Evaluation and optimization of sample size of neonates and infants for pediatric clinical studies on cefiderocol using a model‐based approach

Abstract

When planning pediatric clinical trials, optimizing the sample size of neonates/infants is essential because it is difficult to enroll these subjects. In this simulation study, we evaluated the sample size of neonates/infants using a model‐based optimal approach for identifying their pharmacokinetics for cefiderocol. We assessed the usefulness of data for estimation performance (accuracy and variance of parameter estimation) from adults and the impact of data from very young subjects, including preterm neonates. Stochastic simulation and estimation were utilized to assess the impact of sample size allocation for age categories in estimation performance for population pharmacokinetic parameters in pediatrics. The inclusion of adult pharmacokinetic information improved the estimation performance of population pharmacokinetic parameters as the coefficient of variation (CV) range of parameter estimation decreased from 4.9%–593.7% to 2.3%–17.3%. When sample size allocation was based on the age groups of gestational age and postnatal age, the data showed 15 neonates/infants would be necessary to appropriately estimate pediatric pharmacokinetic parameters (<20%CV). By using the postmenstrual age (PMA), which is theoretically considered to be associated with the maturation of organs, the number of neonates/infants required for appropriate parameter estimation could be reduced to seven (one and six with <32 and >32 weeks PMA, respectively) to nine (three and six with <37 and >37 weeks PMA, respectively) subjects. The model‐based optimal design approach allowed efficient evaluation of the sample size of neonates/infants for estimation of pediatric pharmacokinetic parameters. This approach to assessment should be useful when designing pediatric clinical trials, especially those including young children.

Abbreviations

BSV

between‐subject variability

CL

total clearance

cUTI

complicated urinary tract infections

CV

coefficient variation

GA

gestational age

HILL

steepness of maturation for total clearance

PK

pharmacokinetic

PMA

postmenstrual age

PNA

postnatal age

Q

inter‐compartmental clearance

RUV

residual unidentified variability

SSE

stochastic simulation and estimation

1. INTRODUCTION

Cefiderocol (S‐649266), a new parenteral siderophore cephalosporin, was discovered and developed by Shionogi & Co., Ltd. It has shown strong activity in vivo and in vitro against various carbapenem‐susceptible and carbapenem‐resistant Gram‐negative bacteria: Enterobacterales, Acinetobacter baumannii, Pseudomonas aeruginosa, and Stenotrophomonas maltophilia. ¹ , ² , ³ , ⁴ , ⁵ Cefiderocol was approved as Fetroja® in the United States for patients 18 years of age or older for treatment of complicated urinary tract infections (cUTI) including pyelonephritis, and hospital‐acquired bacterial pneumonia and ventilator‐associated bacterial pneumonia caused by susceptible Gram‐negative microorganisms. ⁶ It was also approved as Fetcroja® by the European Medicines Agency for the treatment of infections due to aerobic Gram‐negative organisms in adult patients with limited treatment options. ⁷ A 2‐g infusion of cefiderocol over 3 h every 8 h is recommended for adult patients with creatinine clearance (CrCL), calculated by the Cockcroft‐Gault Equation, ⁸ of 60 to <120 mL/min. It is adjusted for patients with CrCL of less than 60 mL/min or for patients with CrCL of 120 mL/min or greater, because cefiderocol is primarily excreted unchanged via the kidneys and the total clearance (CL) is dependent on renal function. ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ The population pharmacokinetic (PK) analysis of cefiderocol for adults was performed based on concentration data in healthy subjects, subjects with varying renal functions, and patients with cUTI, acute uncomplicated pyelonephritis, pneumonia, or bloodstream infection/sepsis. ⁹

The carbapenem‐resistant bacteria against which cefiderocol is effective are listed in the global priority list of antibiotic‐resistant bacteria to guide research, discovery, and development of new antibiotics by the World Health Organization, and expanded indications of cefiderocol for not only adults but also pediatric patients are urgently needed. ¹⁴ , ¹⁵ Two Phase 2 clinical trials are ongoing to assess the safety, tolerability, and PK of cefiderocol for pediatric patients 3 months to <18 years of age (https://www.clinicaltrials.gov identifier NCT04335539 and NCT04215991), and a clinical trial for neonates and infants (under 3 months old) is planned.

