Mechanism‐Based Modeling Approaches to Quantify the Effect of Immunogenicity on the Pharmacokinetics of Therapeutic Proteins in Drug Development

ABSTRACT

Therapeutic protein administration in both preclinical and clinical studies can result in the formation of anti‐drug antibodies against the therapeutic protein. Anti‐drug antibody formation may alter the pharmacokinetics of the therapeutic protein, reduce its plasma concentrations, increase exposure variability, and may lead to a loss of efficacy and adverse events. In an effort to quantitatively understand the effect of anti‐drug antibodies on the concentration‐time profile of a therapeutic protein, as well as develop effective strategies to mitigate its impact in the preclinical and clinical development of therapeutic proteins, mathematical models have been developed to characterize the therapeutic protein pharmacokinetics and its modulation by anti‐drug antibodies in vivo. Here, we review several different mechanism‐based modeling frameworks, summarize their approaches to predict immunogenicity effects, and explore the merits and limitations of each model.

1. Introduction

The issue of unwanted immunogenicity has become an important problem in preclinical and clinical drug development of therapeutic proteins (TP). This topic has elicited much research interest and regulatory attention, resulting in a large number of recent scientific publications and related guidelines by the US Food and Drug Administration [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The main cause of immunogenicity is the presence of antigenic components in TPs (such as foreign amino acid sequences, aggregates, or contaminants) which trigger innate and adaptive immune responses that often lead to anti‐drug antibody (ADA) formation against the administered TP [3]. ADAs have the potential to become a serious issue during preclinical and clinical drug development due to their impact on TP pharmacokinetics (PK), pharmacodynamics (PD), efficacy, and safety [1]. The PK of TP is often altered in the presence of ADA due to changes in drug clearance [1, 12]. The mechanism through which ADA increases the TP clearance includes the formation of an immune complex with the TP leading to an enhanced immune‐complex mediated TP uptake via the reticuloendothelial system and subsequent intracellular proteolytic degradation, which ultimately constitutes an additional elimination pathway for the TP and reduces systemic TP exposure [12]. Reduced exposure due to increased elimination of the TP may lead to loss of pharmacological activity of the TP [1, 12]. Although there have been rare cases where ADA increases drug exposure [13], the usual result is increased elimination of the TP‐immune complex which has been well documented [1, 14]. In addition to loss in exposure, a loss of efficacy can also occur through the binding of ADA to the target binding site of the TP, thereby directly neutralizing its pharmacological activity [1, 12]. These ADAs are usually referred to as neutralizing ADAs.

The formation of ADA‐TP immune complexes can also lead to hypersensitivity reactions which may manifest as increased toxicity of the TP [15]. Lastly, if the TP is analogous to an endogenous protein, ADA against the TP may cross‐react with their endogenous counterparts, a severe safety concern that may lead to loss of functionality of the affected endogenous protein with the potential for fatal outcomes, as previously observed for thrombopoietin and erythropoietin drug products [16, 17].

Hence, it is a necessity to conduct immunogenicity assessments during drug development and evaluate the resulting changes in PK, PD, safety, and efficacy in preclinical and clinical studies.

2. Bioanalytical and Physiological Challenges in the Quantification of ADA Impact on TPs

Despite growing research efforts aimed towards developing strategies to assess immunogenicity of TPs, there are challenges to quantitatively measure and characterize ADA and their impact on PK of TPs due to numerous confounding factors. These can be categorized into assay‐related limitations or physiological challenges, and both contribute to the challenges of quantifying ADA impact on TP exposure.

Assay‐related limitations can affect both the assessment of TP concentration and the relative amount of ADA in a sample.

1. Excess levels of ADA in a sample can directly interfere with the analytical measurement of TP concentration. ADA can either bind at the complementarity determining region or the framework region and interfere with the accurate measurement of the TP [1, 18].

2. First ADA detection can only occur when the immunogenic response results in an excess of ADA relative to the TP. This implies that ADA produced early after TP administration, when TP concentrations are relatively high and ADA amounts may still be relatively low, may go undetected, resulting in false‐negative ADA detection. Limited drug tolerance of most ADA assays may further exacerbate this problem [18, 19].

3. Due to the lack of appropriate quantitative laboratory reference standards, the bioanalytical characterization of ADA magnitude is limited to be semi‐quantitative at best. Thus, absolute ADA concentrations cannot be determined. Instead, titer values and signal‐to‐noise (S/N) ratios are often used as a surrogate for the magnitude of ADA response and reflect a hybrid of both antibody concentration and affinity [20]. The S/N ratio is a screening metric used in immunoassays to determine whether a sample is ADA‐positive. Signal is the measured response from the sample and noise is the background signal, typically from a negative control. The S/N ratio is calculated as sample signal/background signal, and samples that exceed a predefined S/N threshold (called the screening cut point) are considered potential ADA‐positive. The ADA titer is a relative measure of ADA concentration. It is usually reported as the reciprocal of the highest dilution of the sample that still gives a positive response in the assay. The titer and S/N values reported can vary depending on the bioanalytical assay conditions, assay sensitivity, and each individual's variable immune response, leading to a value that is not representative of a consistent in vivo response and cannot be easily compared between different individuals and studies, and not at all between different ADA assays and different TPs [21, 22]. A reliable experimental approach for determining ADA affinity is also not yet available [20].

