A General Framework for Assessing In vitro/In vivo Correlation as a Tool for Maximizing the Benefit‐Risk Ratio of a Treatment Using a Convolution‐Based Modeling Approach

Abstract

The net benefit of a treatment can be defined by the relationship between clinical improvement and risk of adverse events: the benefit‐risk ratio. The optimization of the benefit‐risk ratio can be achieved by identifying the most adequate dose (and/or dosage regimen) jointly with the best‐performing in vivo release properties of a drug. A general in silico tool is presented for identifying the dose, the in vitro and the in vivo release properties that maximize the benefit‐risk ratio using convolution‐based modeling, an exposure‐response model, and a surface response analysis. A case study is presented to illustrate how the benefit‐risk ratio of methylphenidate for the treatment of attention deficit hyperactivity disorder can be maximized using the proposed strategy. The results of the analysis identified the characteristics of an optimized dose and in vitro/in vivo release suitable to provide a sustained clinical response with respect to the conventional dosage regimen and formulations.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

☑  The development of a model‐informed approach is currently extensively used for supporting drug development. However, no quantitative framework has been proposed for identifying the best performing in vivo delivery rate appropriate for maximizing the benefit‐risk ratio and for facilitating the development of such a formulation using in vitro/in vivo correlation.

• WHAT QUESTION DID THIS STUDY ADDRESS?

☑  How a model‐informed drug development strategy based on surface‐response analysis can be prospectively developed and applied to optimize the drug development process by identifying the drug properties associated with an optimized benefit‐risk.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

☑  A general in silico tool is presented for identifying the dose, the in vitro and the in vivo release properties that maximize the benefit‐risk ratio using convolution‐based modeling, an exposure‐response model, and a surface response analysis.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

☑  The proposed model‐informed approach provides the pharmaceutical companies with a methodological framework for developing drugs with drug delivery and a dose selection suitable to produce a clinical benefit prospectively defined by the clinicians and not just a clinical response better than the placebo response.

The clinical benefit (CB) of a treatment is usually defined in relation to the size of the treatment effect, such as the baseline corrected change from placebo at study end.

However, the level of efficacy cannot be considered as the unique criterion for determining the CB of a treatment as the safety and tolerability information need to be accounted for. A better definition of the CB of a pharmacological treatment should be based on the concept of benefit‐risk ratio. Accordingly, CB can be defined as a treatment effect with a size sufficiently large to constitute a real clinical improvement with a minimal risk of adverse events (AEs).

The convolution‐based modeling approach has been proposed as a tool for optimizing the CB of a pharmacological treatment.1 The CB optimization can be achieved by identifying the best performing dose and dosage regimen jointly with the best performing in vivo release properties of the drug.

The key components of this model‐informed approach are: (i) the assessment of the in vivo/in vitro correlation (IVIVC), (ii) the characterization of the pharmacokinetics (PKs) of the drug, (iii) the model linking circulating drug exposure and pharmacological response accounting for the placebo effect, and (iv) the optimization tool to determine the optimal dose and in vivo drug release.

The IVIVC can be used: (i) to predict human absorption and the in vivo plasma concentration profiles based on in vitro data, (ii) to optimize dosage forms, (iii) to set dissolution acceptance criteria, and (iv) to establish bioequivalence based on in vitro data.

Many approaches have been proposed for evaluating IVIVC. These methods can be classified as methods requiring deconvolution and methods based on the implementation of a convolution‐based approach. Concerns have been raised about the reliability of traditional deconvolution‐based methods.2, 3 In those approaches, modeling is conducted on deconvoluted data rather than on raw plasma drug concentration‐time data. This analysis strategy frequently leads to unstable and unreliable results.4 In contrast, convolution‐based methods provide more consistent and reliable results.5

One of the most efficient implementations of convolution‐based modeling is based on the translation of a convolution integral into a system of differential equations.6 This method is a single‐stage approach as the model utilizes the observed data directly without transformation (i.e., through deconvolution). One of the benefits of this modeling approach is the ability to directly predict the plasma concentration‐time course resulting from a given in vivo input function.

The objective of this paper is to develop a model‐informed methodology for optimizing the drug development process by identifying drug and formulation properties associated with an optimized benefit‐risk ratio (Figure 1). This was conducted in three steps to: (i) implement IVIVC using a convolution‐based approach applicable when a parametric form of dissolution data can be identified and when in vivo PK is characterized by any parametric model, (ii) evaluate the impact of dose and of in vivo release properties on PK and on pharmacodynamic (PD) outcomes, and (iii) provide an in silico tool for identifying dose and in vitro release properties that maximize the benefit‐risk ratio of a treatment.

