Pharmacokinetic/Pharmacodynamic modeling of abexinostat-induced thrombocytopenia across different patient populations: application for the determination of the maximum tolerated doses in both lymphoma and solid tumour patients

Summary Background

In the comprehensive landscape of oncology drug development, the foundational step of determining the recommended dose (RD) for novel therapeutic agents typically relies on a conventional 3+3 dose-escalation study design during early clinical phases. While widely adopted due to its simplicity and established historical precedence, this rule-based phase I methodology often exhibits inherent limitations. Specifically, it frequently falls short in its capacity to precisely delineate the intricate relationships between drug dose and the resulting toxicity profile. This imprecision can lead to suboptimal dose selection, potentially impacting the safety and efficacy of the drug in later development stages. A more nuanced and robust approach is therefore imperative to accurately characterize these critical dose-toxicity dynamics.

Methods

This study encompassed a substantial cohort of 125 patients, drawing from populations afflicted with either solid tumors or lymphoma. A rich dataset comprising 1217 individual platelet count measurements, meticulously collected over three distinct treatment cycles, was amassed for analysis. This extensive physiological data formed the empirical basis for constructing a sophisticated population pharmacokinetic/pharmacodynamic (PKPD) model. The model was developed utilizing a sequential modeling approach, which systematically integrates drug concentration data with observed physiological responses. The primary objective of this modeling exercise was to predict and characterize the effects of abexinostat, a novel Histone Deacetylase Inhibitor, on platelet kinetics. Once the PKPD model was established and validated, it served as a powerful tool for conducting extensive simulations. These simulations were instrumental in determining model-derived recommended doses (MDRD) for abexinostat across various hypothetical administration schedules. Furthermore, a critical aspect of the methodology involved quantifying the upper bound of the probability that these model-derived optimal doses could actually be identified and reached when employing the standard 3+3 dose-escalation design. This direct comparison aimed to highlight the potential discrepancies between a scientifically optimized dose and one determined by traditional, less precise methods.

Results

The diligently developed PKPD model demonstrated a commendable ability to accurately describe and predict platelet kinetics in both solid tumor and lymphoma patient populations. The model’s predictive power was significantly enhanced by the strategic inclusion of two distinct platelet baseline counts, one for each patient group, which accounted for observed pre-treatment differences. Additionally, a specific disease progression component was incorporated, particularly for patients with lymphoma, to capture the subtle, time-dependent decline in platelet counts observed in this cohort, suggesting a disease-related impact on bone marrow function. The extensive simulation results yielded crucial insights into optimal dosing strategies. Specifically, the data convincingly demonstrated that an administration schedule involving abexinostat treatment during the first four days of each week within a three-week cycle consistently led to a higher model-derived recommended dose when compared to all other administration schedules rigorously evaluated in the simulations. However, despite the identification of these potentially higher and more effective doses, the simulations revealed a significant limitation of the traditional 3+3 design: there was a maximum probability of only 40 percent that these optimized model-derived recommended doses would actually be identified and selected using the conventional dose-escalation approach. This stark finding underscores the inherent imprecision and potential for suboptimal dose selection when relying solely on the 3+3 design.

Conclusions

The sophisticated population pharmacokinetic/pharmacodynamic model successfully established its capability to accurately predict the occurrence and severity of thrombocytopenia following the administration of abexinostat in both solid tumor and lymphoma patient populations. This predictive power is a testament to the model’s robust design and its ability to capture complex physiological interactions. The findings from this study strongly advocate for the integration of a model-based approach in determining recommended doses during phase I clinical trials. Such an approach offers distinct advantages over the long-standing, rule-based 3+3 design, primarily owing to the latter’s demonstrated imprecision and limited capacity to optimally define dose-toxicity relationships. By leveraging advanced modeling and simulation techniques, the process of dose determination can become more data-driven, precise, and potentially lead to more effective and safer therapeutic regimens in oncology.

Keywords

Abexinostat. Thrombocytopenia. PKPD model. Recommended Dose. Simulation. Disease progression

Introduction

The foremost objective of a phase I clinical trial in the realm of oncology is to meticulously determine the recommended dose and/or the most suitable administration schedule for a new investigational drug. This critical initial step serves as the gateway for the drug’s continued advancement into subsequent phases of clinical development, particularly phase II, where efficacy is the primary focus. Consequently, the protocols governing phase I clinical trials must be conceived and executed with the utmost rigor and foresight. The decisions made and the data gathered at this foundational stage exert a profound and lasting influence on the entire trajectory of drug development, shaping everything from patient safety to eventual therapeutic success.

Current phase I trial designs broadly fall into distinct categories. These include rule-based designs, exemplified by the widely recognized and frequently employed classical 3+3 design, which relies on predetermined rules for dose escalation. Another category encompasses model-based designs, such as the continuous reassessment method, which leverage statistical modeling to guide dose adjustments. Lastly, there are specialized designs tailored for trials involving combinations of therapeutic agents. Among these various methodologies, the classical 3+3 design remains the most prevalent and extensively utilized approach in oncology phase I studies, largely due to its straightforward implementation and historical familiarity.