4. The usually sparse nature of ADA sampling time points in preclinical and clinical studies adds further challenges in determining the exact time course and true impact of ADA [14].

Physiological challenges also contribute to the limitations in quantifying the impact of ADA on TP exposure.

1. Due to the polyclonal nature of ADA that results in a heterogeneous population of antibodies with varying binding affinities in one individual, and different heterogeneous populations in different individuals, it is difficult to determine how ADA affects the PK of the TP, and usually only average effects can be described [21, 22].

2. Furthermore, the binding affinity of ADA potentially matures and increases over time with repeated TP administration, which again may modulate the PK of the affected TP in a time‐dependent manner [21].

In summary, the recordable incidence of TP‐induced immune responses is infrequent and difficult to reliably quantify and predict during drug development. For this reason, mathematical modeling approaches have been applied as a complementary or alternative approach to quantitatively assess the ADA response and its effect on the PK of TP. In the following, we will review various modeling approaches to assess and ultimately predict TP‐specific ADA formation and its impact on the PK of TP during different stages of preclinical and clinical drug development. While the first section is a brief introduction to various pharmacostatistical models developed to explore the immunogenicity effect on the PK of TPs, the second section focuses on a more in‐depth review of mechanism‐based modeling approaches that characterize the time course of ADA formation and its impact on TP exposure.

3. Pharmacostatistical Models to Describe ADA Effects on TP Exposure

Two recent publications reviewed general population pharmacokinetic modeling approaches for monoclonal antibodies (mAbs), which included various covariate models for ADA effect on the clearance of the affected TPs [19, 23]. ADA effects were modeled as time‐invariant categorical, time‐varying categorical, or continuous covariates:

1. ADA as a time‐invariant categorical covariate on clearance: In this model, ADA status is coded as present if ADA was detected in a single sample over the entire follow‐up period. For example, this approach has been used to determine the ADA impact against several mAbs such as infliximab [24] and adalimumab [25]. One disadvantage of this approach is that it leads to a biased estimate of baseline clearance, that is, at the beginning of treatment when ADA is absent [19, 23].

2. ADA as a time‐varying categorical covariate on clearance: In this type of modeling, ADA is incorporated as a time‐varying dichotomous covariate, taking a value 0 or 1 at each observation time dependent on the results of the ADA assay in each corresponding sample. This strategy accounts for the effects of ADA only when they are detected. It has been used to study the impact of time‐varying ADA status on the clearance increase in several mAbs, including lebrikizumab [26], infliximab [27], ipilimumab [28], and golimumab [29]. Although this model enabled determination of the time course of ADA formation, it could not be applied to extract more granular ADA information such as putative ADA concentrations over time. In addition, its potential value relies upon the ADA sampling frequency in the respective studies, which is in many cases less frequent than PK sampling.

3. ADA as a continuous covariate on clearance: This approach takes into consideration the intensity of immunogenic response when modeling the effects of ADA that can vary with time at the level of the individual subject. As ADA response matures over time, the associated TP clearance due to ADA formation may also increase with time. This increase cannot be captured with the categorical covariate models. In several studies, authors have used ADA as a time‐varying continuous covariate to overcome this problem. For example, to describe the immunogenic response to certolizumab pegol [30] and infliximab [31], ADA titers at each time point for each patient were utilized after determining a threshold of ADA concentration beyond which an additive factor to quantify the increase in clearance was applied.

4. ADA effects on clearance modeled by statistical titer conversion: A statistical approach was presented by Bonate et al. to model antibody titer data from 87 patients who received agalsidase beta [32]. In this method, firstly, titer data was transformed based on a geometric series using a common ratio of 2 and a scale factor of 50, and then the exponent was analyzed using a zero‐inflated Poisson random effects model. The advantage of this model is that both the probability of developing the ADA response and expected titer can be modeled using a function that includes patient‐specific covariates [32].

5. ADA effects on clearance quantified via inter‐occasion variability: Perez‐Ruixo et al. developed a method to model the ADA effect on TP concentrations by implementing inter‐occasion variability on the PK parameters of the model responsible for drug clearance and potentially impacted by immunogenicity [33]. This led them to generate estimates of the post hoc model parameters that were estimated over time according to the PK data observed at various specified occasions. If these parameters were influenced by the presence of ADA, they were correlated with immunogenicity status as a time‐dependent covariate and studied graphically, which allowed the determination of the effect of ADA on PK of a fully human mAb, AMG 317 [33].