Figure 1.

General framework for maximizing the benefit‐risk ratio of a treatment. PD, pharmacodynamic; PK, pharmacokinetic; IVIVC, in vitro/in vivo correlation.

A case study is presented to illustrate the implementation of the proposed strategy for maximizing the benefit‐risk ratio of methylphenidate hydrochloride (MPH) for the treatment of attention deficit hyperactivity disorder (ADHD).

MPH is a central nervous system stimulant currently considered as the first‐line treatment for school‐aged children or adolescents with ADHD. A variety of extended‐release formulations of MPH have been developed in the attempt to improve symptom control. Among these products, we focus on Ritalin LA (Manufactured for Novartis Pharmaceuticals Corporation East Hanover, New Jersey 07936 By Alkermes Gainesville LLC Gainesville, GA 30504). This formulation is an extended‐release capsule with a bimodal release profile (with two distinct peaks ~ 4 hours apart) developed using a proprietary Spheroidal Oral Drug Absorption System technology.7

The most common AEs reported with MPH included headaches, decreased appetite, nausea, irritability, and insomnia.8, 9 A recent meta‐analysis on the exposure‐response of blood pressure (BP) and heart rate (HR) for MPH in healthy adults indicated that the BP and HR changes were directly related and highly dependent on the MPH PK profiles.10 These safety issues associated with MPH treatment may compromise the treatment course of ADHD in children and also raise parents’ concerns over them. For this reason, it is critical to determine what could be the minimal exposure of MPH associated with a CB that maximizes the benefit‐risk ratio.

Ritalin LA data extracted from the literature were used to implement an IVIVC.11 The PK/PD model previously developed to establish the exposure‐response of MPH was used to estimate the changes in Swanson, Kotkin, Agler, M‐Flynn, and Pelham scale (SKAMP) clinical scores associated with a single dose of 40 mg of Ritalin LA.12 Finally, the optimization algorithm was applied to identify the dose and the in vivo/in vitro release properties expected to maximize the benefit‐risk ratio of a treatment with MPH.1

Methods

Data

The original study enrolled 17 participants in a four‐treatment, four‐period, single‐dose, randomized crossover design study, but only 16 subjects were retained for the final PK analysis.11 The subjects received four treatments, after at least a 10‐hour fast, 3 Ritalin LA capsule formulations (40 mg) and Ritalin IR tablets (two 20 mg given 4 hours apart) as the reference. The three Ritalin LA formulations were selected to provide slow‐release, medium‐release, and fast‐release in vitro dissolution rates, respectively.

Convolution‐based model

The plasma concentration, resulting from an arbitrary dose, was described by convolution as:

$$C_p(t)=f(t)\ast I(t)$$ (1)

$$f(t)=\frac{\mathrm{d}r}{\mathrm{d}t};\frac{\mathrm{d}A}{\mathrm{d}t}=F·\text{Dose}·\frac{\mathrm{d}r}{\mathrm{d}t}-k_{\mathrm{el}}·A;C_p=\frac{A}{V}$$ (2)

where f(t) is the in vivo input function, I(t) is the unitary impulse response (defined, for a one‐compartment process, by the volume of distribution (V) and the first order elimination rate (k _el)), * is the convolution operator, r(t) is the time‐varying fraction of the dose released, A is the amount of drug, and F is the fraction of the dose absorbed.

IVIVC modeling

The present analysis is focused on the development of a level A IVIVC by evaluating a point‐to‐point correlation between the fraction of drug absorbed in vivo (r_vivo (t)) and the fraction of drug dissolved (r _vitro (t)).13 In the IVIVC assessment, the in vitro dissolution and in vivo input curves may be directly superimposable or may be made to be superimposable by using a “scaling factor.” A time‐scaling function was included in the model to account for potential time differences in the in vitro and the in vivo processes (for example, when the dissolution is faster than the in vivo input rate). A general time‐scaling model was applied in the assessment of the IVIVC:

$$\begin{array}{cc}\hfill r_{\mathrm{vivo}}(t)& =a_1+a_2·r_{\mathrm{vitro}}(\text{tt})\hfill \\ \hfill \text{tt}& =b_1+b_2·t^{b_3}\hfill \end{array}$$ (3)

In case of absence of time scaling between r _vivo and r _vitro: a ₁ = 0, a ₂ = 1, b ₁ = 0, b ₂ = 1, and b ₃ = 1. Otherwise, the time scaling can be defined by estimating the appropriate values of the parameters a ₁, a ₂, b ₁, b ₂, and b ₃. Eq. (3) includes a linear component (intercept of a ₁ and slope of a ₂) and a nonlinear component describing the time‐shifting (b ₁), time‐scaling (b ₂), and time‐shaping factor (b ₃).