For cytotoxic agents, which aim to eliminate rapidly dividing cancer cells, the strategy for dose escalation is fundamentally driven by the observed toxicity profile. The underlying assumption is that the highest dose that can be safely administered will also confer the greatest therapeutic efficacy. This premise finds support in both preclinical laboratory models and clinical experiments, which have frequently demonstrated that drug-induced toxicity can serve as a valuable surrogate endpoint for the drug’s anticipated therapeutic effect against the cancer. Within the spectrum of adverse events associated with chemotherapy, myelosuppression, a suppression of bone marrow activity, often leads to a subsequent and significant reduction in platelet counts, a condition known as thrombocytopenia. Thrombocytopenia has progressively emerged as a major dose-limiting toxicity in oncological treatments. Its clinical implications are substantial and include the potential necessity for dose reductions or delays in treatment cycles, which can compromise treatment intensity and efficacy. More gravely, severe thrombocytopenia carries the risk of major complications, including life-threatening bleeding episodes and, in extreme cases, even mortality. The direct relationship between the occurrence of hemorrhage and the severity or duration of thrombocytopenia is well-established in medical literature. However, it is crucial to recognize that the clinical significance and presentation of thrombocytopenia can vary considerably between patients with solid tumors and those diagnosed with hematological malignancies such as acute leukemia or lymphoma, reflecting underlying pathophysiological differences. Histone Deacetylase Inhibitors (HDACi) represent a class of anticancer drugs that frequently induce thrombocytopenia as a dose-limiting toxicity. Abexinostat, also known by its code S-78454, is a new investigational HDACi that has progressed to the phase II stage of clinical development, specifically for the treatment of lymphoma.

Previous research conducted by our team demonstrated that thrombocytopenia was a common and significant observation in two distinct phase I clinical studies involving solid tumor patients treated with abexinostat. This toxicity frequently restricted the ability to escalate doses in these studies. In that earlier investigation, a sophisticated semi-mechanistic pharmacokinetic/pharmacodynamic model was developed specifically to characterize abexinostat-induced thrombocytopenia. Crucially, simulations performed using this initial model guided the definition of an optimal administration schedule for patients with solid tumors. The subsequent amendment of the clinical protocol, which favored a new administration schedule consisting of 4 days ON treatment followed by 3 days OFF each week within a three-week cycle, was predicted to lead to a decrease in the depth of thrombocytopenia. This modification indeed facilitated the dose-escalation process, ultimately enabling the definition of a higher maximum tolerated dose for this newly adopted administration schedule in solid tumor patients. However, a parallel clinical study that included lymphoma patients also underwent a similar protocol amendment, embracing the same 4 days ON, 3 days OFF schedule. Interestingly, this change did not result in the identification of a higher maximum tolerated dose within the lymphoma patient population. This notable discrepancy clearly indicated that the predictions generated by the previous PKPD model were not reliably applicable or accurate for lymphoma patients.

Several plausible explanations were considered for this observed divergence in the pharmacokinetic/pharmacodynamic relationship. One primary hypothesis posited that pathophysiological distinctions inherent to lymphoma patients, when compared to those with solid tumors, might influence their sensitivity to the drug or their response to specific administration schedules. This suggests a disease-related component to the differing outcomes. A second, equally compelling explanation pointed to the intrinsic limitations and inherent weakness of the classical 3+3 dose-escalation design itself in accurately determining the true maximum tolerated dose. This could potentially lead to an erroneous or misleading observed maximum tolerated dose in an amended study. Further investigative analyses into the time-course of platelet counts in patients from both clinical trials, encompassing both solid tumor and lymphoma cohorts, indeed revealed significant differences between the two groups. These differences included, for instance, lower baseline platelet counts at the time of study inclusion for lymphoma patients, and/or a more pronounced, progressive decrease in platelet count over the course of treatment when contrasted with solid tumor patients. Given these critical observations and the identified shortcomings, the current study was conceived with three overarching aims. The first aim was to meticulously refine the previously developed PKPD model that described abexinostat-induced thrombocytopenia in solid tumor patients. This refinement involved rigorously incorporating data from lymphoma patients into the analysis, thereby seeking to achieve accurate prediction of platelet kinetics across both patient populations and, consequently, to determine the safest and most effective dosing regimen for all patients. The second aim involved leveraging the refined and validated PKPD model to perform extensive simulations. The purpose of these simulations was to precisely determine the model-derived recommended doses (MDRD) for both patient populations under various proposed administration schedules, seeking to identify optimal treatment patterns. The third and final aim was to critically assess the capability of the traditional 3+3 dose-escalation design to accurately identify and determine these model-derived recommended doses, thereby providing a robust comparative evaluation of the two methodologies.

