Time-dependent clearance can confound exposure-response analysis of therapeutic antibodies: A comprehensive review of the current literature.

INTRODUCTION

Exposure–response (ER) analysis is a fundamental tool in clinical pharmacology to optimize dose and dose regimens during clinical development. 1 By measuring drug concentration in patients in clinical trials and relating drug exposure to efficacy and safety outcomes, one can infer whether an increased dose may offer improved efficacy, or a decreased dose may reduce occurrence of adverse events. The traditional approach to ER analysis presumes that doses drive drug exposure which in turn drives drug response (Figure 1 ). This implies that the relationship between exposure and response allows for determination of an optimal dose which maximizes efficacy and minimizes toxicity. This paradigm is frequently successful in the development of small molecule drugs which often show higher exposure variability and less confounded ER relationships compared to biologics. ER analysis of therapeutic antibodies can be confounded by the influence from time‐dependent pharmacokinetics (PK) and other baseline prognostic patient factors, which results in departure from what is anticipated from traditional ER analysis and causes difficulty in dose optimization. Uncertainty around the optimal dose is a frequent cause of regulatory delay and denial of drug approval in late‐stage clinical development, 2 suggesting that greater focus on dose optimization prior to initiation of registrational trials will improve the probability of regulatory approval and success.

ER analysis of monoclonal antibodies has been fraught with confounding factors that obscure the true ER relationship and complicate accurate dose optimization. 3 In the ToGA (trastuzumab for gastric cancer) phase III gastric cancer trial, patients were given a single dose level of trastuzumab, an anti‐HER2 monoclonal antibody, and a post hoc ER analysis identified shorter overall survival and lower rate of objective response among patients with the lowest trough drug concentration. 4 These results suggested that an increased dose would raise the trough concentration and offer a survival benefit to these patients. This motivated the subsequent HELOISE postmarketing study evaluating a higher dose of trastuzumab by randomizing patients to receive either the established dose or an increased dose selected by population PK model simulation. 5 Despite higher drug exposure with the increased dose, no improvement in efficacy was observed. The confounded ER relationship identified in ToGA was later attributed to a link between trastuzumab clearance and baseline patient characteristics related to disease severity. Patients with poor prognostic factors and more severe disease typically had higher trastuzumab clearance associated with lower drug exposures. An enrichment of patients with poor baseline prognostic factors associated with both faster drug clearance and greater risk of disease progression confounded the ER relationship derived from the ToGA study. Similarly, an ER analysis of tremlimumab, a monoclonal antibody specific to human cytotoxic T‐lymphocyte‐associated antigen 4 (CTLA‐4), found a relationship between drug clearance and overall survival. 6 This finding motivated a clinical study to evaluate a higher dose that ultimately did not translate to improved efficacy. 7 Post hoc analysis identified several potentially confounding baseline patient factors that influence both drug clearance and response, including tumor size, C‐reactive protein (CRP), and sex. Dose optimization of trastuzumab and tremilimumab represent examples where large randomized trials found no benefit of an increased dose and confirmed that earlier ER analyses were misleading due to the association between drug clearance and disease severity. However, confounded ER relationships have also been identified during analyses of many other therapeutic antibodies prior to evaluating an increased dose, and the underlying cause has been attributed to both an enrichment of poor prognostic factors in patients with faster clearance at baseline, 8 , 9 , 10 and reduction in clearance over time in responding patients. 11 , 12 , 13 , 14 , 15 , 16 This complex relationship between disease severity and systemic clearance of therapeutic antibodies can lead to spurious ER findings, prompting costly clinical studies to evaluate higher doses that fail to provide patient benefit.

The connection between disease severity and drug exposure is a direct consequence of the mechanisms of antibody clearance. Unlike small molecules that are eliminated largely by drug‐metabolizing enzymes in the liver, therapeutic antibodies are eliminated primarily by proteolytic degradation to amino acids within lysosomes in cells. Antibodies enter the cell by either nonspecific fluid uptake in catabolic cells or receptor‐mediated endocytosis in cells expressing the drug target. These elimination pathways are influenced by many factors associated with disease severity including tumor size, target cell counts, albumin, performance status, and lactate dehydrogenase (LDH). 17 As such, patients with more severe disease showing poor prognostic markers at baseline frequently have more rapid antibody clearance. Moreover, many of these factors can evolve over the course of treatment as tumor burden decreases and health status improves, resulting in a time‐dependent reduction of clearance in patients who respond to therapy. 18 Patients who respond to therapy may show greater exposure not because the higher exposure induced a response, but rather clearance was lower from the beginning due to less severe disease at baseline or clearance declined as a result of disease improvement. Both of these factors contribute to the confounding effect of disease status. The result is a tangled web of potential causative relationships between exposure, response, drug clearance, and prognostic patient factors that gives rise to apparent but often spurious ER relationships (Figure 1 ). Therefore, characterization of time‐dependent clearance of therapeutic antibodies is a critical step in understanding the confounding factors in ER analysis and accurately identifying an optimal dose.

The US Food and Drug Administration (FDA) recently initiated Project Optimus, an effort to communicate expectations and develop strategies for dose optimization in oncology. 19 Oncology drugs are frequently advanced to registrational trials at the maximum tolerated dose without further dose optimization despite many examples where a higher dose failed to demonstrate greater clinical benefit and caused a higher incidence of adverse effects. 20 Project Optimus urges drug developers to focus on identifying the optimal dose that maximizes efficacy while minimizing toxicity at an earlier stage. A recent working group recommended several strategies to identify an optimal dose prior to phase III, including randomized evaluation of two or more doses in phase II, use of pharmacokinetic/pharmacodynamic (PK/PD) modeling and simulation, and evaluation of the impact of confounding factors in ER analysis. 21 A recent FDA guidance on dose optimization in oncology specifically urges developers to undertake a study with multiple randomized dosages prior to initiating registrational trials. 22 These approaches aim to account for and disentangle the complex relationships between dose, exposure, response, and disease severity. With the increase in the stringency by which dose and dose regimens are identified for oncology treatments, a greater focus on dose optimization that accounts for confounding baseline and time‐dependent factors of disease status will be essential to avoid common pitfalls and ensure regulatory success.