The final step in the IVIVC analysis is to validate the model by providing quantified evidence of the predictive performance of the model. The model validation can be accomplished using data from the formulations used to build the model (internal validation) or using data obtained from a different (new) formulation (external validation).

The internal validation is implemented using the IVIVC model: the relevant exposure parameters (peak plasma concentration (C_max) and area under the curve to infinity (AUC_∞)) are predicted using the model for each formulation and compared with the observed values. The prediction error (%PE) is calculated for each PK parameter using the equation

$$\%\text{PE}=\frac{1}{n}\sum _1^n\frac{\left|\text{Observed value}-\text{Predicted value}\right|}{\text{Observed value}}·100$$ (4)

where n is the number of formulations. The criteria for assessing the level of predictability are for each PK parameter average %PE ≤ 10% with no individual values > 15%. If criteria are not met, the evaluation of external predictability would be required.13

In addition to AUC_∞ and C_max, additional metrics based on the concept of partial AUC were considered for the assessment of %PE. These criteria were based on the March 2015 recommendations of the US Food and Drug Administration (FDA) for using partial AUC (pAUC) metrics for studies conducted in fasting conditions to assess the bioequivalence of generic extended release formulations of MPH against Ritalin LA.14

The following pAUCs were considered:

• pAUC₀₋₃, AUC from 0−3 hours

• pAUC₃₋₇, AUC from 3−7 hours

• pAUC₇₋₁₂, AUC from 7−12 hours

The IVIVC analysis was conducted using a four‐step approach, as illustrated in Figure 2:

Figure 2.

Schematic of the in vitro/in vivo correlation (IVIVC) analysis: r _vitro = fraction of drug dissolved; r _vivo = fraction of drug absorbed; f(t) = in vivo input function; I(t) = unitary impulse response; V = volume of distribution; kel = first order elimination rate; * = convolution operator; A = amount of drug; C_p = drug concentration; F = relative bioavailability; p_diss = dissolution function; p_scal = time scaling function;  = relative time change for the calculation for numerical approximation of f(t); t” = time scaled; p_PK = pharmacokinetic parameters of the immediate release formulation; C_pref = plasma concentration of the immediate release formulation.

1. Fit the mean PK time‐course of the Ritalin IR formulation (step 1)

2. Individually fit the mean in vitro dissolution data of the slow, medium, and fast formulations using the release function (r(t)) (step 2)

3. Evaluate IVIVC by jointly applying the convolution model to the in vivo data of the slow, medium, and fast formulations (step 3) and by:

   1. Fixing the in vivo drug release parameters for each formulation to the values estimated in step 2

   2. Estimating the time‐scaling factors common to all formulations (Eq. (3))

4. Evaluate the internal predictability by comparing the predicted (estimated in step 3) C_max, AUC_∞, pAUC₀₋₃, pAUC₃₋₇, and pAUC₇₋₁₂ with the observed values (step 4)

As an example, in case of a simple in vitro dissolution and in vivo disposition (i.e., one‐compartment), the convolution‐based model describing plasma concentrations can be written as:

• In vitro dissolution, constant dissolution rate:

  $$r_{\mathrm{vitro}}=\text{Dose}·(1-e^{-k_{\mathrm{a}}·t})$$ (5)

  where k _a is the first order absorption rate constant
• PK disposition, one‐compartment with first order elimination rate:

  $$\frac{\mathrm{d}A}{\mathrm{d}t}=-\text{kel}·A$$ (6)

  with the assumption that r _vivo = r _vitro, the in vivo drug delivery rate is computed (by numerical approximation or by analytical solution) as:

  $$f(t)=\frac{\mathrm{d}{r}_{\mathrm{vivo}}}{\mathrm{d}t}\cong \frac{r_{\mathrm{vitro}}(t-\mathrm{\Delta })-r_{\mathrm{vitro}}(t+\mathrm{\Delta })}{2·\mathrm{\Delta }}=\text{Dose}·k_{\mathrm{a}}·e^{-k_a·t}$$ (7)
• Convolution model:

  $$\frac{\mathrm{d}A}{\mathrm{d}t}=f(t)-\text{kel}·A=F·\text{Dose}·k_{\mathrm{a}}·e^{-k_{\mathrm{a}}·t}-\text{kel}·A;C_p=\frac{A}{V}$$ (8)