The accuracy and variance of parameter estimation (estimation performance) of PK parameters in population PK analysis usually depends on the sample size, and it has been reported that precision improves as the sample size increases. ¹⁶ Furthermore, sample size and the number of PK sampling points per subject are influential factors in optimizing the clinical trial design for pediatric subjects according to various simulation studies using model‐based approaches for the estimation of PK parameters. ¹⁷ , ¹⁸ , ¹⁹ In these studies, optimal sampling points or the number of samples per subject were evaluated to identify PK or pharmacodynamic profiles of drugs. There are few studies for optimization of the sample size considering age categories in detail to evaluate PK profiles in pediatric subjects. Since the PK of pediatric subjects could change dramatically depending on their growth, it is important to enroll a sufficient number of subjects in each age category in order to understand their PK profiles. However, in practice, it is difficult to enroll young subjects in clinical trials, especially preterm neonates. In addition, it could be a challenge to perform rich PK sampling in pediatric clinical trials since the number of blood samples is limited in special populations such as pediatric patients.

In this study, the efficient sample size of neonates and infants was evaluated for pediatric studies for identifying their PK of cefiderocol through population PK analysis with consideration of the maturation of renal function. In addition, the usefulness of data from adult subjects was assessed for pediatric PK parameter estimation. We also evaluated the impact of data from young children including preterm neonates on estimation performance, with consideration of the efficient sample size allocation in each age category.

2. MATERIALS AND METHODS

2.1. Pharmacokinetic model

The pediatric PK model of cefiderocol ²⁰ was used for this simulation study. This model was developed using the reported adult PK model ⁹ and adding allometric scaling for pediatrics. CL, V1, Q, and V2 were scaled using the reported scaling approach ²¹ in which allometric exponents were estimated based on data from parenteral β‐lactam antibiotics including cefiderocol. In this pediatric PK model, body weight and renal function which had a clinically meaningful effect on PK profiles of cefiderocol were included, and the other covariates (infection site and albumin concentration) were not considered because their impacts would be small to PK parameters based on population PK analyses for cefiderocol. ⁹ The PK model was a two‐compartment model with pediatric PK parameters, which were scaled from adult PK parameters using allometric relationships reported for parenteral β‐lactam antibiotics ²¹ with the maturation factor of renal function incorporated into the CL for neonates and infants, ²² as shown in Equations ((1), (2), (3), (4)):

$$\mathrm{CL}=0.508\times {\mathrm{BW}}^{0.578}\times \frac{{\mathrm{PMA}}^{\text{HILL}}}{{\mathrm{PMA}}^{\text{HILL}}+\mathrm{TM}{50}^{\text{HILL}}}$$ (1)

$$\mathrm{V}1=0.460\times {\mathrm{BW}}^{0.677}$$ (2)

$$Q=0.495\times {\mathrm{BW}}^{0.578}$$ (3)

$$\mathrm{V}2=0.318\times {\mathrm{BW}}^{0.677}$$ (4)

where CL is total clearance (L/h), BW is body weight (kg); PMA is postmenstrual age (week); TM50 is maturation half‐time for CL; HILL is the steepness of maturation for CL; V1 and V2 are volumes of distribution in central and peripheral compartments (L), respectively; and Q is inter‐compartmental clearance (L/h). Between‐subject variability (BSV) for CL, V1, and V2 was assumed to be log‐normal distributed with a coefficient variation (CV) of 20%. In this model, the maturation parameters were set to the reported values calculated based on the maturation of the glomerular filtration rate (TM50 and HILL were 47.7 weeks and 3.4, respectively). ²³

2.2. Simulation

Stochastic simulation and estimation (SSE) were performed to evaluate the estimation performance of pediatric PK parameters in each trial design for the sample size allocations described below.

Virtual pediatric subjects were simulated according to the assumed trial design for sample size allocation based on gestational age (GA) and postnatal age (PNA). The GA and PNA were obtained to follow the uniform distribution within each age category. The ratio of females to males was assumed to be 1:1, and their body weights were simulated from age using reported relationships between body weight and age. ²⁴ , ²⁵

Plasma cefiderocol concentrations after single‐dose administration of cefiderocol with 3‐h infusion were simulated based on the pediatric PK model (Equations (1), (2), (3), (4)) as a true model and 300 simulated datasets were obtained. The dosage of cefiderocol was adjusted based on PNA, GA, and body weight as shown in Table S1, which would provides comparable drug exposure and was consistent with the dosing regimen used in the ongoing pediatric clinical trials.