Materials and Methods

The findings presented in this report are derived from the consolidated data collected across four distinct clinical studies. Each of these studies was conducted in strict adherence to the ethical principles unequivocally articulated in the Declaration of Helsinki 1964, as subsequently revised in Seoul, 2008, ensuring patient welfare and scientific integrity. Prior to their initiation, all study protocols received comprehensive approval from independent ethics committees, safeguarding the rights and well-being of the participants. Furthermore, every patient provided their explicit written informed consent before any study-related procedures commenced, signifying their voluntary agreement to participate.

Patients diagnosed with solid tumors were enrolled and received treatment within two specific phase I clinical studies. In parallel, patients diagnosed with lymphoma were included in two separate phase I/II clinical studies. This comprehensive patient recruitment strategy allowed for a robust comparison and modeling across different cancer types.

Platelets Samples and Modeling Datasets

Blood samples were systematically collected from all enrolled patients with the primary purpose of assessing hematological toxicity, with a particular focus on characterizing the temporal profiles of platelet counts throughout the treatment period. For the purposes of the current modeling effort, three distinct datasets were carefully curated from the available study data. This selection exclusively utilized data from the first three cycles of treatment, which spanned approximately 60 days. This decision was based on the observation that samples collected from later cycles were often sparse and offered only limited additional information relevant to the early drug effect on platelet kinetics. From the total pool of 125 patients available across the four clinical studies, a subset of 95 patients was randomly selected to form the “Building dataset.” This dataset was primarily used for the initial development and refinement of the PKPD model. An additional 30 patients were randomly designated for inclusion in the “Advanced internal evaluation dataset,” which served a critical role in independently validating the model’s predictive capabilities. Finally, data from all 125 patients were combined to constitute the “Final dataset,” which was employed for the ultimate estimation of model parameters, leveraging the entirety of the available clinical information.

Modeling Strategy

The intricate platelet-time profiles observed in the study participants were meticulously analyzed using nonlinear mixed effect modeling, commonly referred to as a population approach. This sophisticated statistical methodology is particularly adept at describing drug effects in diverse patient populations while accounting for both inter-individual and intra-individual variability. A sequential pharmacokinetic/pharmacodynamic approach was employed, meaning that pharmacokinetic parameters, which describe how the drug is absorbed, distributed, metabolized, and excreted in the body, were first determined. Specifically, empirical Bayesian estimates of individual pharmacokinetic parameters, derived from a previously established pharmacokinetic model of abexinostat, were incorporated as fixed parameters during the subsequent pharmacodynamic modeling. This streamlined approach allows for a robust estimation of the pharmacodynamic parameters, which characterize the relationship between drug concentration and its effect on platelet counts. Pharmacodynamic parameters were estimated using specialized software and estimation methods.

During the model development process, several different functional forms were rigorously tested to characterize the drug’s effect on platelet proliferation. These included a simple linear model, where the drug effect was directly proportional to its concentration; an Imax model, which describes a saturable drug effect reaching a maximum; and a full sigmoidal Imax model, which allows for a more flexible, S-shaped concentration-effect relationship, often characterized by a Hill coefficient representing the steepness of the curve. These models incorporated parameters such as the patient’s sensitivity to abexinostat-induced hematotoxicity, the intrinsic activity of the drug, its potency (IC50, or the concentration causing 50% of the maximal effect), and the sigmoidicity coefficient.

Significant efforts were dedicated to improving upon the previously developed PKPD structural model, with investigations primarily conducted using the Building dataset. A key refinement involved testing the inclusion of a second feedback mechanism, which specifically impacted the mean transit time parameter. This mechanism aimed to physiologically mimic the bone marrow’s adaptive response, allowing it to either accelerate or decelerate platelet production in response to conditions of thrombocytopenia or thrombocytosis, respectively. Furthermore, to accurately account for the empirically observed differences in baseline platelet counts at study inclusion between the two patient populations, two distinct baseline parameters were tested: one specifically for solid tumor patients and another for lymphoma patients. This differentiation was crucial for capturing the unique physiological states of each group. Additionally, a subtle yet consistent decrease in platelet counts over successive treatment cycles was observed in some patients, suggesting an impact on bone marrow function over time, potentially due to disease progression or chronic drug exposure. To model this phenomenon, various disease progression models were evaluated, all designed to describe a gradual decline in the baseline platelet parameter over time. These included both a simple linear decrease and an Imax-type disease progression model, where the rate of decrease could be saturable with time. These models incorporated the baseline value at inclusion for each patient population and the time elapsed since the first abexinostat administration.

