetam or oxcarbazepine are summarized in Table 3.

Table 3

The recommended remedial regimens for adults with different renal function levels.
AEDs	Dosage (mg)	eGFR (ml/min)	Delayed time (h)
AEDs	Dosage (mg)	eGFR (ml/min)	1	2	3	4	5	6	7	8	9	10	11	12
LEV	500	90	500(B) 250(C)	250(C/D)	250(C)	250(C)	250(C)	250(C)	250(C)	250(C/D)	250(C/D)	250(C/D) 750(E)	250(C/D) 750(E/F)	750(F)
	500	60	500(B)	500(B)	500(B) 250(C/D)	250(C)	250(C)	250(C)	250(C)	250(C)	250(C/D)	250(C/D) 750(E)	250(C/D) 750(E/F)	750(F)
	500	30	500(B)	500(B)	500(B) 250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D) 750(E)	250(C/D) 750(E/F)	750(F)
OXC	600	90	600(B)	600(B) 300(D)	300(D)	300(D)	300(D)	300(D)	300(D) 900(F)	300(D) 900(F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	900(F)
	600	60	600(B)	600(B) 300(D)	300(D)	300(D)	300(D)	300(D)	300(D) 900(F)	300(D) 900(E/F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	300(C/D) 900(E/F)	900(F)
	300	30	150(D)	150(D)	150(D)	150(D)	150(D)	150(D)	150(D) 450(E)	150(D) 450(E)	150(D) 450(E)	150(C/D) 450(E)	150(C/D) 450(E)	450(F)
LEV levetiracetam; OXC oxcarbazepine;

For patients taking AEDs concomitant with inducers such as carbamazepine, phenobarbital, and phenytoin, the recommended remedial strategies were similar to those with monotherapy or with neutral comedications. For children taking lamotrigine and inducers simultaneously, half of the delayed dose was recommended if the dose was delayed between 2 to 3 h, while the whole delayed dose was recommended for those with monotherapy. Moreover, for children taking lamotrigine concomitant with inhibitors such as valproic acid, the whole delayed dose was recommended even the dose was delayed within 5 h. The recommended remedial regimens for patients with various concomitant medications are summarized in Table 4.