The population PK parameters for each simulated dataset were estimated using the first‐order conditional estimation with interactions (FOCE‐I) method and mean, standard deviation, and CV values of PK parameters were calculated for 300 estimations. The predictive performance in each design was assessed by the calculated CV values (standard deviation/mean) for all PK parameters.

2.3. Trial designs for sample size allocation

The trial designs for sample size allocation tested in this simulation study (Designs #1 to #11) were based on consideration of the feasibility of enrollment and the balance of sample size allocation in each age category (Table 1). Age categories were assumed to be five neonate groups (Groups 1–5), one infant group (Group 6), one toddler group (Group 7), two children groups (Groups 8 and 9), and one adolescent group (Group 10) depending on PNA and GA. The observed plasma concentration data for 516 adult subjects (healthy subjects and patients) collected from five clinical studies were assigned as Group 11. ⁹ It was assumed that blood samples for measuring plasma cefiderocol concentrations were collected at 3, 5, and 8 h after the start of infusion for Groups 1–8, and at 1, 3, 3.5, 5, and 8 h for Groups 9 and 10, considering the feasibility of their PK blood sampling. This blood sampling schedule was determined for two ongoing Phase 2 clinical trials for pediatric patients 3 months to <18 years of age (NCT04335539 and NCT04215991) and the planned clinical trial for neonates and infants (under 3 months old) based on D‐optimality with the determinant of Fisher information matrix approach including the peak and trough sampling points. ²⁶ The simulated plasma cefiderocol concentrations at each sampling time after the administration of cefiderocol by 3‐h infusion based on 300 simulations for Design #1 are shown in Figure S1. For subjects aged 3 months to <18 years (Groups 7–10), it was assumed that six subjects would be available for each group as it is relatively easier to enroll such subjects than for the younger groups.

TABLE 1.

Summary of tested designs.

Group		1	2	3	4	5	6	7	8	9	10	11
Category		Neonates (PMA <44 weeks)					Infants	Toddlers	Children		Adolescents	Adults
PNA		0 to <14 days	≧14 days	0 to <14 days	≧14 days	0 to <28 days	28 days to <3 months	3 months to <2 years	2 to <6 years	6 to <12 years	12 to <18 years	18 to <93 years
GA (weeks)		26 to <32	26 to <32	32 to <37	32 to <37	≧37	26 to <44	40	40	40	40	–
PMA (weeks)		26 to <34	28 to <36	32 to <39	34 to <41	37 to <44	30 to <56	–	–	–	–	–
Number of subjects for each group
Design	#1	3	3	3	3	3	3	6	6	6	6	0
	#2, #3	3	3	3	3	3	3	6	6	6	6	516
	#4	3	0				15	6	6	6	6	516
	#5	3	0				15 a	6	6	6	6	516
	#6	3	15					6	6	6	6	516
	#7	0	15					6	6	6	6	516
	#8	18						6	6	6	6	516
	#9	15						6	6	6	6	516
	#10	12						6	6	6	6	516
	#11	9						6	6	6	6	516

Note: Plasma cefiderocol concentrations were measured at 3, 5, and 8 h after the start of infusion in Groups 1 to 8, and at t 1, 3, 3.5. 5, and 8 h in Groups 9 and 10.

Abbreviations: GA, gestational age; PMA, postmenstrual age; PNA, postnatal age.

^a All subjects in this group were fixed at 40 weeks GA.

First, Design #1, which did not include the observed PK data for adults (Group 11), was compared with Design #2, which included Group 11, to evaluate the usefulness of adult data for the estimation of pediatric PK parameters. Second, Design #3, assuming different allometric relationships between adults and pediatrics, was used to assess whether the difference could be detected with population PK analysis. In Design #3, the allometric relationships were assumed separately for adults and pediatrics using the piecewise allometric relationship model with exponents of 0.578 for CL and Q and 0.677 for V1 and V2 for adults (based on empirical allometric scaling with observed adult data) and 0.75 for CL and Q and 1 for V1 and V2 for pediatrics (based on biological principles ²⁷ ). The virtual patients were simulated using the piecewise allometric relationship model, and the PK parameters were estimated with the piecewise allometric relationship model (the same structural model for the simulation) and the alternative model with common allometric relationships between adult and pediatric subjects. The piecewise and common allometric relationship models were compared and selected based on the difference in the objective function values (OFV), for which more than 5.99 is statistically significant at p < .05 with 2 degrees of freedom. The rate of the piecewise model selected (detection power) in the 300 simulations was calculated. Third, to evaluate the impact of the GA range in Group 6 for the estimation, Design #4, in which the GA of the subjects was randomly distributed according to the uniform distribution from 26 to 44 weeks in Group 6, was compared with Design #5, in which GA of all subjects in Group 6 was fixed at 40 weeks. Fourth, Designs #6 (three subjects in Group 1) and #7 (no subject in Group 1) were compared to evaluate the usefulness of data from Group 1 for estimating pediatric PK parameters. Finally, the impact of the total number of neonates and infants on the PK parameter estimation was evaluated for Designs #8 to #11, in which there were different total numbers of neonates and infants (a total of 9–18).