Inter-individual variability, which accounts for differences in drug response among individual patients, was systematically incorporated into the model. A log-normal distribution was generally assumed for most parameters, a common practice for biological parameters that are inherently positive. For a specific parameter related to the maximum effect of disease progression, a normal distribution was assumed. Recognizing that patients underwent treatment over multiple cycles, inter-occasion variability was also rigorously tested on each of the pharmacodynamic parameters. This component accounts for variability in drug response within the same individual across different treatment cycles, thereby enhancing the statistical model’s quality and predictive power. Finally, the residual variability, representing the unexplained random error in the observed data, was effectively modeled using a combined additive and proportional error structure, which had been previously identified as the most suitable description for the residual error in the initial PKPD model.

Model Selection

The process of discriminating between hierarchical models, where one model is a simplified version of another, was primarily based on the objective function value (OFV) provided by the modeling software, utilizing the Likelihood-Ratio-Test (LRT). A statistically significant reduction in the OFV, specifically a difference greater than 3.84, was employed as the criterion for discriminating between two nested models that differed by a single parameter, corresponding to a statistical significance level of 5 percent. Beyond statistical tests, the development and selection of the optimal model were also guided by practical considerations, including the precision of parameter estimates, visual inspection of standard goodness-of-fit plots, which graphically depict how well the model predicts the observed data, and the evaluation of normalized prediction discrepancy errors (NPDE).

To compute these normalized prediction discrepancy errors, 500 simulations were performed using the Building dataset. These simulations were based on the specific dose regimens and sampling time points of each patient within that dataset, utilizing the current pharmacodynamic parameter estimates. The resulting normalized prediction discrepancy errors were then plotted against both time and population predictions to systematically identify any potential biases or systematic deviations in the model’s performance. The final selection of the best model was based on a combination of criteria: it had to demonstrate the most favorable objective function value according to the Likelihood-Ratio-Test, exhibit acceptable precision in its parameter estimates, and show consistent performance supported by the goodness-of-fit plots and the normalized prediction discrepancy errors. This selected model was subsequently designated as the “Intermediate PKPD model” for the subsequent stages of this research.

Advanced Internal Model Evaluation

To rigorously evaluate the capacity of the Intermediate PKPD model to accurately describe and predict data that was not used in its initial development, advanced internal model evaluation techniques were employed. This process involved the use of individual Visual Predictive Checks and Normalized Prediction Distribution Errors. These methods are crucial for assessing a model’s generalizability and its ability to forecast outcomes for unseen data. For this evaluation, 500 simulations were meticulously performed based on the specific dosing regimens and sampling time points of the 30 patients who constituted the Advanced internal evaluation dataset. These simulations utilized both the pharmacokinetic and pharmacodynamic parameter estimates derived from the Intermediate PKPD model. By definition, normalized prediction distribution errors are expected to follow a standard normal distribution if the model adequately describes the data. Consequently, a Kolmogorov-Smirnov test was performed to statistically verify that the distribution of these errors conformed to a standard normal distribution, thereby providing a quantitative assessment of model adequacy and predictive performance.

Final PKPD Model

Following the advanced internal evaluation, the entire dataset, encompassing all available patients from the study, was then analyzed to establish the Final PKPD model. During this final estimation phase, the pharmacodynamic parameters were re-estimated without introducing any modifications to the previously established structural or statistical models. This ensured that the core relationships and assumptions remained consistent, while leveraging the full breadth of the data for parameter precision. To comprehensively evaluate the performance of this Final PKPD model, normalized prediction distribution errors were computed and plotted against both time and population predictions for each patient population independently. Additionally, a Kolmogorov-Smirnov test was again performed to confirm the normality of these errors, providing a final, rigorous assessment of the model’s robust predictive capabilities across both solid tumor and lymphoma patient groups.

Model-derived Recommended Doses Determination for Lymphoma and Solid Tumor Patients

In the traditional 3+3 dose-escalation design, which is a rule-based approach, the determination of the maximum tolerated dose (MTD) and subsequently the recommended dose (RD) for later phases adheres to specific criteria. If, at a given dose level, two or more patients within a cohort of a maximum of six patients experience a dose-limiting toxicity, the dose escalation process is immediately halted. This specific dose level is then designated as the maximum tolerated dose, and the dose level immediately below it is subsequently defined as the recommended dose for further clinical development in phase II trials. Consequently, this established threshold of 33.33 percent (representing two out of six patients) experiencing a dose-limiting toxicity was adopted as the critical benchmark for determining the model-derived recommended doses (MDRD) during the extensive simulations. This threshold was applied consistently across various administration schedules and for each patient type, specifically lymphoma and solid tumor patients.