In summary, the development of various population PK and statistical models provided a quantitative way of understanding the variability in immunogenicity. However, one limitation of these models is that they still lack a mechanistic description of ADA‐mediated TP elimination, and hence cannot offer a deeper understanding of the underlying biological mechanisms behind ADA formation and how changes in biological systems as well as immunogenic stimulus can affect the PK of the TP [23, 34].

4. Mechanism‐Based Modeling Approaches to Determine Time Course of ADA Formation and Their Impact on the PK of TPs

As the incidence, extent, and time course of ADA formation is dynamic and variable, mechanism‐based mathematical models have more recently been applied to characterize the complex disposition kinetics of ADA and the TPs affected by them. Based on reasonable assumptions and practical simplifications of the immune system, mechanism‐based models could provide a viable approach for immunogenicity prediction, thereby quantitatively recapitulating and integrating complicated biological mechanisms, as well as accounting for a multitude of factors that influence immunogenicity [34, 35]. Three examples of mechanism‐based modeling approaches to predict the time course of ADA formation and its impact on the TP PK are discussed in the following.

4.1. Model With Time‐Varying Impact of Immunogenicity on TP PK

Chirmule et al. 2012 and Perez Ruixo et al. 2013 proposed a base model to mechanistically understand the impact of immunogenicity on TP PK (Figure 1) [1, 33]. Building on this model, Chen et al. in 2013 developed a mechanism‐based mathematical model for TP PK and ADA response (referred as the “PK/ADA model”) to simultaneously model the in vivo disposition of TP and ADA based on empirical PK modeling combined with ADA‐TP interactions (Figure 2) [34]. To accommodate the concurrent modeling of TP and ADA, Figure 2 includes additional quantitative terms for two critical delays, a delay in the rise of ADA production that is influenced by TP dose and a delay time required for the ADA to enter the systemic circulation.

FIGURE 1.

PK/ADA model for immunogenicity by Chirmule et al., 2012 and Perez Ruixo et al., 2013. This model acts as a base model to mechanistically describe the impact of immunogenicity, that is, anti‐drug antibodies (ADA), on therapeutic protein (TP) pharmacokinetics (PK). It depicts (a) PK of a TP described by two‐compartment model with intravenous/subcutaneous administration of TP dose (D), amount of the TP in the central and peripheral compartment (TP₁ and TP₂, respectively), intercompartmental transfer rate constant K _{distribution,12} and K _{distribution,21}, and a first‐order linear elimination pathway from the central compartment (represented by elimination rate constant K _elimination) representing proteolytic degradation, (b) the effect of an unwanted immunogenic response to the TP that results in ADA formation. The circulating concentration of the ADA is determined by a homeostatic equilibrium between its formation rate (K _synthesis) and a catabolic turnover process (rate constant K _degradation). The ADA forms an immune complex with the TP (ADA‐TP), leading to subsequent degradation of the immune complex which constitutes an additional clearance pathway for the TP (represented by elimination rate constant K _complex). The dynamic equilibrium for the formation of the resulting ADA‐TP complex is determined through the association rate constant K _on and the dissociation rate constant K _off.

FIGURE 2.

PK/ADA model for Immunogenicity by Chen et al., 2013. Anti‐drug antibody (ADA) formation against a therapeutic protein (TP) was modeled using a limited amount of ADA (A _max) that can be produced in response to repetitively dosing the TP. To account for the time delay in ADA appearance in plasma, ADA is formed in a “deport compartment” and passes through “delay compartments” before entering the central compartment, with a total time delay t _lag. K _synthesis is the rate of ADA formation. A_D is the amount of ADA in the ADA depot compartment, A ₁, A ₂, …A _n are the amounts of ADA in the delay compartments, and K _T is the transfer rate constant of ADA between delay compartments. ADA is the amount of free ADA in the central compartment. K _degradation is the elimination rate constant of unbound ADA from the central compartment. K _complex is the elimination rate constant for the ADA‐TP immune complex. TP₁ and TP₂ are the amounts of free TP in the central and peripheral compartment, respectively. K _elimination is the first‐order elimination rate constant for free TP from the central compartment. The parameters for the distribution of TP between central and peripheral compartments is represented by intercompartmental transfer rate constant K _{distrubution,12} and K _{distrubution,21}. K _on and K _off are the association and dissociation rate constants for TP and ADA binding, respectively.