While both baseline and time‐dependent patient factors of disease status can confound ER analysis of therapeutic antibodies, time‐dependent effects have received comparatively less attention and require more specialized analytical techniques to characterize them. This review assesses the impact of changes in disease state over time on drug clearance of antibodies and the resulting challenges in accurate dose optimization. We summarize time‐dependent clearance observed across published population PK analyses of therapeutic antibodies, review the mechanisms by which it arises, describe the modeling and simulation techniques used to characterize it, and evaluate its impact on interpretation of ER analyses. Additionally, we characterize the magnitude, time scale, and incidence of time‐dependent clearance associated with its underlying mechanisms. While time‐dependent clearance has been reviewed previously, 23 we intend to provide a more comprehensive and updated review on this phenomenon, as data for a significant number of new compounds have been reported since this review. In addition, we present detailed information on compounds not only used in oncology indication but also non‐oncology indications. Since the previous review, the number of compounds reporting time‐dependent clearance has increased by 4.4‐fold (7 vs. 31) for oncology and 3.3‐fold (3 vs. 10) for non‐oncology indications, increasing the available information by 4.1‐fold (10 vs. 41). Finally, efforts are made to provide a detailed examination of trends between the quantitative changes in CL and the responsible mechanisms.

MECHANISMS OF ANTIBODY ELIMINATION

Unlike small molecule drugs, the disease state can influence elimination mechanisms of therapeutic antibodies. Therefore, a therapeutic antibody's activity on disease status can have a significant influence on its own clearance and exposure. Antibody drugs are eliminated primarily through intracellular proteolytic catabolism in lysosomes by either nonspecific or receptor‐mediated pathways. 18 Many cells engulf extracellular fluid into vesicles by pinocytosis, nonspecifically internalizing any proteins dissolved in the engulfed fluid. The vesicles fuse with early endosomes, mature into late endosomes, and eventually fuse with lysosomes where the acidic environment and hydrolytic enzymes digest proteins to amino acids. 24 Endothelial cells lining the vasculature and hematopoietic cells in the blood are primarily responsible for clearance of therapeutic antibodies by nonspecific catabolism due to their high rate of pinocytosis, prevalence, and accessibility to plasma. 25 The neonatal Fc receptor (FcRn) prolongs the half‐life of gamma immunoglobulins (IgG, the most common subtype among therapeutic antibodies) in the serum by rescuing them from endosomes and recycling them to the extracellular space 26 (Figure 2 ). FcRn binds to the fragment crystallizable (Fc) portion of the antibody with high affinity in the acidic environment of endosomes and localizes to a recycling endosome that is returned to the cell surface where it releases bound antibodies at physiological pH of the plasma. 27 FcRn‐deficient mice show drastically reduced serum IgG levels and rapid elimination of administered antibodies. 26 The rate of nonspecific uptake by pinocytosis is proportional to the concentration of the antibody in the plasma, and is not a saturable process, so it manifests as linear PK.

In addition to nonspecific catabolism, antibodies are eliminated by target‐mediated drug disposition (TMDD), where antibodies bound to their target receptor are internalized by endocytosis and degraded in the lysosome (Figure 2 ). TMDD is a saturable process that reaches a maximum rate of elimination when all receptor binding sites are occupied, and typically results in dose‐dependent nonlinear PK. At higher drug concentration, total clearance declines as nonlinear elimination saturates. In cases where the antibody is administered at sufficient dose to saturate the target, the impact of TMDD is typically minimal relative to nonspecific catabolism and the PK appear linear. The effect of TMDD is more pronounced when the antibody has high affinity to a membrane‐bound target, and the target has high expression level, broad distribution of target cells, and rapid internalization. 28 Soluble antibody targets usually do not result in TMDD because the antibody–antigen complex is not membrane‐bound, and therefore is not readily internalized. 29 However, some soluble multimeric targets form large antibody–antigen immune complexes containing many antibodies that are rapidly cleared through binding and internalization via the Fcγ receptor on innate immune cells, resulting in saturable receptor‐mediated elimination. 30 Time‐dependent clearance of therapeutic antibodies can be driven by changes over time to both specific and nonspecific clearance pathways through several mechanisms.

MECHANISMS OF TIME‐DEPENDENT CLEARANCE

Cachexia is an inflammatory condition that occurs in patients with advanced cancer and is associated with increased catabolic elimination of antibodies and other proteins. The symptoms of cachexia manifest as a pronounced loss of body mass, anorexia, general inflammation, muscle‐wasting, and decreased quality of life. 31 Tumors secrete many proinflammatory cytokines that increase tumor growth and promote cachexia. 32 These cytokines precipitate systemic effects in several organ systems, including increased catabolism in muscles, induction of anorexia and depression in the brain, and endocrine dysfunction. Moreover, inflammation associated with cachexia leads to increased catabolic activity and more rapid turnover of serum proteins, 33 causing greater catabolic elimination of antibodies. Hypoalbuminemia is a marker of cachexia due to increased catabolic elimination of albumin in cachectic patients, and serum albumin levels are frequently inversely associated with clearance of therapeutic antibodies. 18 The prevalence of cachexia among people with cancer ranges between 40% and 80%, and it is a marker of poor prognosis and a direct cause of approximately 20% of cancer deaths. 34 Cachexia correlates with shorter survival in several cancer types, 35 , 36 , 37 and signs of cachexia at baseline have been shown to be predictive of treatment resistance. 38 , 39 Disease improvement due to treatment response can ameliorate cachexia, simultaneously reducing systemic clearance of therapeutic antibodies with time. 40 This results in a time‐dependent increase in drug exposure that is more pronounced among responding patients as their underlying disease and cachexia improves.