The simulations themselves were conducted using the robust Final PKPD model. To ensure a comprehensive exploration of dose-toxicity relationships, the platelet time-course was simulated for a large virtual cohort of patients: 3000 patients with solid tumors and an equivalent 3000 patients with lymphoma. Each of these simulated patients received abexinostat over three treatment cycles. This large number of simulated patients allowed for the creation of 500 distinct cohorts of six patients for each population, mirroring the cohort size in the 3+3 design. Doses were systematically explored, starting from 20 mg per day and escalating in 20 mg increments up to a maximum of 500 mg per day, administered once daily. Several distinct administration schedules were rigorously tested to identify optimal dosing patterns. These included a schedule of 14 consecutive days of treatment followed by 7 days off within a three-week cycle (designated as 14ON7OFF); a more intermittent schedule of 4 days on treatment followed by 3 days off every week within a three-week cycle (designated as 4ON3OFF); and a schedule of 5 days on treatment followed by 2 days off during the first two weeks of a three-week cycle (designated as 5ON2OFF). The sampling schedule for platelet counts in these simulations was precisely matched to that of one of the clinical studies to maintain consistency. From the extensive simulation outputs, the percentage of patients experiencing Grade 4 thrombocytopenia was meticulously computed. Grade 4 thrombocytopenia was specifically defined as a platelet count falling below 25 × 10^9 platelets per liter, representing a severe and clinically significant toxicity. The model-derived recommended dose was then precisely defined as the dose level immediately below the one at which the percentage of Grade 4 thrombocytopenia exceeded the predefined 33.33 percent toxicity threshold.

DLT Percentages at the MDRD in a 3+3 Dose Escalation Design

In an ideal, asymptotic scenario, where an infinite number of patients could be studied, at the true recommended dose level, the probability of escalating to a higher dose level would theoretically be 100 percent. However, real-world clinical trials, particularly those employing rule-based designs like the 3+3, operate with finite patient numbers and inherent limitations. To rigorously assess how well the traditional 3+3 dose-escalation design would identify the model-derived recommended doses, a specific simulation strategy was employed. For each of the administration schedules that had been tested (14ON7OFF, 4ON3OFF, and 5ON2OFF), 500 distinct cohorts, each comprising 6 patients with either solid tumors or lymphoma, were simulated. Crucially, these simulations were performed *at the precise model-derived recommended dose* identified earlier using the Final PKPD model.

Within these simulations, the “Probability of Reaching a Higher Dose” (PRD) was then meticulously calculated. The PRD represented the percentage of these 6-patient cohorts in which only zero or one patient experienced a dose-limiting toxicity. This calculation directly reflects the specific rule of the 3+3 design, where the occurrence of zero or one dose-limiting toxicity within a cohort permits dose escalation to the next level. By performing these simulations, the study aimed to quantitatively determine the likelihood that a conventional 3+3 design would effectively identify and proceed with a dose that the robust PKPD model had identified as optimal. The sampling schedule for the platelet count within these specific simulations remained identical to that used in one of the primary clinical studies, ensuring methodological consistency across the investigative phases.

Results

Intermediate PKPD Model

The initial phase of model development utilized the Building dataset, which comprehensively contained 925 meticulously collected platelet counts. These measurements spanned the first three treatment cycles and were derived from a cohort of 95 patients, comprising 49 individuals with solid tumors and 46 individuals with lymphoma. This rich dataset served as the foundation for significant enhancements to the previously established pharmacokinetic/pharmacodynamic (PKPD) model.

A crucial improvement involved the integration of a sophisticated feedback mechanism that specifically influenced the mean transit time (MTT) of platelets. This mechanism was designed to dynamically regulate the bone marrow’s maturation process, allowing it to either accelerate or decelerate platelet production in response to fluctuating platelet counts—specifically, quickening in instances of thrombocytopenia (low platelet count) and slowing down during thrombocytosis (high platelet count). This physiological feedback loop aligns with established biological principles governing hematopoiesis. Furthermore, the mathematical description of abexinostat’s effect on the proliferation rate of platelet precursors was most accurately represented by an Imax model, a finding consistent with prior research in similar pharmacodynamic contexts.

Distinguishing features between the patient populations were also meticulously incorporated. Two distinct baseline platelet parameters were estimated to account for observed physiological differences at the start of the study: an average of 203 × 10^9 platelets per liter for lymphoma patients and a higher average of 274 × 10^9 platelets per liter for solid tumor patients. This differentiation was vital for providing a precise starting point for modeling platelet kinetics in each group. Lastly, the model’s ability to describe the longitudinal changes in platelet counts, particularly in lymphoma patients, was notably enhanced by the inclusion of a disease progression model applied to the baseline platelet parameter. This addition captured the subtle yet persistent decrease in platelet counts over time that was observed in some patients, likely reflecting the impact of their underlying disease on bone marrow function. The Imax model was found to be the most appropriate description for this disease progression, characterized by an IT50 parameter representing the time required to achieve half of the maximum observed decrease (IMAT).

Inter-individual variability, reflecting inherent differences between patients, was estimated for all parameters with the notable exceptions of Imax and IT50. It was also determined that the baseline parameters for solid tumor patients and lymphoma patients shared a common inter-individual variability, suggesting a similar degree of interpersonal differences in their initial platelet levels. Inter-occasion variability, accounting for fluctuations within the same patient across different treatment cycles, significantly improved the model’s fit only when estimated for the delta (δ) and IC50 parameters, indicating that variability in bone marrow feedback and drug potency were relevant across cycles.