In this model, with repeated TP dosing, a strong ADA response is elicited [34]. The cumulative TP dose drives the generation of ADA. The dose of ADA is modeled as a saturable function depending on the cumulative TP dose, which is an indicator for the accumulated drug exposure. The amount of ADA produced initially increases with the cumulative TP dose, until it reaches a plateau (A _max). To account for the time delay in ADA formation, putative ADA doses are injected as boluses into a hypothetical depot compartment (“ADA depot”; denoted by the dashed arrow in Figure 2). The entry of ADA from the depot into the central compartment is assumed to also undergo a time delay and is modeled through a series of delay compartments. Both components result in a time delay (t _lag) in ADA response. The t _lag of 7–8 days was based on the assumption that no ADA is produced during the first dosing interval (i.e., 7 days). This reflects the relatively consistent lag time for ADA development within mammalian species due to commonly shared immune system processes. The primary ADA response generally begins several days after initial antigen exposure, as immune cells require time to activate and differentiate. Once ADA reaches the central compartment, it binds to the TP reversibly with a second‐order rate constant K _on and forms an ADA‐TP complex. The ADA‐TP complex can subsequently be eliminated via a first‐order elimination process with the parameter K _complex, thereby adding an additional elimination route to the overall disposition of TP. The affinity maturation of ADA (i.e., the expected increase in affinity with time following successive TP doses) is modeled by decreasing the ADA‐TP dissociation rate constant (K _off) dependent on TP exposure time. The natural turnover of ADA molecules is implemented by the elimination rate constant K _degradation for unbound ADA. The TP PK was added to this ADA model using a two‐compartmental model with first‐order absorption process for subcutaneously administered TP as frequently observed for mAbs [36].

The PK/ADA model is based on a framework of basic assumptions, including the following:

1. ADA formation results in an alteration of the PK of the affected TP [34].

2. ADA production requires a certain time period to be activated since it is influenced by the cumulative TP dose with repeated TP injections. To model this delay in ADA production, it was assumed that no ADA is formed during the first 7 days of dosing. This assumption is based on reports that the time delay in the occurrence of ADA during the primary immune response varies anywhere from 7 days to several weeks [21]. As a consequence, the model would not be directly applicable to a situation where ADA formation occurs sooner than 7 days after the initiation of TP therapy or with pre‐existing ADA [34].

3. The elimination rate constant for ADA (K _degradation) was assumed to be the same as the elimination rate for endogenous immunoglobulin G (IgG) antibodies. This was assumed because the physicochemical properties of IgG‐based ADA are not expected to be different from those of other endogenous IgG molecules [34]. This approach, however, does not account for IgA‐based ADA.

4. The K_on for ADA–TP complex formation was kept constant, while K _off was modeled to decrease with time [37, 38]. This assumption was made based on the observation that antibody affinity maturation exhibited time dependency, and that K _off of antibodies varies with time during affinity maturation, whereas K _on was relatively constant [34].

5. The volume of distribution for the ADA and the ADA‐TP complex was assumed to be the same as that of the central compartment for the TP [34].

The PK/ADA model has been utilized several times to estimate and characterize the time course of ADA formation against TPs in preclinical species [21, 34]. Firstly, Chen et al. used it to explore the generation of ADA responses against two TPs, an interferon Fc‐fusion protein and a mAb, in Cynomolgus macaques at different dose levels [34]. The mAb was administered intravenously once a week for 4 weeks, whereas the Fc‐fusion protein was given subcutaneously twice a week for 25 days [34]. The model allowed description of the concentration‐time profiles for the TPs (mAb and fusion protein), ADA, and ADA‐TP complex, as well as estimation of the affinity maturation time profile for both TPs [34]. PK parameters of free TP were estimated using TP concentration‐time data from ADA negative animals or ADA positive animals during the first 7 days of dosing and thus were independent of ADA formation. The ADA model parameters were subsequently estimated by fitting the model to the TP concentration‐time profiles of ADA positive animals from the 7th day onward. The model predicted that the concentration of ADA increased with repeated TP dosing, which correlated well with the observed high ADA titers and faster TP elimination over time. The model also adequately described the ADA‐TP complex concentration‐time profiles and estimated the complex elimination rate parameter K _complex, which directly impacted the TP elimination. For both TPs, ADA‐TP complexes exhibited shorter half‐lives compared to free ADA, indicating a faster elimination for the complexes compared to the free ADA. In addition, the model quantitatively captured the affinity maturation process of ADA. Time‐dependent affinity maturation resulted in tighter binding between the drug and ADA that pushed the equilibrium towards complex formation and increased drug clearance over time. The cumulative TP dose with repeated TP dosing over a month caused the drug binding affinity of ADA (K _on/K _off) to increase by approximately 100‐fold and 1.2‐fold for the fusion protein and the mAb, respectively. A sensitivity analysis identified A _max (maximum amount of ADA bolus that can be produced), t _lag, and K _complex as the most sensitive model parameters affecting TP concentrations [34].