Patients with autoimmune and inflammatory diseases often have high systemic inflammation that can similarly be associated with antibody clearance. 41 The mechanisms that mediate increased catabolic activity in these diseases likely resemble those caused by cachexia‐related inflammation in cancer. Therapeutic antibodies that treat inflammatory diseases reduce systemic inflammation and can in turn reduce drug clearance over time by improvement of the underlying disease. 42 , 43 Because the time‐dependent effects are the result of disease improvement, the greatest increases in exposure are expected in patients who respond to treatment. An observed ER relationship could therefore materialize not because higher exposure increases the probability of a response, but instead because declining clearance in responding patients increases their exposure. Furthermore, the ER relationship may shift over time as clearance evolves in response to treatment, and conclusions may differ when using data from earlier versus later timepoints. The onset of time‐dependent clearance will dictate when this transition occurs, and characterization of time‐dependent clearance is necessary to understand its influence on ER analysis.

TMDD of antibodies often exhibits a time‐dependent profile. The magnitude of elimination by TMDD of an antibody drug is proportional to the distribution of target‐expressing cells and expression level of the target. Many antibody drugs, such as those that treat cancer, substantially deplete target cells over time. 11 An objective response to cancer drug treatment is defined as a reduction in tumor burden from baseline below a predefined threshold, so a decline in cells expressing the target receptor over time is observed in responding patients. This results in a reduction in TMDD and total drug clearance, and a potential explanation for higher exposure among patients who respond. The time‐dependent effect is likely to be dose‐dependent, and antibodies administered with a sufficient dose to saturate the target will exhibit linear PK without substantial time‐dependence. Furthermore, antibodies whose mechanism does not deplete the target cells or target molecules will likely not demonstrate time‐dependent clearance by this mechanism.

SURVEY OF TIME‐DEPENDENT CLEARANCE AMONG APPROVED THERAPEUTIC ANTIBODIES

In this study, we conducted a comprehensive review of time‐dependent PK reported in population PK analyses among 158 monoclonal antibodies and antibody drug conjugates included in the Antibody Society's list of antibody therapeutics approved or in regulatory review. 44 All estimates of time‐dependent clearance were gathered from original research publications or regulatory reports using population PK modeling. PK analyses for each antibody were manually searched within the literature, the US FDA's Drugs@FDA database, and the European Medicines Agency website. Time‐dependent clearance was reported for 41 antibodies (26% of all antibodies approved or in review), and therefore is a common phenomenon. No published population PK analysis was available for 48 antibodies, the absence of a time‐dependent effect was reported for 17 antibodies, and time‐dependence was not discussed for 52 (Figure 3a ). It is unknown how many of the latter analyses evaluated time‐dependent clearance, found it was not significant, and chose not to discuss it. In many cases, patients who do not respond to therapy drop out of the study, introducing a bias in the patient data. This may impede the estimation of time‐dependent clearance because the increasing clearance associated with disease progression is not included in any potential analyses. This is a potential explanation as to why time‐dependent clearance could be underreported among some antibodies.

Most antibodies that showed time‐dependent clearance were first approved for cancer (76%, 31/41), while nine were approved for inflammatory or autoimmune diseases, and one for cardiology (Figure 3b ). Anticancer antibodies more frequently showed time‐dependent clearance, comprising 76% of those with time‐dependent clearance, but 44% of all antibodies considered in this review. Many anticancer antibody drugs deplete target cells and reverse cachexia during treatment, resulting in potential time‐dependent clearance by multiple mechanisms. Likewise, some antibodies that treat inflammatory and autoimmune disease deplete target immune cells, and many reduce systemic inflammation, potentially causing a decrease over time in both nonspecific and target‐mediated clearance. No antibody for treatment of infectious disease showed time‐dependent clearance. While elimination of an infection would reduce systemic inflammation often associated with increased antibody clearance, changes in drug clearance are likely difficult to be observed over the relatively short course of an acute infection or during prophylactic treatment. Similarly, antibodies in neurology did not show time‐dependent clearance. Most antibodies in this therapeutic area target small soluble peptides, do not deplete target cells, and do not regulate systemic inflammation, so they are not prone to the common mechanisms of time‐dependent clearance.

Antibody PK was described using a two‐compartment model in 92% of population PK analyses that included time‐dependent clearance. A two compartment‐model is the typical model used to describe antibody PK since it captures the initial distribution phase followed by the elimination phase often seen in antibody concentration–time profiles. Only five analyses used a one‐compartment model, several of which were fitted to data from subcutaneous dosing where the distribution phase can be obscured by the overlapping absorption phase. Linear clearance alone was used in 71% of models, while parallel linear and nonlinear elimination was used in 29%. The time‐dependent model parameter was linear clearance in 83% of models and was a nonlinear elimination parameter in the remaining 17% (maximal rate of nonlinear elimination, V max ; concentration of half‐maximal nonlinear elimination, K m ; or receptor level). Therefore, time‐dependent clearance frequently occurs in the absence of observed nonlinear elimination and is most commonly described using linear models.

Many analyses provided a mechanistic interpretation of the time‐dependent effect: 19 were attributed to disease improvement (cachexia or systemic inflammation) over time, 25 were attributed to reduction in TMDD, and 20 analyses did not state an interpretation or offered multiple potential explanations (Table 1 ). Analyses of oncology and inflammatory disease populations attributed time‐dependence to TMDD (37% vs. 31%) and disease improvement (30% vs. 31%) with similar frequency. Moreover, the median decline in clearance was 22% in inflammatory disease and 28% in oncology, suggesting that the effect is comparable between therapeutic areas (Table S1 ).