The estimated parameters for the Intermediate PKPD model, along with their relative standard errors and associated variability components, are comprehensively presented in Table 2. Visual assessment through goodness-of-fit plots and normalized prediction discrepancy errors (NPDE) indicated satisfactory model performance. The statistical evaluation further supported the model’s robustness, with the p-value of the Kolmogorov-Smirnov test for NPDE distribution being approximately 0.13. This value suggested that the null hypothesis of the NPDE following a standard normal distribution could not be rejected, indicating that the model’s residuals were well-behaved.

To further validate its predictive capabilities, the Intermediate PKPD model underwent a rigorous evaluation using data from an additional 30 patients, which had not been included in the initial model building phase. Individual Visual Predictive Checks were found to be satisfactory, and the analysis of normalized prediction discrepancy errors confirmed the absence of any discernible bias within the structural model. These findings collectively indicated that the Intermediate PKPD model possessed a strong ability to accurately predict the individual platelet time-course for patients undergoing treatment with abexinostat. However, despite these positive visual and qualitative assessments, the Kolmogorov-Smirnov test for the advanced internal evaluation yielded a p-value of 3.8 × 10^-5, which statistically led to the rejection of the null hypothesis of normality for the NPDE. This result, while statistically significant, warranted further discussion in the context of dataset size and test sensitivity.

Final PKPD Model

Building upon the robust foundation of the Intermediate PKPD model, the final step involved re-estimating the pharmacodynamic parameters using the comprehensive Final dataset. This dataset incorporated all available platelet samples, totaling 1217 measurements from 125 patients (56 with lymphoma and 69 with solid tumors), meticulously collected over three treatment cycles. The re-estimated parameters for the Final PKPD model, along with their associated variabilities, are detailed in Table 2.

A thorough assessment of the Final PKPD model confirmed its exceptional ability to describe the observed data. This was evidenced by the consistency observed in goodness-of-fit plots, individual patient plots, and normalized prediction discrepancy errors plotted against both time and population predictions. These visual diagnostics clearly demonstrated that the Final PKPD model possessed a strong capacity to accurately describe and predict the platelet time-course for both lymphoma and solid tumor patients treated with abexinostat. Furthermore, the Kolmogorov-Smirnov test for the Final PKPD model yielded a p-value of 0.12, which indicated that the null hypothesis of a standard normal distribution for the NPDE could not be rejected. This result provided statistical confirmation of the model’s overall good performance and reliable predictive accuracy across the entire, more heterogeneous patient population.

Model-Derived Recommended Doses (MDRD) Determination for Both Lymphoma and Solid Tumor Patients

The refined Final PKPD model was subsequently employed in extensive simulation studies to determine the model-derived recommended doses (MDRD) for abexinostat across various administration schedules and for both patient populations. The objective was to identify the optimal daily dose that would maintain an acceptable toxicity profile, specifically defined by a threshold of 33.33 percent (equivalent to 2 out of 6 patients) experiencing Grade 4 thrombocytopenia.

For lymphoma patients, the simulations revealed distinct model-derived recommended daily doses depending on the administration schedule. For the 14 days ON, 7 days OFF schedule (14ON7OFF), the MDRD was determined to be 80 mg/day. When considering the 4 days ON, 3 days OFF every week schedule (4ON3OFF), a substantially higher MDRD of 200 mg/day was identified. Lastly, for the 5 days ON, 2 days OFF for the first two weeks schedule (5ON2OFF), the MDRD was 140 mg/day. Translating these daily doses into cumulative amounts per cycle, the 14ON7OFF schedule resulted in a total of 1,120 mg per cycle, the 4ON3OFF schedule led to a cumulative dose of 2,400 mg per cycle, and the 5ON2OFF schedule yielded 1,400 mg per cycle.

For solid tumor patients, the model-derived recommended doses were consistently higher across all administration schedules, reflecting their generally greater tolerance to abexinostat-induced thrombocytopenia. Specifically, the MDRD for the 14ON7OFF schedule was determined to be 180 mg/day. The 4ON3OFF schedule allowed for a significantly higher MDRD of 440 mg/day. For the 5ON2OFF schedule, the MDRD was 280 mg/day. The corresponding cumulative doses per cycle for solid tumor patients were 2,520 mg for 14ON7OFF, an impressive 5,280 mg for 4ON3OFF, and 2,800 mg for 5ON2OFF. These results underscore the importance of tailored dosing strategies based on both administration schedule and patient population to optimize therapeutic benefit while managing toxicity.

DLT Percentages at the MDRD in a 3+3 Dose Escalation Design

While theoretically, with an infinite number of patients, the probability of escalating to a higher dose level at the recommended dose (RD) should be 100 percent, real-world clinical designs, particularly the 3+3 method, operate under inherent limitations. To critically assess the practical ability of the 3+3 design to identify and proceed with the model-derived recommended doses (MDRD), extensive simulations were conducted. For both lymphoma and solid tumor patients, 500 distinct cohorts of six patients each were simulated at their respective MDRDs for each administration schedule.