In the analysis of MPH:

• The Ritalin LA multiphase in vitro dissolution data were described by a double Weibull function r _vitro(t):

  $$r_{\mathrm{vitro}}(t)=\text{Dose}·\left[1-\left(\text{ff}·e^{-\left({\left(\frac{\mathrm{time}}{\mathrm{td}}\right)}^{\mathrm{ss}}\right)}+(1-\text{ff})·e^{-\left({\left(\frac{\mathrm{time}}{\mathrm{td}1}\right)}^{\mathrm{ss}1}\right)}\right)\right]$$ (9)

  where ff = fraction of the dose released in the first process, td and td1 =  times to release 63.2% of the dose in the first and in the second process, ss and ss1 =  sigmoidicity factors for the first and the second process.15

• The f(t) function was approximated using a finite difference approach

• The Ritalin IR PK was described by a one‐compartment model with first order elimination and an absorption lag‐time

• The final convolution model was defined by:

  $$r_{\mathrm{vivo}}(t)=a_1+a_2·r_{\mathrm{vitro}}(\text{tt});\text{tt}=b_1+b_2·t^{b_3}$$ (10)

  $$f(t)=\frac{\mathrm{d}{r}_{\mathrm{vivo}}}{\mathrm{d}t}\cong \frac{r_{\mathrm{vivo}}(t-\mathrm{\Delta })-r_{\mathrm{vivo}}(t+\mathrm{\Delta })}{2·\mathrm{\Delta }}$$ (11)

  $$\frac{\mathrm{d}A}{\mathrm{d}t}=F_i·{\text{Dose}}_i·f_i(t)-\text{kel}·A;C_p=\frac{A}{V}$$ (12)

  where i represents the formulation, F the relative bioavailability, and dose the in vivo dose.

Exposure‐response

The assessment of the exposure‐response relationship was implemented using the PK/PD model previously developed describing the relationship of MPH concentrations (resulting from the administration of Concerta, Janssen‐Cilag Manufacturing, LLC Gurabo, Puerto Rico 00778) with the SKAMP scores describing the ADHD impairment.12

The placebo response evaluated with the SKAMP scores was described by an indirect response model (P(t)):

$$\frac{\mathrm{d}P}{\mathrm{d}t}=k_{\mathrm{in}}·(1+\text{AA}·(e^{-t·P1}-e^{-t·P2}))-k_{\mathrm{out}}P$$ (13)

where k _in = zero‐order rate constant for production of response (P), k _out = first‐order rate constant for the loss of response; AA = amplitude of the placebo effect, and P1 and P2 =  rate of onset and offset of placebo effect.

The MPH effect was described by a drug‐related change from placebo using a maximum effect (E _max) model. The E _max represented the maximal achievable MPH‐related effect. The tolerance effect was included in the model assuming that half‐maximal effective concentration (EC₅₀) increases with time.16 Finally, a Delta parameter accounted for the score difference at baseline between the placebo and active arms:

$$\text{PD}(t)=P(t)+\text{Delta}-\frac{E_{\max }·C_p}{{\text{EC}}_{50}(t)+C_p}$$ (14)

A time‐dependent EC₅₀ (EC₅₀(t)) value was used to account for tachyphylaxis:

$${\text{EC}}_{50}(t)={\text{EC}}_{50\mathrm{b}}\left(1+\frac{t^{\mathrm{ga}}}{t{50}^{\mathrm{ga}}+t^{\mathrm{ga}}}\right)$$ (15)

where EC_50b represents the EC₅₀ value at time 0, t50 is the time at which half of the tachyphylaxis occurs (the time at which 50% of the maximal change in EC₅₀(t) is reached), and ga is the rate of change of the EC₅₀(t).

Optimize the benefit‐risk

The optimization of CB as a function of dose and in vivo release (defined by: ff, ss, ss1, td, and td1) was conducted using a response surface analysis (Figure 3). The optimal benefit‐risk ratio was defined by the minimal MPH exposure providing a constant and sustained improvement in the SKAMP scores during all day. The assumption underlying this definition was that the increase in the risk of AEs and the risk of elevation of the cardiovascular parameters was proportional to the MPH exposure.

Figure 3.