Time‐dependent clearance attributed to cachexia or inflammation typically demonstrated a median 21% decrease (interquartile range [IQR]: 15%–25%) in linear clearance and median 13 (IQR: 8–15) weeks to half‐maximal change (Figure 3c,d ). This was observed frequently for immune checkpoint inhibitors for treatment of cancer, which are largely dosed in the linear range and thus have little impact from TMDD on exposure. Patients who respond to therapy show a decrease in markers of cachexia, and a subsequent decrease in nonspecific catabolic clearance of the drug. A population PK analysis of nivolumab, an anti‐PD‐1 antibody, found that the time‐dependent effect on linear clearance varied based on the patient response: those with a partial or complete response had the greatest decrease in clearance and increase in exposure over time. 12 A similar phenomenon of decreased clearance in responders was observed for pembrolizumab, another anti‐PD‐1 antibody. 16 A population PK analysis of durvalumab, an anti‐PD‐L1 antibody, directly connected changes in linear drug clearance to markers of disease status over time including serum albumin and tumor size, 40 showing that clearance correlates over time with changes in markers of cachexia, and providing evidence that clearance changes were the result of disease improvement.

Time‐dependent clearance attributed to TMDD demonstrated more pronounced reductions in drug clearance (median: 62%, IQR: 43%–87%) with a shorter time to half‐maximal change (median: 3 weeks, IQR: 1–12 weeks) compared to those caused by cachexia or systemic inflammation (Figure 3c,d ). This mechanism was observed more frequently in antibodies for treatment of hematological cancer due to wide distribution of target cells and high expression of target receptors. Drug treatment results in killing of target cancer cells, a consequent reduction in receptor expression, and ultimately a decline in TMDD over time. Rituximab, an anti‐CD20 antibody for treatment of B cell malignancies, showed an 87% decrease in clearance which was described by an exponential decay with a half‐life of the change in clearance of 17 days in patients with chronic lymphocytic leukemia. 11 Interestingly, the change in clearance occurred over a slower time scale than the decline in B cells in the blood, suggesting that a significant portion of the TMDD is caused by B cells in the tissue, and their depletion requires more time than those circulating in the blood. Similarly, an analysis of obinutuzumab, another anti‐CD20 antibody for treatment of chronic lymphocytic leukemia and non‐Hodgkin's lymphoma, found that the reduction in clearance occurred more slowly than the observed decline in circulating B cells. 64 This complicates construction of a more mechanistic model that connects the time‐dependent clearance to blood biomarkers of cancer cell burden, and the phenomenon must be described using an empirical approach. A population PK analysis of polatuzumab vedotin, an anti‐CD79b antibody drug conjugate for treatment of non‐Hodgkin's lymphoma, described its time‐dependent clearance by two processes: one fast‐ and one slow‐acting. 85 The fast process was described by an exponential decline with a half‐life of 6.3 days and was attributed to a rapid depletion in target‐expressing cells and thus a decline in TMDD. The slow time‐dependent change in clearance was described by a sigmoidal function with a time to half‐maximal change of 3.5 months and was attributed to a decrease in nonspecific clearance due to improvement in health status. This analysis suggests that time‐dependent antibody clearance could be caused simultaneously by changes in target‐mediated and nonspecific clearance at different time scales. It is unlikely this dual‐mechanism model structure was frequently evaluated for other antibodies, so this phenomenon may be underreported and warrants investigation in future population PK analyses.

POPULATION PK MODELING OF TIME‐DEPENDENT CLEARANCE

Population PK methods are often used to estimate exposure for ER analysis due to their robustness to sparse blood sampling that is frequently used in late‐stage clinical trials. Furthermore, these methods quantify typical PK characteristics across patients, including time‐dependent clearance, nonlinear clearance, and influential patient factors, revealing potential confounding effects that may be faced in subsequent ER analysis. The population PK approach describes the PK profile over time by a system of ordinary differential equations representing the rate of change in drug concentration due to drug absorption, distribution, and elimination. The variability between patients in each model parameter is incorporated as a random effect in a nonlinear mixed effects model allowing estimation of the profile of a typical patient in addition to the interindividual spread. Time‐dependent clearance is captured by incorporating a function of time into the clearance expression using several mathematical approaches, including empirical models, mechanistic models, and semi‐mechanistic time‐dependent covariates. While empirical methods are more descriptive of the observed data, mechanistic models connect the changing clearance to underlying biology and provide insight into the processes that govern it. However, estimation of all these models is reliant on the available patient data, which can be biased by earlier dropout of patients who do not respond to therapy.

Empirical models

Empirical models of time‐dependent clearance seek to describe the magnitude and time scale of the change in clearance over time without directly establishing an interpretation of its cause. The clearance parameter is adjusted in the model equations by a smooth mathematical function of time, such as exponential decay or a sigmoidal function. This approach is unbiased and effective for exploratory assessment of the PK profile without the need for extensive biomarker data that explain the change in clearance. In many cases, a reliable biomarker of time‐dependent clearance may not be known and therefore the empirical approach is necessary. Despite their flexibility, empirical approaches typically apply a monotonic function over time, and therefore fail to capture more complex patterns, such as an initial decline in clearance followed by later increase when a patient progresses. Of the population PK analyses surveyed, 22 used an empirical exponential decay model, 21 used an empirical sigmoidal model, and seven used other empirical models.

Empirical models using exponential decay describe drug clearance that rapidly decreases from an initial value to a terminal value according to an exponential rate constant. It is best suited for changes in clearance that begin immediately after the first dose because the exponential decay function cannot describe any time delay in the change in clearance (Figure 4 ). It is typically fitted with three parameters (Equation 1 ): the terminal clearance (CL inf ), the time‐dependent portion of the clearance (CL T ), and the rate constant of the exponential decay ( k des ). The time to half‐maximal change in clearance is estimated by ln 2 k des , and the clearance at time zero is described by CL inf + CL T . Population PK analyses that attributed time‐dependent clearance to TMDD frequently used exponential decay models to describe the effect, including rituximab, 11 ocrelizumab, 73 and gemtuzumab ozogomicin. 82 This suggests that changes in TMDD tend to begin immediately after the first dose of the antibody. While most analyses apply exponential decay to linear clearance (CL), several used a similar approach for nonlinear elimination parameters. A population PK analysis of daratumumab included parallel linear and nonlinear elimination pathways, and the rate of maximal nonlinear elimination ( V max ) was described with an exponential decay function to capture the decrease in TMDD after dosing. 59 A similar approach was used to describe the decrease in V max of inebilizumab, 91 and the rate of receptor synthesis ( k syn ) of ofatumumab 72 over time.