In Designs #1 to #11, PMA ranges of age groups (Groups 1–10) overlapped with each other as shown in Table 1. Therefore, the designs for allocating sample size based on PMA for neonates and infants, which is theoretically associated with maturation, were assessed based on Designs #12 to #21 as summarized in Table 2. There was no overlap for PMA among Groups A to F in these Designs. The PMA was also obtained to follow the uniform distribution within each PMA range.

TABLE 2.

Summary of tested designs based on postmenstrual age (PMA).

Group		A	B	C	D	E	F	G	H	I	J	K
Category		Neonates and infants						Toddlers	Children		Adolescents	Adults
PNA		–	–	–	–	–	–	3 months to <2 years	2 to <6 years	6 to <12 years	12 to <18 years	18 to <93 years
PMA (weeks)		26 to <32	32 to <37	37 to <42	42 to <47	47 to <52	52 to <57	– a	– a	– a	– a	–
Number of subjects for each group
Design	#12	3	3	3	3	3	3	6	6	6	6	516
	#13	0			18			6	6	6	6	516
	#14	3		9				6	6	6	6	516
	#15	3	9					6	6	6	6	516
	#16	3		6				6	6	6	6	516
	#17	3	6					6	6	6	6	516
	#18	2		6				6	6	6	6	516
	#19	1		6				6	6	6	6	516
	#20	1	6					6	6	6	6	516
	#21	0	6					6	6	6	6	516

Note: Plasma cefiderocol concentrations were measured at 3, 5, and 8 h after the start of infusion in Groups A to H, and at 1, 3, 3.5. 5, and 8 h in Groups I and J.

Abbreviations: PMA, postmenstrual age; PNA, postnatal age.

^a All subjects in this group were fixed at 40 weeks GA (gestational age).

2.4. Software

SSE was performed using NONMEM version 7.3.0 (ICON Development Solutions, Ellicott City, MD, USA), ²⁸ Perl‐speaks NONMEM (version 4.2.0), ²⁹ , ³⁰ and Pirana (version 2.9.4). ³⁰ R (version 3.5.1) ³¹ was used for graphical analysis.

3. RESULTS

The summary of all simulation results is shown in Table 3.

TABLE 3.

Summary of designs and stochastic simulation and estimation results.