Schematic of the benefit‐risk analysis. PD, pharmacodynamic; PK, pharmacokinetic.

For the analysis, the maintenance of the SKAMP scores from 8−10 during 12 hours was arbitrarily considered as the target clinical response.

The optimization algorithm searched for the minimal value of the cumulative time during which the SKAMP scores fail to comply with the CB definition as a function of the dose, and the ff, ss, ss1, td, and td1 parameters.

The minimization of this criterion is equivalent to maximizing the time during which the SKAMP scores are compliant with the CB definition.

Software

The data used in the analyses were extracted from the publication of Wang et al.11 using Plot Digitizer software, version 2.0 (University of South Alabama, Mobile, AL, USA). The analyses were conducted using NONMEM, version 7.4 (ICON Development Solutions, Hanover, MD, USA). NONMEM model code is provided in the supplementary information. Simulations and optimization of CB were conducted in R using the NLOPTR nonlinear‐optimization library, version 3.2.5 (R Foundation for Statistical Computing).

Results

Step 1: ritalin IR analysis

The disposition and elimination of the Ritalin IR formulation was characterized by a one‐compartment model with k _a, absorption lag time (Lag), k _el, and V. The model was fitted to data assuming an additive residual model. The model was selected based on the available data and on the prior models developed for describing the Ritalin IR PK.17

The estimated parameter values are presented in Table S1. The mean MPH concentrations for the Ritalin IR formulation with the model‐predicted curve are presented in Figure S1.

Step 2: dissolution data analysis

Details of dissolution testing procedures can be found in Wang et al.11 The Weibull model was individually fitted to the mean in vitro dissolution data of the slow, medium, and fast formulations.

The estimated parameter values are presented in Table S2. The mean dissolution data for each formulation with the model predictions are presented in Figure 4. These results indicated that the dissolution model well characterizes the dissolution data for each formulation.

Figure 4.

Mean dissolution data for the slow, medium, and fast formulations (dots) with the model‐predicted dissolution curves (solid lines).

The time requested to dissolve the first fraction of the dose (td) is similar for the three formulations, whereas the time necessary for dissolving the second fraction of the dose (td1) seems to decrease proportionally from the slow (9.91‐hour) formulation to the fast (5.42‐hour) formulation. Similarly, the shape of the dissolution (ss1) decreases proportionally from the slow (3.59) to the fast (1.75) formulation.

Step 3: IVIVC

The MPH concentrations of the three formulations were jointly fitted to estimate the time‐scaling parameters (a₁, a₂, b₁, b₂, and b₃) and the fraction of the dose administered available for the systemic circulation (F_slow, F_medium, and F_fast). The F_ parameters represent a dose‐scaling value with respect to the reference Ritalin IR formulation. A value < 1 indicates that a formulation is expected to have a lower relative bioavailability than the Ritalin IR formulation.

The time‐scaling parameters were fixed to a common value for all formulations and estimated as fixed‐effect parameters. No random effect was associated with any parameter of the convolution model. In this framework, the absorption was purely driven by the in vitro release time‐scaled properties. Two analysis scenarios were considered: in the first one, three distinct F_ parameters were estimated, and in the second one, the same F_value was assumed for the three formulations. The comparison of the change in the objective function value using the log‐likelihood ratio test in the two scenarios indicated that the assumption of a common F_value was the preferred option.

The estimated parameter values are presented in Table S3. The mean observed and model‐predicted MPH in vivo concentrations for the three formulations with the 80%, 90%, and 95% prediction intervals are presented in Figure 5.

Figure 5.

Mean pharmacokinetic observed concentrations (orange dots) with the predicted values by the convolution model (blue solid lines) by formulation. The shaded areas represent the 80%, 90%, and 95% prediction intervals. CI, confidence interval.

Step 4: Validation

The in vitro dissolution data and the convolution model were used to predict in vivo PK profiles of the three formulations. The convolution model predictions were in close agreement with the observed concentrations (Figure S2 and Table S4). The regression analysis on the predicted vs. observed values indicated that the intercept was not statistically different from 0 and that the slope was not statistically different from 1 as the 95% confidence limits included 0 for intercept and 1 for slope.

The area under the PK curves was estimated using a log‐linear trapezoidal rule. The %PEs were estimated for C_max, AUC_∞, pAUC₀₋₃, pAUC₃₋₇, and pAUC₇₋₁₂ (Table 1). The largest %PE (= 11.19%) was estimated for pAUC₇₋₁₂ of the fast formulation. The average %PE across the formulations were below the 10% reference value. These results support the level A IVIVC.