The model behavior was subsequently explored by simulating a wide range of TP dose levels and the resulting free ADA exposures [34]. The results showed a bell‐shaped curve between the TP dose and free ADA exposures. The authors rationalized this behavior with the following argumentation: When TP dosing is low, the amount of ADA formation increases with the TP dose. Therefore, more ADA is introduced into the system when TP dosing is increased, and the free ADA exposure increases with the TP dose. When the TP dose level is further escalated, the amount of ADA production reaches at some point a plateau regardless of the increase of the TP dose. Excessive drug exposure at the higher TP doses then by far exceeds ADA exposure, thereby forming more ADA‐TP complexes, and by that driving down the concentration of free ADA. This observation shows a saturable relationship between cumulative drug dose and ADA production, which is in agreement with the immunology literature [39, 40, 41].

Ryman et al. also utilized the PK/ADA model to characterize the impact of ADA formation on the PK of a fully human mAb in the presence and absence of immunosuppressive pharmacotherapy in a preclinical study in rats [21]. The results showed that the model adequately described the experimentally determined mAb concentration‐time data and ADA data. All model parameters were estimated with satisfactory accuracy and precision, and the stability of the parameters was validated by a bootstrap analysis. Large interindividual variability with coefficients of variation of 74% and 129% was observed in selected parameters of the ADA section of the model, K _synthesis, which represented the molar rate of ADA moving into the ADA delay compartments, and K _complex, respectively. The high interindividual variability for the K _synthesis parameter was rationalized by the fact that each animal's immune system's response to the mAb is unique, different, and likely polyclonal. The large variability in the K _complex parameter was attributed to an increase in ADA‐TP complex elimination with the increasing magnitude of the ADA response (the clearance in ADA positive animals was 2‐ to 500‐fold higher compared to ADA negative animals). The model was also applied to simulate a hypothetical preclinical toxicology study to inform the total number of animals necessary to establish a safe target exposure range in the presence of ADA formation. This work highlighted the potential benefit of the mechanism‐based modeling approach in the design of appropriately powered preclinical toxicology studies [21].

In conclusion, this PK/ADA model presented a novel approach to study the effect of immunogenicity on TP PK by considering the interaction of ADA and TP with ADA production driven by cumulative TP dose and delayed appearance of ADA in the systemic circulation. The model quantitatively characterized the ADA generation, including maximum ADA response, sensitivity of ADA response to cumulative TP doses, affinity maturation rate, time lag to observe ADA response, and elimination rate for the ADA‐TP complex [21, 34].

One major limitation of this model, however, is the lack of independent experimental validation for the model‐predicted ADA concentrations due to the challenges associated with the measurement of absolute ADA concentrations and affinities [21, 34]. Furthermore, the model did not account for many drug‐ or patient‐related factors that influence immunogenicity, such as size, aggregation status, sequence, and structure of the TP or genetic background of the individual. Therefore, the model is not applicable to informing changes to dosing regimens or co‐therapy in the management of immunogenicity in human patients [21, 34].

4.2. Mechanism‐Based Model of the Immune System for Predicting the Immunogenicity Effects on TP PK

In a first attempt to model the ADA and TP interactions with the immune system, Chen et al. in 2014 developed a mechanism‐based model of the adaptive immune response to predict ADA formation against TPs (designated as the “CHV model”) [35]. This model was based on mass transfer differential equations, included the kinetics of immune cell populations involved in the generation of ADA, and also covered the in vivo disposition of ADA and TP.

The model was divided into subcellular, cellular, and whole‐body systems (Figure 3) [35]:

1. The subcellular level represented antigen presentation by mature dendritic cells (DCs) during which the processing of antigenic TP into T‐epitopes and binding between MHC‐II and T‐epitopes takes place. In this process, TP is endocytosed by DCs and is digested into T‐epitope peptides, which subsequently bind to MHC‐II to appear on the DC surface as T‐epitope–MHC complexes for T‐helper cell activation. The model also included processing and presentation of endogenous competing proteins by DCs to reflect the competition between endogenous peptides and antigenic T‐epitopes for antigen presentation. This model component integrated TP‐specific information, particularly the number of T‐epitopes and MHC‐II binding affinity of T‐epitopes, as well as host‐specific information such as MHC allele genotype, which can all be obtained through in silico or in vitro experiments [42, 43].

2. The cellular level accounted for T‐ and B‐cell kinetics. Through the recognition of T‐epitope–MHC‐II on DCs via the T‐cell receptor, the naïve T‐helper cells become active. The activated T‐helper cells either proliferate and differentiate into functional T‐helper cells or differentiate into memory T‐helper cells. Functional T‐helper cells are responsible for downstream B‐cell activation, whereas memory T‐helper cells can be immediately activated via interacting with mature DCs during a secondary antigen exposure. Upon stimulation from functional T‐helper cells, naïve B‐cells are activated, which recognize antigen through the B‐cell receptor. Activated B‐cells proliferate and differentiate either into short‐lived or long‐lived plasma cells, or into memory B‐cells. The plasma cells synthesize and secrete ADA, which may interact with the TP in plasma, while the memory B‐cells maintain the immune memory and immediately react to a secondary antigen challenge. This model component incorporated TP‐specific parameters such as B‐cell epitope content and antigen‐binding affinity, and host‐specific parameters such as naïve T‐ and B‐cell numbers [35].