While exponential models describe an immediate change in clearance, sigmoidal models are more flexible and can describe changes in clearance that occur on a longer time scale (Figure 4 ). This approach is commonly estimated with four parameters (Equation 2 ): the initial clearance (CL 0 ), the maximal fold change in clearance over time ( I max ), the time to half‐maximal clearance (TI 50 ), and the Hill slope (γ). The drug clearance converges to CL 0 × exp I max at later timepoints ( t >> TI 50 ), where the steepness of the transition is determined by γ. Sigmoidal models were used frequently in population PK analyses that attributed time‐dependent clearance to improvement in health status (specifically reduction in cachexia or systemic inflammation), as changes in clearance were typically observed after 8–15 weeks and would not fit well to an exponential decay function. For example, a population PK analysis of dostarlimab, an anti‐PD‐1 antibody, characterized time‐dependent clearance using a sigmoidal model with a TI 50 of 108 days and a 15% maximal decrease. 50 Similarly, a population PK analysis of cemiplimab, an anti‐PD‐1 antibody, used a sigmoidal model and estimated a TI 50 of 74 days and 16% maximal decrease in clearance. 10

Several population PK analyses used a simpler mathematical approach with fewer parameters than the exponential decay or sigmoidal models, likely to avoid parameters with poor identifiability. Models using a piecewise step function can be described by three parameters: the clearance before (CL 1 ), and after (CL 2 ), and an instantaneous change point ( t c ) (Equation 3 ). A population PK analysis of the antibody drug conjugate moxetumomab pasudotox employed this approach to describe rapid clearance at baseline, followed by an instantaneous 85% decrease in clearance at 48 h. 81 Under this model, clearances change instantaneously rather than via a smooth transition from initial to final clearance as in a sigmoidal or exponential decay model. An analysis of the antibody drug conjugate trastuzumab deruxtecan described a continual decrease in clearance using a power function of the dosing cycle resulting in a decrease of 45% by cycle 20. In cases of clinical studies with sparse PK sampling or short duration, it is more difficult to describe the full time‐course of the change in clearance, and a simple model with fewer parameters may be more appropriate.

Mechanistic models

Some models directly incorporate biological processes that quantitatively describe the mechanism of time‐dependent clearance. Because these models include a mechanistic hypothesis, they can be applied to understanding the underlying causes and influential factors of time‐dependent clearance. For the purpose of this review, any model that explicitly characterized the trajectory of longitudinal PD markers, such as the target receptor concentration, tumor size, or target cell burden, in addition to the drug concentration were considered mechanistic, and only five models met this definition. 54 , 62 , 68 , 71 , 72 The mechanistic approach is less common than empirical models due to the difficulty of identifying a secondary process or biomarker that accurately describes the time‐dependent clearance and the challenge of fitting more complex models to the available data. Additionally, development of biomarker assays and collection of additional data from all patients increases the cost and logistical burden of clinical trials.

A population PK analysis of ofatumumab, an anti‐CD20 antibody for treatment of B cell malignancies, modeled the time‐varying target level in addition to drug concentration over time. 71 The model bidirectionally describes the rate of drug elimination proportional to the target burden, and the depletion of target proportional to the drug level (Figure 5 ). By including a dynamic target burden component in the model, it captured the reduction in elimination over time observed in the data and how it differed between different B cell malignancies. Although the model was not fitted to the post‐baseline B cell burden, the model‐estimated target burden agreed with the trend in observed B cell counts over time. While patients with chronic lymphocytic leukemia (CLL) had higher circulating B cell levels in the blood, patients with follicular lymphoma (FL) showed greater TMDD compared to CLL relative to the circulating B cell level, potentially reflecting the greater accumulation of neoplastic cells in lymphoid tissues in FL. Only by incorporating disease processes directly into the model could this analysis provide mechanistic insight into the disease factors that govern time‐dependent clearance. An analysis of elotuzumab, an anti‐SLAM7 antibody for treatment of multiple myeloma, described time‐dependent PK using a TMDD model with non‐renewable receptor level in the peripheral compartment. 62 A typical TMDD model describes the target receptor with a natural turnover mediated by a constant rate of synthesis and first‐order degradation, resulting in concentration‐dependent elimination with a consistent profile across subsequent doses (i.e., time‐independent). In contrast, the TMDD model of elotuzumab does not include a target receptor synthesis process, so once it has bound and internalized the drug, the total receptor level decreases over time until it reaches zero. This reflects the depletion of target cells by the drug resulting in a decrease in its own TMDD over time. While many empirical models describe changes in TMDD in a simple descriptive manner, this mechanistic approach facilitated meaningful comparisons of the clearance mechanism between drug indications, offering insight into the biology of the disease and drug action.