Table 1.

Comparison of the C_max, AUC_∞, pAUC₀₋₃, pAUC₃₋₇, and pAUC₇₋₁₂ values estimated on the observed MPH PK data with the values estimated using the convolution model predicted PK data with the assessment of the %PE

Formulation	Observed values			Predicted values			Prediction error
	Cmax (ng/mL)		AUC∞ (ng·hour/mL)	Cmax (ng/mL)		AUC∞ (ng·hour/mL)	%PE AUC		%PE Cmax
Slow	13.01		126.97	14.12		122.94	3.17		8.56
Medium	14.02		130.56	14.6		123.77	5.2		4.08
Fast	14.67		131.29	14.7		123.47	5.96		0.2
Average							4.78		4.28

Formulation	pAUC0−3 (ng·hour/mL)	pAUC3−7 (ng·hour/mL)	pAUC7−12 (ng·hour/mL)	pAUC0−3 (ng·hour/mL)	pAUC3−7 (ng·hour/mL)	pAUC7−12 (ng·hour/mL)	%PE pAUC0−3	%PE pAUC3−7	%PE pAUC7−12
Slow	25.83	44.69	25.66	25.49	40.98	27.43	1.28	8.3	6.87
Medium	27.54	46.7	25.32	26.95	47.2	23.9	2.13	1.09	5.6
Fast	27.57	53.26	35.15	26.41	53.39	31.22	4.19	0.25	11.19
Average							2.53	3.21	7.89

%PE, prediction error; AUC_∞, area under the curve to infinity; C_max, peak plasma concentration; MPH, methylphenidate hydrochloride; pAUC, partial area under the curve; PK, pharmacokinetic.

Exposure‐response

The change from placebo of the SKAMP scores associated with the MPH exposure expected after the treatment with Ritalin LA at the dose of 40 mg were estimated using the model defined in Eqs. (13), (14), (15) and the parameter values previously estimated.12

Figure S3 shows the model‐predicted MPH plasma concentrations and the associated model‐predicted trajectories of the SKAMP scores for the three formulations. Simulations were conducted to estimate MPH exposure and SKAMP scores in the range of the recommended doses of Ritalin LA: 10 mg to 40 mg/day (Figure 6a).

Figure 6.

Simulation results: (a) Simulated Swanson, Kotkin, Alger, M‐Flynn, and Pelham (SKAMP) scores and methylphenidate hydrochloride (MPH) exposure at the recommended doses of Ritalin LA: 10–40 mg/day. (b) Simulated SKAMP score) and MPH exposure at the optimized in vitro/in vivo drug release/absorption, at the optimized dose of 10 mg/day. The shaded areas represent the target region of the response: SKAMP score) in the range 8–10 during all day. CI, confidence interval.

The simulated response showed a similar shape of SKAMP trajectories at different doses with an important drop in the early part of the day followed by a constant loss of response during the rest of the day. However, none of the doses seem to provide a constant and sustained response during all day consistent with the target expectation.

The results of the joint optimization of the in vitro/in vivo drug release/absorption and the dose strength are presented in Figure 6b with the simulated MPH PK and SKAMP scores at the dose of 10 mg/day of the reference formulation.

The objective of the optimization was to estimate the MPH plasma concentration and the shape of the MPH PK time course associated with a SKAMP response compliant with the target CB. For the purpose of the present analysis, CB was arbitrarily defined as sustained and constant SKAMP score values in the range 8–10 during 12 hours.

The optimization was conducted considering MPH PK and SKAMP scores at the dose of 40 mg of Ritalin LA as reference. The results indicated that the dose of 10 mg/day with a maximal MPH concentration of 3.38 ng/mL and an improved in vitro/in vivo drug release/absorption profile was sufficient to assure the target CB. The estimated dissolution parameters with the in vitro dissolution profiles of the optimized and reference formulations are presented in Figure S4. The comparison of the optimized dissolution values jointly with the comparison of the reference and the optimal dissolution profiles presented in Figure S4 indicated that the optimal values of the dissolution parameters remain in a domain that could be easily accommodated by the currently available pharmaceutical development technologies. One of the benefits of the present modeling framework is to facilitate the comparison of alternative hypothetical test product performances and to provide quantitative criteria for selecting the best product to move forward.