Table 4

The recommended remedial regimens for typical adults with different concomitant medications.
Patient type	AEDs	Dosage (mg)	Co-Med	Delayed time (h)
Patient type	AEDs	Dosage (mg)	Co-Med	1	2	3	4	5	6	7	8	9	10	11	12
Children	LTG	50	/	50(B)	50 (B)	50 (B) 25(C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D)	25 (C/D) 75(E)	25 (C/D) 75(E/F)	75 (F)
			IND	50 (B) 25(C)	25(C)	25(C)	25(C)	25(C)	25(C)	25(C)	25 (C/D)	25 (C/D)	25 (D) 75(E)	25 (D) 75(E)	75 (F)
			INH	50(B)	50 (B)	50 (B)	50 (B)	50(B) 25 (D)	25 (D)	25 (D)	25 (D) 75(F)	25 (D) 75(E/F)	25 (C/D) 75(E/F)	25 (C/D) 75(E/F)	75 (F)
Adults	LTG	100	/	100(B)	100(B)	100(B) 50(D)	100(B) 50(C/D)	50(D)	50(D)	50(D)	50(D) 150(F)	50(D) 150(E/F)	50(C/D) 150(E/F)	50(C/D) 150(E/F)	150(F)
	LTG		IND	100(B)	100(B)	100(B) 50(D)	50(C/D)	50(C)	50(C)	50(C)	50(C)	50(C/D)	50(C/D) 150(E)	50(C/D) 150(E/F)	150(F)
			INH	50(D)	50(D)	50(D)	50(D)	50(D)	50(D)	50(D)	50(D)	50(D) 150(F)	50(D) 150(E/F)	50(C/D) 150(E/F)	150(F)
Children	TPM	100	/	100(B)	100(B) 50(C/D)	50(C/D)	50(C)	50(C)	50(C)	50(C/D)	50(D)	50(D)	100(A)	100(A)	100(A)
			IND	100(B)	100(B) 50(C/D)	50(C/D)	50(C)	50(C)	50(C)	50(C)	50(D)	50(D)	100(A)	100(A)	100(A)
			VPA	100(B) 50(C/D)	50(C/D)	50(C)	50(C)	50(C)	50(C)	50(C/D)	50(D)	50(D)	100(A)	100(A)	100(A)
Adults	TPM	200	/	200(B) 100(C/D)	100(C/D)	100(C/D)	100(C/D)	100(C)	100(C/D)	100(C/D)	100(D)	100(D)	100(D) 300(E)	200(A)	200(A)
	TPM	200	IND	200(B) 100(C/D)	100(C/D)	100(C/D)	100(C/D)	100(C)	100(C/D)	100(C/D)	100(D)	100(D)	100(D) 300(E)	200(A)	200(A)
			VPA	200(B) 100(C/D)	100(C/D)	100(C/D)	100(C/D)	100(C)	100(C/D)	100(D)	100(D)	100(D)	100(D)	300(E)	200(A)
Table 4 (continue)
Patient type	AEDs	Dosage (mg)	Co-Med	Delayed time (h)
Patient type	AEDs	Dosage (mg)	Co-Med	1	2	3	4	5	6	7	8	9	10	11	12
Children	VPA	500	/	250(B)	250(B)	250(B) 125(C/D)	250(B) 125(C/D)	125(C/D)	125(C)	125(C)	125(C)	125(C/D)	125(C/D) 375(E)	125(C/D) 375(E)	375(F)
			CBZ	250(B)	250(B) 125(C)	250(B) 125(C)	125(C)	125(C)	125(C)	125(C)	125(C)	125(C/D)	125(C/D)	125(C/D) 375(E)	375(F)
Adults	VPA	500	/	500(B)	500(B)	500(B)	500(B)	250(C/D) 500(B)	250(C/D)	250(C/D) 750(F)	250(C/D) 750(F)	250(D) 750(F)	250(C/D) 750(E/F)	250(C/D) 750(E/F)	750(F)
			CBZ	500(B)	500(B)	500(B) 250(C)	500(B) 250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D) 750(F)	250(C/D) 750(E/F)	750(F)
			PHT	500(B)	500(B)	500(B)	500(B) 250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D) 750(E)	250(C/D) 750(E/F)	750(F)
			PB	500(B)	500(B)	500(B)	500(B) 250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D)	250(C/D) 750(F)	250(C/D) 750(E/F)	250(C/D) 750(E/F)	750(F)
CBZ carbamazepine; IND enzyme inducer like carbamazepine; INH enzyme inhibitor like valproate acid; LTG lamotrigine; PB phenobarbital; PHT phenytoin; TPM topiramate; VPA valproate acid;
Supplementary materials

The remedial regimens were also dependent on the dosing interval. For example, one-and-a-half of missed valproic acid doses were recommended to be taken immediately (Strategy F) when it was within 5 h to the next dose for q12 h and within 3 h for q24 h. The remedial regimens for dosing intervals of 24 h are summarized in Supplementary Table 2.

Web-based dashboard

The web-based dashboard for individual remedial regimens could be visited at https://make-up-dose.shinyapps.io/shinyapp/. After inputting the patient’s demographics, regular dosing regimens, concomitant medication, minimum remedial dose unit, and delayed time, the individual therapeutic range could be estimated within a few seconds. Meanwhile, the deviation time for all six remedial strategies was displayed and the optimal remedial regimens would be recommended.