The results of these simulations starkly highlighted the limitations of the 3+3 design. For lymphoma patients, even when the actual MDRD was administered, the simulated probabilities of successfully escalating to a higher dose level were surprisingly low. Specifically, these probabilities were only 45.6 percent for the 14ON7OFF administration schedule, 36.6 percent for 4ON3OFF, and 36.2 percent for 5ON2OFF. This means that in a significant majority of simulated scenarios, the 3+3 design would have prematurely stopped dose escalation at or below the optimal MDRD.

Similarly, for solid tumor patients, the probabilities of escalating to a higher dose level at their respective MDRDs were also quite low, demonstrating a consistent challenge for the 3+3 design. These probabilities were 40 percent for the 14ON7OFF schedule, 39.8 percent for 4ON3OFF, and 39.6 percent for 5ON2OFF. These findings across both patient populations and all tested administration schedules underscore a fundamental drawback of the 3+3 design: its inherent insensitivity often leads to a substantial risk of stopping dose escalation prematurely, preventing the identification of the true, optimal recommended dose that a model-based approach can predict.

Discussion

Thrombocytopenia stands as the predominant dose-limiting toxicity associated with Histone Deacetylase Inhibitors such as abexinostat. To effectively define the intricate relationship between drug dose and its ensuing toxicity, it is absolutely essential to both accurately describe and reliably predict the time-course of platelet counts across the entire study population. This comprehensive study has successfully refined the previously established pharmacokinetic/pharmacodynamic (PKPD) model to meticulously describe platelet profiles following abexinostat administration, now encompassing both patients with solid tumors and those with lymphoma. The expanded semi-mechanistic PKPD model served as a powerful platform for a simulation study, which rigorously determined the model-derived recommended doses (MDRD) for various administration schedules and patient populations. Furthermore, a critical aspect of this research involved a simulation-based evaluation of the conventional 3+3 dose-escalation design’s inherent ability to accurately ascertain these model-derived recommended doses.

It is worth noting that while the Kolmogorov-Smirnov test statistically rejected the null-hypothesis of normality for the normalized prediction discrepancy errors (NPDE) in the advanced internal evaluation step, yielding a p-value of 3.8 × 10^-5, a closer examination of the NPDE plots versus time, population predictions, and quantile-quantile plots revealed that the Intermediate PKPD model still demonstrated robust predictability features. As has been suggested by other researchers, the normality assumption test for NPDE distribution can be exceptionally powerful, particularly when applied to rich datasets, and thus may sometimes be considered overly conservative. Indeed, the visual inspection of the NPDE graphs in this study consistently supported the model’s strong descriptive and predictive capabilities. It is plausible that the Advanced internal evaluation dataset, comprising 292 platelet counts from a relatively small cohort of 30 patients, was simply too limited in size to facilitate a sufficiently powerful Kolmogorov-Smirnov test that would yield a non-significant result despite good model performance.

Ultimately, the pharmacodynamic parameters were re-estimated using the complete Final dataset, which encompassed 1217 platelet counts from 125 patients treated under six distinct administration schedules. This comprehensive dataset allowed for the development of the Final PKPD model. Visual diagnostics, including goodness-of-fit plots, individual patient profiles, and normalized prediction discrepancy errors plotted against time or population predictions, unequivocally demonstrated that this final model provided an excellent description of the observed data. Consequently, the Final PKPD model exhibited a remarkable ability to accurately describe and predict platelet time-course in a larger and more heterogeneous patient population, adeptly accounting for meaningful physiological differences observed between solid tumor and lymphoma patients. A key finding was that lymphoma patients exhibited a notably lower baseline platelet count compared to solid tumor patients (195 versus 273 × 10^9/L). This difference is plausibly attributed to a pre-existing weakening of their bone marrow function, potentially related to their disease. The subtle yet progressive decrease in platelet counts observed over time in some patients was also effectively captured by incorporating the effect of disease progression onto the baseline platelet parameter (specifically, BASE0 LY for lymphoma patients). It was compellingly demonstrated that disease progression, as it affected platelet counts, was only statistically significant and evident in lymphoma patients. Inter-occasion variability, representing fluctuations in response from one treatment cycle to the next, was thoughtfully integrated for the IC50 and delta parameters, with population estimates of approximately 10 and 5 percent respectively, as detailed in Table 2.