Discussion

Although the benefit‐risk analysis is usually conducted by jointly assessing both favorable (i.e., efficacy) and unfavorable effects of a treatment (i.e., AEs), the present analysis of risk assessment was focused on the optimization of dose and formulation properties considered as drivers of efficacy and tolerability (i.e., BP and HR changes). The aim of the methodology presented is to identify the best performing dose and the best performing in vitro release properties of a drug providing an improved CB while minimizing potential safety issues.

The SKAMP scores show almost superimposable trajectories for the three formulations with a maximal drop from baseline at about 1.5 hours postdose and with a constant deterioration in the response after this time. Wang et al.11 conducted a bioequivalence analysis among the three Ritalin LA formulations using primary PK parameters (C_max, time of maximum plasma concentration (T_max), AUC_0−t, and AUC_0−∞) and secondary PK parameters describing the bimodal shape of the PK time course (C_{max 0–4}, T_{max 0−4}, and AUC₀₋₄ for the first peak and C_{max 4−8}, T_{max 4−8}, and AUC₄₋₈ for the second peak). Wang et al.11 concluded that the three formulations were bioequivalent despite a different shape of the PK time courses. It should be noted that the criteria used by Wang et al.11 to assess the bioequivalence of MPH formulations (Ritalin LA) are not the same as the current recommendations of the FDA.14 The current criteria indicate that bioequivalence can be assessed when the 90% confidence intervals (CIs) of the geometric mean of the test/reference ratios for the metrics (C_max, AUC₀₋₃, AUC₃₋₇, AUC₇₋₁₂, and AUC_0−∞) fall within the limits of 80−125%.

A convolution‐based modeling approach was proposed for facilitating the development of drug formulations with optimal in vivo release properties by using IVIVC. Finally, a surface‐response analysis was used to identify the drug‐related properties that could affect the CB of a treatment by connecting in vitro and in vivo drug release, in vivo drug release to PK, and PK to PD. The overall objective was to provide a quantitative framework facilitating the development of new medications with an improved benefit‐risk ratio.

The evaluation of the benefit‐risk ratio of a new treatment represents a critical milestone in the regulatory approval process. This assessment provides rational criteria for characterizing the clinical relevance of a new medicine for the benefit of the patients accounting for potential safety risks.

Structured approaches have been proposed to formally address benefit‐risk given the multidimensional nature of the data required for this assessment.18, 19 More recently, quantitative approaches based on modeling and simulation were also proposed to formally assess the benefit‐risk ratio.20

These methods utilize the exposure‐response relationship, assessed by modeling multiple end points related to efficacy and safety and trial simulation to assess benefit‐risk across different dose and dosage regimens. In the context of regulatory approval of new drugs, the assessments drug benefit‐risk represent a template for product reviews, as well as a criterion to support regulatory decisions.

At variance of this approach, where the benefit‐risk ratio is utilized to summarize the properties of new medications at the end of the drug development process, we are proposing a model‐informed methodology that can be prospectively applied to optimize the drug development process by identifying the drug properties associated with an optimized benefit‐risk ratio.

A case study is presented to illustrate how the benefit‐risk ratio of MPH for the treatment of ADHD can be optimized. A large number of MPH formulations have been developed (and are currently in development) with different rates of drug delivery. The choice of the delivery rate was established on the basis of empirical approaches in the attempt: (i) to mimic the PK of some reference compounds or (ii) to explore alternative delivery mechanisms. In any case, none of these approaches was developed having as a target the maximization of the expected CB of a treatment as defined by a physician and as expected by the parents. On the basis of this target, the paper provided a methodological framework to pharmaceutical companies for the development of formulations with drug delivery suitable to produce a CB expected by clinicians and not just a response better than placebo.

For the present analysis, the target CB was arbitrarily defined as constant SKAMP scores in the range 8–10 during 12 hours. The proposed algorithm can easily be generalized to account for any alternative target CB. The optimization procedure was applied to identify the in vivo MPH delivery appropriate for attending this target using the MPH PK and the SKAMP scores at the dose of 40 mg of Ritalin LA as reference. The results of the optimization indicated that the dose of 10 mg/day with a maximal MPH concentration of 3.38 ng/mL and an improved in vitro/in vivo drug release/absorption profile was sufficient to deliver the target CB. The presence of a tolerance effect for MPH represents a potential issue associated with the optimized formulation resulting in a low C_max value. The proposed model accounted for a time‐dependent loss of efficacy by providing an estimate of the optimal MPH PK time course characterized by a dual peaks shape with the second peak greater than the first one for counteracting the loss of efficacy due to a tachyphylaxis effect (Figure 6b).