Time‐dependent covariates

Whereas empirical or mechanistic models aim to estimate smooth mathematical functions to the concentration–time profile, time‐varying covariates are a semi‐mechanistic approach that describe changes in clearance proportional to observed laboratory measurements or other patient characteristics as they change over time, and do not directly model the trajectory of those biomarkers. Covariate screening is a fundamental aspect of population PK modeling, where the relationship between PK model parameters and patient characteristics is explored, such as renal function, hepatic function, demographics, or disease status. Typically baseline measurements are used for simplicity, but time‐dependent covariates include longitudinal measurements encoded using a “last observation carried forward” approach where its value at each timepoint is the most recent prior measurement. For example, clearance (CL) could be described by the typical value of clearance (TVCL) adjusted by a power function of the patient‐specific albumin measurements over time ( ALB t ) normalized by the median albumin level ( ALB ¯ ) raised to a scaling exponent θ (Equation 4 ). Unlike the mechanistic approach where a model function is fitted to the explanatory value (e.g., target level, tumor burden), time‐dependent covariates directly use the observed data to adjust the clearance. This approach is less prone to unidentifiability or poor structural fit because it makes fewer assumptions and requires fewer parameters. Even so, it incorporates mechanistic insight because the covariate relationships offer clinical interpretation of the time‐dependent effects that correlate to observed changes in health status, target expression, or disease burden. However, because the estimated time‐dependent changes are tied to changes in covariate values, this approach is less effective at summarizing the typical magnitude and time scale of clearance changes compared to more direct empirical models. In total, 16 population PK analyses employed time‐dependent covariates, eight of which included other parallel time‐dependent components such as empirical or mechanistic models (Table S2 ). The most frequent time‐dependent covariate was albumin level (identified in 11 analyses) which is linked to cachexia, while other common covariates included body weight, tumor size, LDH, and measures of liver function (Figure 6 ).

A population PK analysis of durvalumab, an anti‐PD‐L1 antibody, in patients with advanced solid tumors found that a time‐dependent covariate model better described the observed PK profile over time compared to an empirical sigmoidal time‐dependent model. 40 The authors included four time‐dependent covariates: albumin, LDH, neutrophil‐to‐lymphocyte ratio (NLR), and tumor size. All time‐dependent covariates were associated with linear clearance, suggesting that they influenced nonspecific clearance rather than TMDD. Moreover, these covariates are prognostic factors associated with disease outcome and treatment response. The model estimated that a decrease in tumor size during treatment was associated with a decrease in clearance, establishing a direct association between response and drug exposure. Recovery of albumin indicates a reversal of cachexia, and the model estimated it is associated with a reduction in clearance. Reduction in LDH indicates a decrease in tumor burden, 98 which the model similarly associated with a reduction in clearance. A subsequent population PK analysis of durvalumab in hematologic malignancies similarly described changes in clearance over time using albumin and IgG measurements (a measure of disease burden in multiple myeloma). 52 The time‐dependent covariate approach went beyond description of the time course of clearance by connecting it to a reduction in cachexia and tumor burden, offering a meaningful interpretation of the relationship.

Time‐dependent covariates are often combined with other methods to describe time‐dependent clearance. A population PK model of nivolumab included longitudinal tumor size as a covariate of drug clearance. Inclusion of a parallel empirical model of time‐dependent clearance resulted in significant model improvement over the longitudinal covariate approach alone, suggesting the covariates were unable to fully explain the reduction in clearance. A similar model of ipilimumab included time‐dependent covariates of LDH, albumin, and Eastern Cooperative Oncology Group Performance Status (ECOG‐PS) in addition to an empirical sigmoidal clearance model. 14 In these cases, the inclusion of time‐dependent covariates helped to establish a mechanistic connection between the change in clearance and improvement in health status, while parallel inclusion of an empirical model fully describes the residual effect that is unexplained by disease markers.

INFLUENCE OF TIME‐DEPENDENT CLEARANCE ON ER ANALYSIS

ER analysis typically evaluates the relationship between summary measures of drug exposure (e.g., C max or area under the curve [AUC]) and response end points (e.g., patient survival, reduction in tumor size, or improvement in disease score) using regression models that do not consider time as a factor. 99 These techniques have been fundamental in quantitative assessment of the need for dose adjustment to increase efficacy or improve safety of a drug regimen, often using data entirely or primarily from a single dose level. Baseline patient factors such as disease burden or health status may be considered simultaneously with exposure in a multiple regression approach to account for the confounding effect of factors that influence both exposure and patient response. However, time‐dependent clearance of therapeutic antibodies further confounds the true ER relationship and cannot be accounted for by traditional time‐invariant regression methods. This can lead to significant erroneous ER relationships from data obtained from a single dose level even after accounting for baseline factors, as patients who respond to therapy tend to show the greatest decreases in drug clearance due to reduction in TMDD or improvement of health status over time. Decreasing clearance and therefore higher exposure among responding patients leads to an apparent ER relationship that suggests higher concentrations and therefore higher doses provide improved efficacy, but determining causality remains challenging. In many of these cases, the response drives changes in exposure, and increasing the dose was unlikely to provide improved efficacy despite the observed ER relationship.

Many therapeutic antibodies have demonstrated a relationship between the magnitude or rate of change in clearance over time to the response outcome, including rituximab, 65 cetuximab, 15 infliximab, 42 isatuximab, 13 tremelimumab, 56 ipilimumab, 14 avelumab, 53 nivolumab, 12 , 48 and pembrolizumab. 16 , 45 Cancer patients who respond positively to treatment have reduced tumor burden compared to baseline, often causing a decrease in both TMDD and cachexia. Patients with inflammatory disease who respond to treatment may show a decrease in systemic inflammation that translates to reduced protein catabolism. 42 Early reduction in drug clearance has been shown to be predictive of overall survival, suggesting it could even be used as a prognostic biomarker. 45 Moreover, reduced clearance translates to increased drug exposure in responders, and therefore influences ER analysis. The response to the drug may cause an increase in exposure as opposed to higher exposures being responsible for increasing the probability of response, which is the traditional interpretation of ER analyses (Figure 1 ).