Design	Assumption	CV range (%)	CV for HILL (%)	Comments on the results
#1	Not including the observed PK data for adults	4.9–593.7	28.3	PK data from adults was informative for pediatric PK parameter estimation
#2	Including the observed PK data for adults	2.3–17.3	16.6
#3	Evaluation for allometric relationships between pediatrics and adults	2.6–17.3	17.3/17.9	The difference between them could be detected
#4	GA was distributed from 26 to 44 weeks in Group 6 (PNA: 28 days to <3 months)	2.4–17.3	14.4	The variation of GA of infants did not affect the estimation of PK parameters
#5	GA of all subjects in Group 6 (PNA: 28 days to <3 months) was 40 weeks	2.5–17.3	14.8
#6	Including three subjects in Group 1 (PMA: 0 to <14 days, GA: 26 to <32 weeks)	2.6–17.9	17.0	The availability of data for Group 1 was not critical for pediatric PK parameter estimation
#7	No subject in Group 1 (PNA: 0 to <14 days, GA: 26 to <32 weeks)	2.6–18.7	18.7
#8	The total number of neonates and infants was 18 subjects	2.5–17.3	17.1	Pediatric PK parameters could be estimated appropriately with data from at least 15 neonates and infants
#9	The total number of neonates and infants was 15 subjects	2.6–18.7	18.7
#10	The total number of neonates and infants was 12 subjects	2.7–22.7	22.7
#11	The total number of neonates and infants was nine subjects	3.0–24.5	24.5
#12	Including nine subjects <42 weeks of PMA	2.4–17.3	14.2	Subjects <42 weeks of PMA would provide valuable information for parameter estimation
#13	Not including subject <42 weeks of PMA	2.6–31.4	31.4
#14	Total 12 neonates and infants including three subjects <37 weeks of PMA	2.7–17.9	17.0	Design #16 (total of nine neonates and infants including three subjects <37 weeks of PMA) or Design #20 (total of seven neonates and infants including one subject <32 weeks of PMA) would provide an appropriate estimation of pediatric PK parameters
#15	Total 12 neonates and infants including three subjects <32 weeks of PMA	2.7–17.9	15.6
#16	Total nine neonates and infants including three subjects <37 weeks of PMA	3.0–18.7	18.7
#17	Total nine neonates and infants including three subjects <32 weeks of PMA	3.0–17.4	17.0
#18	Total eight neonates and infants including two subjects <37 weeks of PMA	3.0–20.0	20.0
#19	Total seven neonates and infants including one subject <37 weeks of PMA	3.1–22.2	22.2
#20	Total seven neonates and infants including one subject <32 weeks of PMA	3.1–19.4	19.4
#21	Total of six neonates and infants and all subjects were more than 32 weeks of PMA	3.0–28.9	28.9

Abbreviations: CV, coefficient variation; GA, gestational age; HILL, steepness of maturation for total clearance (CL); PK, pharmacokinetic; PMA, postmenstrual age; PNA, postnatal age.

The usefulness of adult information for the estimation of pediatric PK parameters was evaluated by comparing Design #1 (without adult data) and Design #2 (with adult data). The median (range) values of CV for all parameter estimates in Design #1 and Design #2 were 30.6% (4.9%–593.7%) and 7.2% (2.3%–17.3%), respectively. In Design #1, CV values of some parameters were above 20% (especially 593.7% for BSV on V1 and 269.8% for BSV on V2), as shown in Table 4. The mean value of the estimated BSV on V1 (0.17) in Design #1 was different from the true value (0.040), while the mean values of estimated PK parameters in Design #2 were close to the true values, including BSV for V1. These results suggested that PK data from adults was informative for pediatric PK parameter estimation. The ability to detect a difference in allometric relationships between adults and pediatrics was assessed with Design #3. As shown in Table 5, when the true model with piecewise allometric relationships (the same structural model as simulation) was used for estimation, the mean values of the estimated parameters were similar to the true values and the CVs were lower than 20% for all pediatric PK parameters. The mean OFV difference from SSE 300 times between the piecewise model and the common model was −328 in Design #3, and the detection power to select the right model (the piecewise model) was 100%. The simulation results suggested that the different allometric relationships between adults and pediatrics could be detected in the course of population PK analysis if data from pediatrics and adults were sufficiently available, indicating that adult data would be useful even when allometric relationships were different between adults and pediatrics.

TABLE 4.

Results of stochastic simulation and estimation in Design #1 and #2.

Parameter	True Value	Design #1		Design #2
		Mean	CV (%)	Mean	CV (%)
CL (L/h)	0.508	0.555	29.6	0.526	11.3
V1 (L)	0.460	0.436	31.5	0.464	6.9
Q (L/h)	0.495	0.700	78.4	0.508	12.3
V2 (L)	0.318	0.388	61.1	0.319	7.1
Power on CL and Q	0.578	0.567	14.9	0.575	4.5
Power on V1 and V2	0.677	0.679	4.9	0.677	2.3
HILL	3.40	3.56	28.3	3.42	16.6
TM50 (week)	47.7	48.4	11.2	47.7	7.2
BSV_CL	0.040	0.036	33.4	0.040	7.1
BSV_V1	0.040	0.17	593.7	0.039	16.8
BSV_V2	0.040	0.057	269.8	0.037	17.3
RUVprop	0.040	0.039	17.6	0.040	3.2
Successful rate (%)		98.0		96.7

Abbreviations: BSV, between‐subject variability; CL, total clearance; CV, coefficient variation; HILL, steepness of maturation for CL; Q, inter‐compartmental clearance; RUV, residual unidentified variability; Successful rate, rate of minimization successful in population pharmacokinetic analyses using 300 simulated datasets; TM50, maturation half‐life for CL; V1, volume of distribution in central compartment; V2, volume of distribution in peripheral compartment.