3. The whole‐body level accounted for TP in vivo disposition to accurately describe the PK of the TP. It was represented by a two‐compartmental model with linear clearance of free TP and an additional elimination through immune complex formation [35].

FIGURE 3.

Mechanism‐based model for immunogenicity by Chen et al. 2014. The “CHV model” includes structural elements at the cellular, subcellular and whole‐body level, including immune cells, antigen, and anti‐drug antibody to assess immunogenicity generation and its impact on the PK of an antigenic TP. The depicted “CHV model” was updated to include T regulatory cells (Treg adjusted model). AB, activated B‐cells; AMB, activated memory B‐cells; AMT_hlp, activated memory T‐helper cells; AT_hlp, activated T‐helper cells; AT_Reg, activated T‐regulatory cells; FT_hlp, functional T‐helper cells; MB, memory B‐cells; mDC, mature dendritic cells; MS, maturation signal; MT_hlp, memory T‐helper cells; nDC, Naïve dendritic cells; NT_hlp, Naïve T‐helper cells; NT_Reg, Naïve T‐regulatory cells; NB, Naïve B‐cells; P_L, long‐lived plasma cells; P_S, short‐lived plasma cells; Other abbreviations are explained in the legend to Figure 2.

The model simulated the human kinetic profiles for DCs, T‐cells, B‐cells, ADA, and average antigen‐binding affinity of ADA over time for a hypothetical antigen [35]. Simulation results were described as follows:

1. Generation of strong immune response by rapid activation and proliferation of DCs, T‐ and B‐cells that resulted in ADA formation over time [35].

2. Enhanced secondary immune response which resulted in high magnitudes of ADA formation, modeled by lower activation threshold and higher proliferation rate for memory T‐ and memory B‐cells compared to the naïve‐T and naïve‐B cells [35].

3. The average antigen‐binding affinity of ADA increased over time. This was achieved by the interaction of B‐cell epitopes with a polyclonal population of ADA with different antigen‐binding affinities. For example, B‐epitopes with higher binding affinity to the antigen produced ADA with higher average affinity over time [35]. These results were consistent with the “affinity maturation” phenomenon as previously discussed in the PK/ADA model.

4. A bell‐shaped antigen dose‐ADA response curve showed a saturable relationship between the variables and aligned well with the observations from the previously discussed PK/ADA model and the immunology literature [39, 40, 41].

This model was applied to predict the immunogenicity for a fully human mAb, adalimumab, in various inflammatory and autoimmune disease patient populations under chronic dosing, considering adalimumab‐specific and patient‐specific information as described above [44]. The model simulated ADA and adalimumab concentration‐time profiles for 1000 patients that were dosed with 40 mg adalimumab subcutaneously every 2 weeks for 574 days. The patients were stratified according to the number of strong T‐epitope‐MHC binding pairs. Simulation results showed that there was a statistically significant increase in ADA concentration with the increase in the number of T‐epitope‐MHC binding pairs, which suggested a significant impact of the number of T‐epitope‐MHC complexes on the ADA response. The model predicted ADA‐concentration time profiles suggested 75.3% of the simulated patient population would develop ADA after 574 days of drug treatment. The model was further utilized to simulate the reduction in adalimumab exposure due to ADA emergence. The cutoff values for adalimumab trough concentration were chosen at 1/2, 1/5, 1/10, 1/20, and 1/50 of the average drug concentration in patients who carry zero T‐epitope‐MHC binding pairs and thus do not develop ADA. The model derived adalimumab concentration‐time profiles suggested that up to 70% of the patients can have a two‐fold reduction, and 26.4% of the patients can experience a severe (50‐fold) reduction of the adalimumab trough concentration after 574 days. The model predicted the overall trend of lower adalimumab concentrations in ADA‐positive patients compared to ADA‐negative patients was in agreement with published clinical trial observations [45]. The model, however, slightly overpredicted the ADA incidence (75.3%) compared to the literature reported range of 5%–89% in clinical trials with adalimumab [46, 47, 48].