An ER analysis of rituximab found that trough concentration below 32 μg/mL was strongly associated with shorter progression‐free survival. 11 The same analysis characterized a rapid 87% decrease in drug clearance which occurred with a half‐life of 17 days and was attributed to a depletion of cancerous cells and consequent reduction in TMDD. This reduction in clearance is expected to occur in responding patients, while those who do not respond will experience continued TMDD. Furthermore, due to the rapid onset of the change in clearance, even exposure measured in the first treatment cycle is influenced by time‐dependent clearance. Multivariable regression was used in an attempt to account for confounding effects of other patient factors, including tumor size. However, the data collected from a single dose level with strongly time‐dependent clearance were insufficient to conclude whether higher exposure caused patients to respond, or patients who responded had the most rapid decrease in clearance and thus the highest exposure. Similarly, characterization of time‐dependent clearance and adjustment for baseline prognostic factors were unable to fully mitigate confounding in an ER analysis of pembrolizumab. 9 These examples demonstrate that many factors are responsible for confounding in ER analyses, and despite the improvement, characterizing the time‐dependent clearance still may not be sufficient to resolve the true ER relationship using traditional ER methods.

ER analysis during clinical development of nivolumab revealed an apparent positive relationship between drug exposure and probability of an objective response, particularly within dose groups. 100 Responders clustered at higher drug exposure within each dose group, but when all dose levels were analyzed together, patients with the highest exposure in lower dose groups responded better than patients with the lowest exposure in higher dose groups despite no exposure overlap between dose groups. This suggests that the within‐dose ER relationship was confounded by declining clearance and increased exposure in responders over time. In contrast, if greater exposure were a causal driver of response, an increasing ER relationship that spanned across dose groups would be expected. Because exposure is determined by both dose and clearance, a study with multiple dose levels has differences in exposure that are greater than the variability in clearance, reducing the relative influence of patient factors such as disease severity on exposure and aiding to uncover the true ER relationship. In the study of nivolumab, pharmacodynamic data of receptor occupancy and tumor shrinkage showed that the mechanism of action was saturated regardless of exposure, 100 further supporting a flat ER relationship. This analysis highlights the benefit of randomized evaluation of multiple doses during clinical development to combat the confounding effect of time‐dependent clearance in ER analysis, since spurious findings are more likely with a single dose level. Beyond that, efficacy can be compared between dose groups without consideration of exposure as a secondary analysis to confirm trends observed in ER analysis.

Multivariable regression is a common approach used to account for confounding variables in ER analysis. Summary measures of exposure are included as independent variables along with other baseline prognostic patient factors (e.g., tumor burden, albumin, health status) in a logistic model for binary responses, or a Cox proportional hazards model for survival end points. When the effect of exposure is statistically significant after accounting for other potentially confounding variables, it is considered stronger support that exposure influences response. However, this approach does not account for evolution of exposure or patient factors over time. A population PK analysis of the anti‐CD19 antibody–drug conjugate loncastuximab tesirine identified time‐dependent clearance that was attributed to a depletion of target cells and decline in TMDD during treatment with a time to half‐maximal change in clearance of 20 days. 84 Furthermore, the average drug concentration in cycle 1 was significantly associated with both the probability of an objective response and overall survival. When analyzed with multivariable regression, exposure remained statistically significant along with other prognostic patient factors, including baseline albumin level, baseline tumor size, and disease classification. However, this analysis disregards time, as the concentration–time profile is summarized by a single measure and only baseline values of prognostic biomarkers are considered. While this approach may account for an imbalance of prognostic factors at baseline, it fails to capture that clearance likely decreases more rapidly among the patients who respond to therapy, thereby increasing their exposure and producing a potentially spurious ER relationship.

While time‐stationary models are fundamentally limited in addressing time‐dependent clearance effects in ER analysis, longitudinal PK/PD models hold promise to capture the bidirectional relationship between PK and PD over time more directly. A mechanistic PK/PD model of the anti‐PD‐L1 antibody avelumab described the bidirectional relationship between PK and tumor growth dynamics. 54 Parameters in the model estimated the influence of drug concentration on the tumor shrinkage rate and the simultaneous effect of tumor size on the drug clearance over time. The clearance decreased as the tumor shrunk in size, inherently describing the effect of response on exposure. However, the model suggested that at the doses administered, differences in avelumab exposure had little impact on response, consistent with findings of other immune checkpoint inhibitors. While this study only accounted for one response biomarker (tumor size), the same methodology could be extended to incorporate further markers of cachexia or disease status, such as albumin or LDH. Whereas traditional methods of ER analysis collapse time into summary statistics, longitudinal models are inherently suited to describe time‐dependent effects. Change in clearance over time has been shown to exert an immense influence over ER analysis, and longitudinal PK/PD models will play a critical role in avoiding common pitfalls and identifying optimal doses for future studies.

SIMULATION CASE STUDY: TIME‐DEPENDENT CLEARANCE CAN CONFOUND ER

We present a case study using population PK model simulation to explore how false ER relationships can arise through the bidirectional relationship between PK and disease status. A virtual population was generated using a population PK model of pembrolizumab that estimated time‐dependent clearance with different trajectories depending on the patient's best overall response (BOR). 16 Those with a complete (CR) or partial response (PR) showed the largest decreases, while those with stable disease (SD) or progressive disease (PD) had minimal decrease in clearance. In the simulation as designed, the dose–response relationship is flat at all dose levels, as the BOR of each patient was sampled from the observed response rate with equal probability. Conversely, clearance varies over time depending on the patient's response according to the parameters of the population PK model (Figure 7a ). Detailed methods are provided in the Supplementary Material .

The relationship between AUC was compared to the occurrence of objective response (CR or PR) with a single dose level of 3 mg/kg q.3.w. using traditional time‐stationary ER analysis by logistic regression of the simulated data. A steep “false” ER relationship is observed using AUC at cycle 6 with a single dose level (Figure 7b ), while a flat “true” relationship is observed with multiple randomized dose levels (Figure 7c ) or when using AUC at cycle 1 with a single dose level (Figure 7d ). Because the clearance decreases according to a sigmoidal model with a time to half‐maximal change in clearance of 67 days, the exposure has not substantially diverged by the end of cycle 1 between responders and non‐responders. In contrast, a strong “false” ER relationship is observed with AUC at cycle 6 because patients who responded to treatment exhibited an increase in exposure. Traditional ER analysis would suggest that an increased dose would improve response based on this result. However, this conclusion is inaccurate since the simulation was designed such that higher exposure does not provide an increased probability of response, and an increased dose results in comparable efficacy.