TABLE 5.

Results of 300 times stochastic simulation and estimation in Design #3.

Parameter	True value	Model with piecewise allometric relationships (same as the simulation model)		Model with common allometric relationships between adults and pediatrics
		Mean	CV (%)	Mean	CV (%)
CL (L/h)	0.508	0.524	13.7	0.754	11.3
V1 (L)	0.460	0.464	7.9	0.752	8.1
Q (L/h)	0.495	0.506	14.6	0.725	12.5
V2 (L)	0.318	0.319	8.1	0.521	8.2
Power on CL and Q for pediatrics	0.750	0.753	5.9	0.495 a	5.3 a
Power on V1 and V2 for pediatrics	1.00	1.00	3.1	0.570 a	3.2 a
Power on CL and Q for adults	0.578	0.577	5.4	0.495 a	5.3 a
Power on V1 and V2 for adults	0.677	0.677	2.6	0.570 a	3.2 a
HILL	3.40	3.43	17.3	5.50	17.9
TM50 (week)	47.7	47.6	7.4	45.7	5.4
BSV_CL	0.040	0.040	7.1	0.042	7.2
BSV_V1	0.040	0.039	16.7	0.054	30.0
BSV_V2	0.040	0.037	17.3	0.045	22.6
RUVprop	0.040	0.040	3.1	0.043	3.6
Successful rate (%)		97.7		96.0

Abbreviations: BSV, between‐subject variability; CL, total clearance; CV, coefficient variation; HILL, steepness of maturation for CL; Q, inter‐compartmental clearance; RUV, residual unidentified variability; Successful rate, rate of minimization successful in population pharmacokinetic analyses using 300 simulated datasets; TM50, maturation half‐life for CL; V1, volume of distribution in central compartment; V2, volume of distribution in peripheral compartment.

^a Powers for CL/Q and V1/V2 were common between adults and pediatrics.

When comparing Design #4 (GA was randomly distributed in 26–44 weeks in Group 6) and Design #5 (GA for all subjects was fixed at 40 weeks in Group 6), all the mean values of estimated PK parameters were close to the true values in both models (Table S2) and the CV ranges of estimated PK parameters (Figure 1) were comparable between Design #4 and Design #5. This suggested that the variation of GA of infants did not affect the estimation of PK parameters. When comparing Design #6 (three subjects in Group 1) and Design #7 (no subject in Group 1), all the mean values of estimated PK parameters were close to the true values in both models (Table S2) and the CVs of estimated PK parameters (Figure 1) were lower than 20%. These simulations suggested that the availability of data for the youngest group (Group 1) was not critical for pediatric PK parameter estimation. This is probably because subjects with low PMA could be included in Group 2 in this simulation study as PMA ranges overlapped each other between Group 1 and Group 2. When comparing Designs #8 to #11 with different numbers of subjects of neonates and infants, all the mean values of estimated PK parameters were close to the true values in all the models (Table S2) and the CVs of estimated PK parameters (Figure 1) were lower than 20% except for HILL. The CV values for HILL were dependent of the number of neonates and infants, as shown in Table 3. The simulation results for Designs #4 to #11 suggested that pediatric PK parameters of cefiderocol could be estimated appropriately with data from at least 15 neonates and infants with PNA and GA randomly distributed if sufficient data were available from pediatrics aged 3 months or more and adult subjects.

FIGURE 1.

CV values of pediatric pharmacokinetic parameters obtained from stochastic simulation and estimation in Design #4 to #21. BSV, between‐subject variability; CL, total clearance; CV, coefficient variation; HILL, steepness of maturation for CL; Q, inter‐compartmental clearance; RUV, residual unidentified variability; TM50, Maturation half‐life for CL; V1, volume of distribution in the central compartment; V2, volume of distribution in peripheral compartment.