The authors suggested several confounding factors that could have resulted in large variations between the model simulations and the clinical observations. The different sizes, duration, and dosing regimens of the clinical studies, together with the ADA assay format, its sensitivity, and drug tolerance, could potentially affect the ADA assessment. Patient‐related variability, such as population genetic background (e.g., MHC allele frequencies), disease indication, immune status, and comedications such as immunosuppressive compounds, are additional factors that further complicate the ADA predictions and can partially contribute to the discrepancy between the clinical trials and the current model simulated ADA data [44]. A sensitivity analysis revealed that ADA kinetics were sensitive to model parameters involved in activation, proliferation, and differentiation of T‐cells and B‐cells, number and MHC binding affinity of T‐epitopes, and T‐cell–B‐cell interactions [35, 44].

In summary, this model was unique with respect to the preceding models of immunogenicity in that it linked in silico peptide sequence‐based T‐epitope predictions and in vitro T‐epitope‐MHC binding predictions to downstream T‐ and B‐cell interactions required for ADA formation, and integrated these components into a drug disposition model to evaluate the impact of ADA on TP PK [35]. The model reasonably reproduced many immunological phenomena related to immunogenicity such as memory immune response, saturable TP and ADA kinetics, and ADA affinity maturation [35].

Following its publication, this model was further utilized and refined by several others to predict immunogenicity in clinical settings. Hamuro et al. in 2019 integrated a previously developed target‐specific population PK model for a phase 1 Fc‐fusion protein (ATI‐1465) with the CHV model to predict ADA formation for ATI‐1465 [49]. The model reasonably predicted the ADA concentration‐time profile for ATI‐1465 after a single dose, but overpredicted ADA concentration‐time profiles after multiple dosing. In response, the authors made further improvements to the CHV model by adding T‐regulatory (Tregs) cells to reduce the ADA overprediction bias after multiple dosing. Tregs were included downstream from antigen presentation and were induced in parallel to activated T‐helper cells, representing a more realistic biological scenario (Figure 3). They were shown to interfere with the ability of activated functional T‐helper cells and activated memory T‐helper cells to proliferate (Figure 3). Inclusion of Tregs resulted in reduced ADA overprediction with a relative decrease in the predicted ADA incidence rate of 21.5%–59.3% across multiple dose levels, and model predictions were comparable to the observed data [49]. The model predicted that there was no impact of ADA formation on PK in multiple dose cohorts and these results were also consistent with the clinical observations. The authors further utilized the “Treg adjusted CHV model” to simulate ADA incidence for a prospective phase 2 trial including co‐medication effects in the form of corticosteroid induced immunosuppression. The immunosuppressive effect of corticosteroids on lymphocyte proliferation was included in the model [49]. A 20 mg oral dose of prednisolone (approximately 0.75 mg/kg/day for a 27 kg pediatric patient) was used in the simulations. Based on an IC₅₀ of 51.4 nM for prednisolone's inhibition of lymphocyte proliferation and average steady‐state free plasma concentrations of 30–40 nM in adults, corticosteroid effects were modeled as a 25% and 50% reduction in activated lymphocyte proliferation, which aligned well with clinical observations [49]. This work demonstrated the potential utility of mechanism‐based modeling approaches to predict ADA during different stages of clinical drug development [49].

Ryman et al. in 2019 used the “Treg adjusted CHV model” to identify the immunogenicity risk of various approved therapeutic mAbs based on the presence of foreign T‐cell epitopes in their amino acid sequence and the number of non‐self T‐epitope‐MHC binding pairs [50]. The results illustrated that the model adequately captured the impact of non‐self T‐epitope‐MHC binding pairs on immunogenicity incidence rates in patient populations for several mAbs. mAbs such as trastuzumab and alirocumab with minimal non‐self T‐epitope‐MHC clusters were shown to lack clinical immunogenicity and related effects on the PK (Table 1). In contrast, mAbs with a greater number of non‐self T‐epitope‐MHC clusters including, infliximab, adalimumab and bococizumab were associated with higher rates of ADA incidence that aligned well with the reported ADA incidences in the clinic (Table 1). The ADA development resulted in confounding impact on the respective mAb PK profile as shown in table 1 [50].

TABLE 1.

Predicting immunogenicity risk of therapeutic monoclonal antibodies based on the number of non‐self T‐epitope‐MHC binding pairs.

Therapeutic protein	Number of T‐epitope‐MHC clusters	Observed immunogenicity in % patient population	Model‐predicted immunogenicity in % patient population	PK impact in % patient population
Trastuzumab	0	0.11%	0%	0%
Alirocumab	1	5.5%	0%	0%
Infliximab	3	36%–61%	87%	70%
Adalimumab	3	12%–95%	92%	89%
Bococizumab	2	55%	36%	29%