The simulation using exposure during cycle 1 suggests that utilizing exposure measures from earlier timepoints may alleviate confounding from time‐dependent effects, particularly when change in clearance has a slow onset and little impact during the first cycle. However, many antibodies have shown changes in clearance within the first week of treatment, 63 , 65 , 81 where this approach may be unsuccessful. A similar simulation using a PK model of rituximab 65 with fast‐onset time‐dependent clearance confirmed a steep ER relationship emerges when using cycle 1 AUC (Figure S1 ). Furthermore, prognostic patient factors at baseline can influence exposure and result in a false ER relationship in the absence of time‐dependent clearance. Therefore, using early PK measures alone cannot eliminate confounding effects.

Randomized evaluation of multiple dose levels is another strategy to mitigate the confounding effect of time‐dependent clearance. 21 In a clinical study with a single dose level, variability in exposure can be considerable and is influenced by differences in clearance between responders and non‐responders. When studying multiple dose groups with a sufficient dose range, the greatest differences in exposure are driven by the dose level, while variation in clearance due to disease status holds less influence. When the ER simulation using exposure at cycle 6 is repeated with three dose levels, the ER relationship flattens, consistent with the true nature of the simulated data (Figure 7c ). This result is consistent with clinical studies of trastuzumab and tremelimumab that failed to demonstrate benefit of higher doses motivated by apparent ER relationships observed earlier in studies with a single dose level. 5 , 7 While phase II studies in oncology frequently include a single dose level, this simulation supports that clinical data from multiple dose levels is valuable to deconvolute the complex bidirectional relationship between exposure and response.

CONCLUSIONS

Time‐dependent clearance is often observed in PK assessment of therapeutic antibodies and has presented a unique challenge to the traditional paradigm of clinical pharmacology. Time‐dependent effects are often tied to disease treatment end points with greater reduction in clearance over time in patients who respond to treatment. While the traditional interpretation of ER analysis is unidirectional (i.e., dose drives exposure which drives response), complex time‐dependent interactions between response, disease severity, clearance, and exposure introduce a bidirectional relationship that makes causality difficult to infer. A disregard for these confounding factors can lead to identification of spurious ER relationships and initiation of costly, unnecessary clinical trials to evaluate higher doses. Identifying whether time‐dependent clearance occurs is critical prior to embarking on ER analysis to accurately describe the PK profile and to avoid these pitfalls. A primary purpose of this review was to provide a comprehensive evaluation of the magnitude and time scale of changes in clearance based upon underlying cause across a comprehensive range of compounds in the literature. This has not been performed in the past as the breadth of data was far less than what is available currently. We have identified that time‐dependent changes in clearance due to TMDD are of a higher magnitude (62% vs. 21% reduction) and occur over a shorter timeframe (3 vs. 13 weeks) compared to change in clearance mediated by cachexia or inflammation.

Several strategies have been identified to mitigate the impact of confounding factors in ER analysis of therapeutic antibodies. Studies with a single dose level are highly prone to influence from response on clearance over time, while investigations with multiple randomized dose levels more reliably identify true ER relationships. Dose optimization prior to registrational trials is critical to maximize efficacy and probability of regulatory success, so phase II studies should ideally include evaluation of two or more dose levels. Model simulations presented in this review illustrate how false ER findings can arise from typical time‐dependent clearance using traditional methods of ER analysis. These methods do not consider time as a factor, and instead reduce the concentration–time profile of each patient to a summary statistic. In contrast, longitudinal PK/PD models offer a more nuanced approach that estimates the impact of exposure on response biomarkers such as tumor size, receptor occupancy, or albumin, over time. By simultaneously characterizing the dynamics of both exposure and response over time, they are less prone to the confounding effect of time‐dependent clearance. The success of PK/PD modeling could be maximized by consideration of multiple informative PD assays, from standard laboratory tests like albumin and LDH to newer techniques such as circulating tumor DNA and soluble target levels.

Time‐dependent clearance is not the only source of confounding effects in ER analysis. The same factors that influence clearance over time and result in time‐dependent clearance, such as tumor volume or albumin, have substantial variation at baseline. These baseline measurements can also be prognostic, where patients with less severe disease at baseline are more likely to respond to treatment. 3 Therefore, patients with more severe baseline disease may have higher clearance, lower exposure, and lower probability of response without a true ER relationship or any changes in clearance over time. It is important to evaluate confounding effects that are present at baseline in addition to those that evolve over time. Multivariable regression and case–control analysis can account for baseline effects simultaneously with exposure to the extent that they can be explained by measured prognostic factors. 101 Evidently, the consideration of time‐dependent clearance in addition to other confounding effects is critical to accurate dose optimization and regulatory success of therapeutic antibodies.

FUNDING INFORMATION

J.R.P. was funded by a 4‐year doctoral fellowship from the University of British Columbia for this work.

CONFLICT OF INTEREST STATEMENT

The authors declared no competing interests for this work.

Supporting information

Figure S1

Click here for additional data file.

Table S1

Click here for additional data file.

Table S2

Click here for additional data file.

Data S1

Click here for additional data file.

ACKNOWLEDGMENTS

We would like to extend our sincere gratitude to Lisa Cheng who provided invaluable assistance in editing and proofreading the final manuscript.

Proctor JR, Wong H. Time‐dependent clearance can confound exposure–response analysis of therapeutic antibodies: A comprehensive review of the current literature. Clin Transl Sci. 2024;17:e13676. doi: 10.1111/cts.13676

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Associated Data

Supplementary Materials

Figure S1

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Table S1

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Table S2

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Data S1

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