The Final PKPD model was then extensively utilized for simulation studies, which aimed to precisely determine the model-derived recommended doses (MDRD) for each patient population across various administration schedules. When compared to the other administration schedules rigorously tested, the 4ON3OFF schedule consistently emerged as a safer and more favorable option. This was because it permitted the administration of a notably higher dose of abexinostat to both patient populations while maintaining an acceptable level of toxicity. One potential explanation for these observed differences among schedules might relate to the duration of the initial sequence of dose administration. Longer initial exposure to the treatment could lead to a more pronounced and rapid decrease in platelet counts. It was also consistently observed that the model-derived recommended dose was approximately twice as high for solid tumor patients compared to lymphoma patients, regardless of the administration schedule. This significant difference robustly reflects the impact of the distinct pathophysiology of lymphoma patients, characterized by their lower baseline platelet counts at inclusion and a tendency for platelet counts to decrease over time, likely due to disease-related factors influencing bone marrow function.

A compelling comparison was drawn between the model’s predictions and real-world clinical observations. The Observed Recommended Dose (ORD) associated with the 14ON7OFF administration schedule in a specific clinical study for solid tumor patients was indeed lower than the ORD associated with the 4ON3OFF schedule, a finding that aligns perfectly with the Modeling & Simulations (M & S) predictions regarding their respective model-derived recommended doses. However, in another clinical study involving lymphoma patients, the Observed Recommended Doses remained consistent irrespective of the administration schedule. This stood in contrast to the M & S predictions, which clearly demonstrated that the MDRD for the 14ON7OFF administration schedule was considerably lower than that for the 4ON3OFF schedule in lymphoma patients. The fact that this predicted difference was not observed in a real clinical setting can be partly explained by the inherent weakness and insufficient sensitivity of the traditional 3+3 design to adequately discriminate between different administration schedules. The change in dose schedule from 14ON7OFF to 4ON3OFF led to a more substantial increase in the MDRD for solid tumor patients (an increase of 260 mg/day) compared to lymphoma patients (an increase of 120 mg/day), making the impact of the schedule change more readily detectable in the solid tumor cohort.

Despite the widespread prevalence of the 3+3 design in phase I clinical trials, its utility in accurately determining the maximum tolerated dose and, consequently, the recommended dose is often compromised, leading to potentially erroneous dose selections. Our comprehensive simulation study provided compelling evidence for this limitation. For every administration schedule tested and for both patient populations, the maximum probability of actually reaching the model-derived recommended dose, assuming the actual RD was precisely known, was approximately 40 percent. This simulation specifically isolated a single step of the 3+3 dose-escalation design. This implies a significant minimum risk of 60 percent that the dose-escalation process would be prematurely halted just before the actual recommended dose is achieved. Therefore, with the 3+3 design, the probability of stopping dose escalation at any given step is notably high, which inherently means that the probability of successfully reaching the true recommended dose is poor. Conversely, the very small number of patients typically included at each step of a 3+3 design can inadvertently lead to an erroneously high recommended dose if the few patients included happen to possess an unusually high tolerance profile to the drug’s toxicity. In a rule-based 3+3 design, critical decisions to either escalate the dose or stop the escalation are based on extremely limited information, typically derived from a mere 3 to 6 patients at a specific dose level. Therefore, advanced Modeling & Simulations emerge as an invaluable tool to complement and support the classical 3+3 design. By integrating all the information systematically gathered throughout the dose-escalation process, M&S can provide a more comprehensive understanding of the dose-toxicity relationship and offer superior guidance for the clinical development of a drug. While the determination of model-derived recommended doses through simulations inherently relies on the prior availability and analysis of pharmacokinetic and pharmacodynamic data, and thus requires the establishment of a robust PKPD model, such a model-based approach can nevertheless be powerfully applied at the culmination of a classical 3+3 dose escalation. This allows for a final, data-driven determination of the optimal recommended dose, thereby overcoming many of the limitations inherent in rule-based designs alone.

Conclusion

Thrombocytopenia unequivocally represents the primary dose-limiting toxicity associated with abexinostat in early-phase clinical trials. This study has successfully refined the previously established semi-mechanistic pharmacokinetic/pharmacodynamic model of thrombocytopenia, which was originally developed for solid tumor patients treated with abexinostat. This refinement has significantly expanded the model’s utility, enabling it to accurately predict the complex dose-toxicity relationship within a broader and more heterogeneous patient population, now including individuals with lymphoma.

The enhanced PKPD model proved instrumental in guiding the development of an optimal administration schedule: 4 days ON treatment, followed by 3 days OFF, repeating every week within a three-week cycle. This schedule was identified as particularly advantageous, as it was associated with model-based recommended doses of abexinostat of 200 mg per day for lymphoma patients and a considerably higher 440 mg per day for solid tumor patients. Crucially, this research has rigorously demonstrated the inherent weakness of the traditional 3+3 dose-escalation design in its ability to precisely determine the true maximum tolerated dose and, consequently, the recommended dose. The findings from this comprehensive study unequivocally underscore the substantial value and superior precision offered by a model-based approach within the dose-escalation process. Such an approach provides a more robust and scientifically sound method for investigating and establishing the recommended dose for future phase II clinical trials, ultimately leading to more optimized and safer therapeutic regimens.