The screenshots of this dashboard are present in Fig. 3, which indicated the example of a 10-year-old pediatric patient weighing 30 kg and having an eGFR of 90 mL/min, who was taking 300 mg oxcarbazepine monotherapy q12 h (Fig. 3a). Two scenarios including a delayed dose of 2 and 11 h were investigated in this example. The oxcarbazepine is usually used as the immediate-release tablet, which can be taken by splitting half. Therefore, the minimum dose unit for providing remedial regimens was assumed to be half of the tablet (150 mg).

When the dose was delayed within 2 h, the Strategy B (administer 300 mg immediately followed by 300 mg at the next scheduled time) showed a total deviation time of 6.9 h (4.9 h above the upper limit + 2.0 h below the lower limit), Strategy C (administer 150 mg immediately followed by 300 mg at the next scheduled time) showed a similar total deviation time of 6.6 h (0 h above the upper limit + 6.6 h below the lower limit), and Strategy D (administer 300 mg immediately followed by 150 mg at the next scheduled time) showed the total deviation time of 7.2 h (7.2 h below the lower limit + 0 h above the upper limit) as indicated in Fig. 3b. The proposed PK profiles of all six remedial strategies with deviation time are shown in Fig. 3c.

For patients with a high risk of epilepsy recurrence, Strategy B with the lowest deviation time below the lower limit was preferred, while for patients with low tolerance of adverse drug reactions, Strategy C or D with less deviation time above the upper limit could be more appropriate.

When the dose was delayed by 11 h, the total deviation time was 11.9 h (11.4 h below the lower limit + 0.5 h above the upper limit) for Strategy D and 12.6 h (11.2 h below the lower limit + 1.4 h above the upper limit) for Strategy E (administer 450 mg immediately and skip the next scheduled time).

Therefore, in such a scenario, both Strategy D and E were recommended. Moreover, since strategy E recommended taking a large dose immediately, it could rapidly restore to the therapeutic range, which is more proper for patients who have a high risk of seizure recurrence.

The user-defined module is also provided in the dashboard, which could be visited at https://make-up-dose-user-defined.shinyapps.io/shinyapp2/. In the user-defined module, all PK parameters (absorption rate, apparent clearance, and apparent volume of distribution) and the individual therapeutic window (upper and lower limit as well as the weight for estimation of the total deviation time) could be modified according to the clinical setting.

Figure 4a showed a specific pediatric patient taking an AED, who had an absorption rate constant of 0.83 h^− 1, clearance of 2.5 L/h, and distribution volume of 14.7 L. Moreover, the therapeutic window was set as 3–20 mg/L. When the dose was delayed by 2 h, only Strategy B with a total deviation time of 1.9 h (0 h above the upper limit + 1.9 h below the lower limit) was recommended as shown in Fig. 4b. The deviation time and concentration-time curves of all remedial strategies are present in Fig. 4c.

This study aimed to comprehensively provide individualized remedial regimens for delayed or missed doses of commonly used AEDs. The influences of patients’ demographics, concomitant medication, and scheduled dosing regimens on remedial regimens were investigated. Moreover, a web-based dashboard was established to facilitate optimal remedial regimens for the individual patient.

There is a clear relationship between exposure and response for the AEDs.^{27, 50} Therefore, the FDA and EMA have recommended and approved the dosing regimens of AEDs in children extrapolated from adults by pharmacokinetic (PK) modeling and simulation approach without the confirmatory clinical trials.⁵¹ In this study, the same approach of modeling and simulation was employed to reliably provide individualized remedial regimens.

For patients with epilepsy, because of the high inter-individual variability in the PK characteristics of AEDs, the therapeutic window can differ remarkably from patient to patient. Therefore, the individual therapeutic range was recommended by the International League against Epilepsy as the range associated with the optimal response in a particular patient,^{27, 50} which was adopted in this study instead of a fixed reference range.