These results indicated that a substantial reduction in the circulating MPH exposure can be associated with an optimized MPH release and dose values. The dose expected to deliver a clinically relevant benefit was estimated at 10 mg/day based on optimized in vivo delivery rate. At this dose, a significant reduction of the maximal exposure is expected with respect to the reference formulation: C_max = 3.73 ng/mL at the dose of 10 mg/day for the optimized formulation vs. C_max = 3.96 ng/mL, 7.92 ng/mL, and 15.85 ng/mL at the dose of 10, 20, and 40 mg/day for the reference formulations, respectively.

These data have to be considered in the context of the recent meta‐analysis on the relationship between MPH exposure and BP and HR changes. This meta‐analysis showed that the effect of MPH exposure on cardiovascular parameters is different between Ritalin IR and ER formulations and that a linear model (in the concentration range of 0–25 ng/mL) described the relationship between MPH and changes in cardiovascular parameters.

Furthermore, it was shown that MPH has the greatest effect on HR, followed by systolic blood pressure, and diastolic blood pressure, with 1 ng/mL MPH concentration resulting in a percentage increase of 0.33% for systolic blood pressure, 0.27% for diastolic blood pressure, and 0.98% for HR.

In conclusion, the proposed model‐informed approach provided an operational framework for the development of formulations with optimized in vitro/in vivo releases and for the selection of the dose that delivers the minimal exposure associated with a CB matching the expectation of the clinicians.

Funding

Funding for this article was possible, in part, by the US Food and Drug Adminstration (FDA) through grant 1U01FD005240‐02.

Conflict of Interest/Disclosures

Disclosures within the last 36 months for Dr Thomas Spencer: Dr Thomas Spencer receives research support or is a consultant from the following sources: Alcobra, Enzymotec Ltd., Heptares, Impax, Ironshore, Lundbeck Shire Laboratories Inc., Sunovion, VayaPharma, the FDA, and the Department of Defense. Consultant fees are paid to the MGH Clinical Trials Network and not directly to Dr Spencer. Dr Thomas Spencer is on an advisory board for the following pharmaceutical companies: Alcobra, he receives research support from Royalties and Licensing fees on copyrighted ADHD scales through MGH Corporate Sponsored Research and Licensing. Dr. Spencer has a US Patent Application pending (Provisional Number 61/233,686), through MGH corporate licensing, on a method to prevent stimulant abuse. In the past year, Dr Faraone received income, potential income, travel expenses, and/or research support from Lundbeck, Rhodes, Arbor, Pfizer, Ironshore, Shire, Akili Interactive Labs, CogCubed, Alcobra, VAYA Pharma, and NeuroLifeSciences. With his institution, he has US patent US20130217707 A1 for the use of sodium‐hydrogen exchange inhibitors in the treatment of ADHD. In the past year, R. Gomeni was consultant for Ironshore, Sunovion, Supernus, and UCB. The other authors declare no conflict of interest.

Author Contributions

R.G., F.M.M.B.‐G., T.J.S., S.V.F., L.F., and A.B. wrote the manuscript. R.G., F.M.M.B.‐G., T.J.S., S.V.F., and A.B. designed the research. R.G. and F.M.M.B.‐G. performed the research. R.G. and F.M.M.B.‐G. analyzed the data.

Disclaimer

The views expressed in this article do not necessarily reflect the official policies of the Department of Health and Human Services, nor does any mention of trade names, commercial practices, or organization imply endorsement by the United States Government.

Supporting information

Figure S1. Mean MPH concentrations for the Ritalin IR formulation in linear and log‐linear scale.

Figure S2. Regression analysis of the predicted concentration by the convolution model vs. the observed concentrations (open circle) for the slow, medium, and fast formulations.

Figure S3. Predicted MPH plasma concentrations (left panel) and the associated trajectories of the SKAMP scores (right panel) for the slow, medium, and fast formulations.

Figure S4. Comparison of the in vitro dissolution profiles of the optimized and the reference formulations.

Table S1. Estimated MPH parameter values for the Ritalin IR formulation.

Table S2. Estimated dissolution data parameters for the slow, medium, and fast formulations (RSE).

Table S3. Estimated parameter values in the convolution analysis. SE is the standard error and RSE is the relative standard error of the parameters.

Table S4. Results of the regression analysis of the predicted vs. the observed concentrations.

Model code. NONMEM control stream (IVIVC_NONMEM_code.txt) for the IVIVC analysis.