The designs for allocating sample size based on PMA for neonates and infants, which is theoretically associated with maturation, were assessed based on Designs #12 to #21 (Table 2). For all tested designs for sample size allocation based on PMA, all the mean values of estimated PK parameters were close to the true values and the CV values of all the PK parameters were less than 20%, except for the CV value for HILL. This suggested that when sufficient PK information from subjects aged 3 months or older (adults, toddlers, children, and adolescents) was available, the pediatric PK parameters could be appropriately estimated except for the maturation parameters. The CV value of HILL for Design #12 (with nine subjects <42 weeks of PMA) was lower than that for Design #13 (without subjects <42 weeks of PMA), as shown in Table 3. The simulations confirmed that the inclusion of subjects with less than 42 weeks of PMA would provide valuable information to appropriately estimate pediatric PK parameters. The simulations for Designs #14 to #19 with different numbers of subjects in Groups A and B (preterm neonates) suggested that Design #16 (three preterm neonates with <37 weeks PMA and six neonates/infants) would most efficiently estimate pediatric PK parameters when CV of less than 20% for all estimated PK parameters (including HILL) was assumed to be the threshold for appropriate parameter estimation. In addition, in a case where one preterm neonate with <32 weeks PMA (Group A) was available, a total of seven neonates/infants would provide appropriate estimation of pediatric PK parameters with <20% CV for all the PK parameters (Design #20).

4. DISCUSSION

In this simulation study, the clinical trial designs of cefiderocol for allocating sample size for neonates and infants were evaluated using a model‐based approach in terms of estimation performance.

We were able to confirm that adult data would provide valuable information for identifying the pediatric PK including the maturation parameters (for neonates and infants) in a situation where it would be difficult to collect rich data from such subjects. This is consistent with the proposition of the US Food and Drug Administration in 1994 that maximizing the use of adult data when designing pediatric drug development ³² and leveraging available adult PK data could improve the efficiency of pediatric studies by reducing the required sample size. ³³ If only PK parameter estimates of population PK model for adults are available and raw adult data are not available, it could be possible to estimate parameters related to maturation and body size accurately only based on pediatric data by using population PK parameter estimates for adults as prior information (Table S3). Our simulation confirmed that adult data would contribute to estimating pediatric PK parameters even in the case of different allometric relationships between adults and pediatrics as shown with the assessment in Design #3. This result is consistent with the findings of Hsu et al. ³³ that prior information based on adult data was useful for estimating the population mean values of PK parameters for pediatrics even when the parameter values were different between adults and pediatrics using the Bayesian commensurate prior approach. The pediatric PK parameters were scaled from adult PK parameters using allometric relationships reported for parenteral β‐lactam antibiotics ²¹ in this study, and it was confirmed that the SSE results were similar to those using the model with centering body weight at 70 kg (Table S4). In addition, the allometric exponent for CL was used estimated value (0.578) based on the previous study. ²¹ The allometric exponent was reported as 0.632 by Rhodin et al. ²² if the renal function maturation was incorporated, and the difference between the values of the allometric exponent would not affect the result of SSE significantly (Table S5).

As the maturation of elimination organs is theoretically associated with PMA, ²³ it is reasonable to set the age groups for pediatric clinical trials based on PMA. Our simulation study confirmed that this could reduce the total sample size compared with the age groups based on GA and PNA. In our simulation study, a few subjects with small PNA (<15 days) were included, and it was also confirmed that data from very young populations such as preterm infants would provide valuable information for estimating pediatric PK parameters, especially for the maturation parameters. In the case of pediatric PK parameter estimation for cefiderocol, when three neonates with <37 weeks PMA are available, pediatric PK parameters including the maturation parameters can be appropriately estimated (<20% CV for all the PK parameters) with a total of nine neonates/infants, if sufficient data from subjects aged >3 months and adults are available (Design #16). In addition, when one neonate with <32 weeks PMA is available, the total number of neonates/infants could be reduced to seven (Design #20). These youngest subjects aged <32 weeks PMA would be particularly necessary to identify the maturation parameters, and it was suggested that the PK parameters could be estimated accurately without these subjects if maturation parameters were fixed (Table S6). The optimization for the number of the neonates and infants was mainly focused on in this study, and it could be possible to reduce the total number of pediatric subjects if the optimization for the age category and the number of subjects aged 3 months or older is performed.