The optimal remedial dosing strategy for non-adherence scenarios was dependent on the half-life of the AEDs in the individual patient. This is consistent with the findings by Counterman et al.⁵² using a theoretical mathematical approach. This could explain the large differences in remedial regiments between adults and pediatric patients since the children showed higher clearance per weight and lower half-life than adult patients.^36–49 It could also be attributed to the difference in remedial regimens for patients with renal impairment or concomitant medications compared to those with normal renal function or monotherapy because both renal function and concomitant medications have significant impacts on the half-life of some AEDs.^{37, 40, 43, 45}

This study systematically examined six remedial strategies for the delayed or missed dose. Among them, Strategy B was often recommended in delayed time less than 2 h. Strategy C or D was often recommended when the delayed time was more than 2 h and up to 2 h to the next scheduled time. Moreover, when the dose was delayed within 2 h to the next dose, Strategy E or F was often recommended. This conclusion is consistent with the previous studies for carbamazepine,²² valproic acid,²³ and lamotrigine.²⁴

Among all six strategies, Strategy B usually had deviation time both above the upper and below the lower limit of the individual therapeutic range, while Strategy C or D usually had deviation time only below the lower limit. Therefore, although their total deviation time is close, for patients with a high risk of epilepsy recurrence, Strategy B with lower deviation time below the lower limit of the individual therapeutic range is more appropriate. In contrast, patients with a lower tolerance for high concentrations of AEDs should choose the strategies with lower deviation time above the upper limit of the individual therapeutic range (Strategy C or D).

Meanwhile, compared to Strategy C, Strategy D or E could rapidly return the concentration to the therapeutic range. Therefore, for patients who have high seizure frequency, when the total deviation time of Strategy C, D, and E are similar, Strategy D or E may be more appropriate. In the established dashboard, when it is necessary to select optimal remedial regimens according to the patient’s medical records, both the deviation time higher than the upper limit and deviation time lower than the lower limit of the individual therapeutic range could be provided.

In addition, in the user-defined module of the web-based dashboard, the individual PK parameters could be defined by the user according to the Bayesian forecasting with or without therapeutic drug monitoring. Moreover, the upper and lower limit of individual therapeutic range along with their weight for estimation of total deviation time could also be adjusted to compensate the drug forgiveness or other requirements in the clinical settings. By altering the parameters when necessary, this dashboard could provide more precise remedial regimens for the individual patient in specific situations.

This study still has several limitations. First, only immediate-release tablets, oral suspensions, and syrup formulations were investigated in this study. The extended-release formulations were not assessed due to the lack of population PK studies on these formulations. Secondly, only remedial regimens for single delayed or missed doses were established in this study. In real life, the non-adherence patterns may be complex and present with a combination of multiple delayed and missed doses. If the nonadherence patterns of AEDs could be captured by Medication Event Monitoring System (MEMS), more appropriate remedial strategies for dynamic non-adherence patterns may be developed through modeling and simulation approach.^53–55

Individual remedial regimens for the delayed or missed AEDs dose should be recommended based on the AEDs, patient’s demographics, concomitant medication, scheduled dosing interval, and the delayed time. A web-based remedial regimen dashboard using a population PK-based Monte Carlo simulation approach has been developed to provide individual remedial regimens for commonly used AEDs.

Acknowledgements

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Study funding

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Competing interests: The authors declare no competing interests.

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TableS1.formular0329.docx
Table S1. The characteristics and final parameter estimate of each identified model.
TableS2.q24h0329.docx
Table S2. The remedial regimens for dosing interval of 24 h.

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Handling Delayed or Missed Dose of Antiepileptic Drugs: A Model-Informed Individual Remedial Dosing

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Introduction

Methods

Rationale

Remedial dosing regimen

Population PK characteristics of AEDs

Remedial dosing regimen design

Impact of patients’ demographics, concomitant medication, and scheduled dosing interval

Web-based dashboard

Results

Population PK characteristics of AEDs

Remedial dosing regimens

Impact of patient’s demographics, concomitant medication, and scheduled dosing regimen

Web-based dashboard

Discussion

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References

Supplementary Files

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