Weathered et al. in 2023 further utilized the CHV model and performed a meta‐analysis of clinical studies to find a consistent trend of the effect of immunomodulatory co‐medications like methotrexate on the immunogenicity incidence of adalimumab [51]. Methotrexate was incorporated into the model to have an inhibitory effect on T‐ and B‐cell proliferation rates. ADA incidence was compared between the clinical studies where subjects received either adalimumab alone or in combination with methotrexate. The results showed that treatment with methotrexate decreased the ADA incidence on average by 60% compared to the treatment with adalimumab alone, and these results aligned well with the published clinical observations [52, 53]. Previously published PK/PD models of methotrexate were unable to adequately predict this substantial change in ADA incidence [51]. This underlines the potential advantage of mechanism‐based models over classic PK/PD models of methotrexate in predicting this decrease in immunogenicity [51]. While the model was successfully applied to predict the impact of methotrexate on ADA formation, it is important to note that the effects of different immunosuppressive agents can vary depending on their mechanism of action, potency, and inhibitory concentration.

While the above CHV model applications have until now only utilized the model to predict immunogenicity in humans, species‐specific parameters from preclinical animals can also be integrated into the model to simulate immune responses in animals as well since immunogenicity depends on both the antigenic properties of the TP and the immunological environment of the host [35]. The CHV model thus addresses one of the limitations of the previously discussed “PK/ADA” model [34].

While the current model has shown utility in predicting ADA for TPs including mAbs and Fc fusion proteins, there are several model assumptions and limitations that set the scope for additional future improvements:

1. Plasma was modeled as the space for all immune reactions by assuming that lymphocytes move fast between lymph organs and the blood. Thus, the model did not account for the interactions that ideally take place in lymphoid organs such as spleen, lymph nodes, and bone marrow, where TP concentrations may not be reflective of plasma levels [35, 49].

2. The model represented a healthy individual with classical innate and adaptive immune responses and did not account for deviations in immune response that may arise from disease conditions or impaired immune status of the individual [49].

3. The model assumed the predicted T‐epitopes and their MHC binding affinities from the in silico or in vitro experiments translate to the in vivo situation. This may account for errors in the ADA predictions as differences were previously reported between the number of T‐cell epitopes predicted by the in silico methods and the observed rates of clinical ADA incidences [43, 49, 54].

4. No immunomodulatory cytokines were included in the model [35, 49].

5. The model predicted ADA concentrations cannot be directly compared to experimental results as ADA measurements are limited to semi‐quantitative assessments [49].

4.3. Quantitative System Pharmacology Model to Predict and Manage Immunogenicity of TPs

The development of a mechanism‐based model of the immune system by Chen et al. 2014 opened up new avenues towards prediction of the impact of ADA formation on PK of TPs in patient populations considering a number of important factors related to the management of immunogenicity, including TP properties, patient characteristics, and the effects of concomitant therapy [35]. Extending the model of Chen et al., an immunogenicity simulator (abbreviated as the “IG simulator”) was developed that coupled the CHV model with a physiologically based pharmacokinetic (PBPK) model of TPs [55]. It considers cell circulation, ADA and TP distribution between plasma, vascular space, and lymph compartments, thereby overcoming the first limitation of the CHV model where plasma was modeled as the space for all immune cells to reside in and interact with the TP [35]. The IG simulator could integrate a variety of input data such as TP sequence, in vitro and in silico assay predictions, patient and demographic parameters, and actual clinical data to simulate concentration‐time profiles of TP and ADA for virtual patients as well as whole trial populations [55]. For example, it has been used to perform a virtual trial simulation of adalimumab to simulate a clinical trial in a European population. The simulations were carried out in 500 virtual subjects who received 40 mg of adalimumab every 2 weeks divided into three groups based on the amount (titer) of ADA formed, that is, low, medium, or high. The model simulations described the clinical data with reasonable accuracy in all three groups to inform immunogenicity management in patients [56]. The model is being further improved to serve as a platform to guide decision‐making across various TPs and novel modalities, including bispecifics and biosimilars [56].

5. Conclusions

Immunogenicity, particularly ADA formation against the TP, is a major challenge in drug development and patient care. Immunogenicity assessment and prediction practices have become increasingly more prevalent. The bioanalytical characterization of ADA; however, faces various physiological and assay‐related limitations which significantly hinder its interpretation. Therefore, various pharmacostatistical and mechanism‐based mathematical models have been developed as a complementary approach to clinical experiments and are increasingly used to assess and explore ADA formation in preclinical species and/or humans and may be applied toward differentiating TP candidate compounds or selecting the appropriate TP dose level with minimal immune response. With further improvements that address current model limitations, these models are likely to rapidly gain an increasing role in predicting immunogenicity in drug development by quantitatively integrating therapeutic protein‐, host‐, and species‐specific information from in silico, in vitro, preclinical, and clinical studies.

Conflicts of Interest

J.T.R. is an employee of EMD Serono and owns EMD Serono stocks. V.J. is an employee of Bristol Myers Squibb and owns Bristol Myers Squibb stocks. All other authors declared no competing interests for this work.