Since cefiderocol is mainly excreted via the kidney, maturation of the renal function was taken into consideration in our simulation study. This model‐based approach could also be applied to renal‐excretion‐type drugs such as β‐lactam antibiotics for allocating sample size of age groups for pediatric clinical studies, since PK characteristics for these drugs have been well‐characterized and are predictable. The applicability of this approach to drugs with other elimination profiles, such as metabolized by CYP, would need to be further investigated. The GA and PNA have usually been used to set age groups for neonates and infants for the clinical trials of β‐lactam antibiotics (ceftaroline, meropenem, ceftazidime, and doripenem) (https://www.clinicaltrials.gov identifier NCT02424734, NCT00621192, NCT04126031, and NCT01381848). ³⁴ , ³⁵ , ³⁶ Phase 2 study of ceftaroline consisted of three cohorts: very young infants (PNA 28 to <60 days), term neonates (GA >37 weeks and PNA 7 to 28 days), and preterm neonates (GA 34 to <37 weeks and PNA 7 to 28 days), and the total number of subjects was 11 for evaluation of PK. Phase 1 study of doripenem consisted of six cohorts: GA <32 weeks and PNA <14 days, GA <32 weeks and PNA 14 days to 4 < weeks, GA 32 to <44 weeks and PNA <14 days, GA 32 to <44 weeks and PNA 14 days to <4 weeks, GA <32 weeks and PNA 4 to <12 weeks, and GA 32 to <44 weeks and PNA 4 to <12 weeks. The total number of subjects was 52. For these studies, the PMA ranges of the age cohorts (as the sum of GA and PNA) were 38 to 52.5, 38 to <48, and 35 to <41 weeks for ceftaroline, and 26 to <32, 28 to <36, 32 to <46, 34 to <48, 30 to <44, and 36 to <56 weeks for doripenem. The PMA ranges in these trial designs highly overlapped among the cohorts, and the overlap was also observed for the studies of meropenem and ceftazidime. The sample size could be reduced for these clinical trials with the model‐based approach by using the sample size allocation based on PMA since an appropriate distribution of PMA could enhance the efficiency of pediatric PK parameter estimation. This approach could suggest the minimum sample size to characterize the PK profile, and the actual sample size for a clinical trial should be determined considering the other objectives of the study (e.g., safety assessment) or dropout rates.

In our model‐based approach, we assumed that PK profiles for pediatric patients would be predictable based on the population PK model for adults, and the evaluation for predictive performance would be performed based on the assumption that the estimation model could fit the true PK. Pediatric patients may have differences in PK profiles from adults (e.g., more compartments, non‐linear elimination, and other residual error model). For the optimization of the sample size in these situations, further investigation would be required. In addition, blood sampling schedules per each age group could further be optimized especially for all neonates and infants since the blood volume to be taken should be limited for these age populations. Dried blood spots are known to minimize the blood volume to be collected, ³⁷ , ³⁸ and this method should help up collect blood samples to evaluate PK appropriately.

5. CONCLUSION

Based on the model‐based optimal design approach, sample size allocation for neonates and infants was assessed for pediatric PK parameter estimation of cefiderocol. Adult PK data was found to be informative for the estimation of pediatric PK parameters, and the inclusion of PK data for very young subjects (PMA <37 weeks) was valuable for the estimation of the maturation parameters. Given that it is difficult to enroll sufficient numbers of neonates and infants in pediatric clinical trials and that it is also difficult to collect rich PK blood samplings from pediatric patients, study design including sample size allocation of neonates and infants should be carefully assessed prior to the initiation of pediatric clinical trials, and this model‐based approach is one of the useful ways to assess them.

AUTHOR CONTRIBUTIONS

Performed data analysis: D.Y., T.K.; Wrote or contributed to the writing of the manuscript: D.Y., T.K., T.W.; Final approval of manuscript: All authors.

FUNDING INFORMATION

This study was funded by Shionogi & Co., Ltd.

CONFLICT OF INTEREST STATEMENT

Daichi Yamaguchi, Takayuki Katsube are employees of Shionogi & Co., Ltd. Toshihiro Wajima was an employee of Shionogi & Co. Ltd.

ETHICS STATEMENT

This article is based on previously conducted studies and does not contain any new studies with human participants or animals performed by any of the authors. Please see the referenced articles for ethics relating to the original studies.

Supporting information

Data S1

Yamaguchi D, Katsube T, Wajima T. Evaluation and optimization of sample size of neonates and infants for pediatric clinical studies on cefiderocol using a model‐based approach. Pharmacol Res Perspect. 2024;12:e70001. doi: 10.1002/prp2.70001

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.