Modelling a spontaneously reported side effect by use of a Markov mixed-effects model

Exposure-response modeling for nausea incidence for cotadutide using a Markov modeling approach

Cotadutide is a dual glucagon-like peptide-1 (GLP-1)/glucagon receptor agonist. Gastrointestinal adverse effects are known to be associated with GLP-1 receptor agonism and can be mitigated through tolerance development via a gradual up-titration. This analysis aimed to characterize the relationship between exposure and nausea incidence and to optimize titration schemes. The model was developed with pooled data from cotadutide-administrated studies. Three different modeling approaches, proportional odds (PO), discrete-time Markov, and two-stage discrete-time Markov models, were employed to characterize the exposure-nausea relationship. The severity of nausea was modeled as different states (non-nausea, mild, and moderate/severe). The most appropriate model was selected to perform the covariate analysis, and the final covariate model was used to simulate the nausea event rates for various titration scenarios. The two Markov models demonstrated comparable performance and were better than the PO model. The covariate analysis was conducted with the standard Markov model for operational simplification and identified disease indications (NASH, obesity) and sex as covariates on Markov parameters. The simulations indicated that the biweekly titration with twofold dose escalation is superior to other titration schemes with a relatively low predicted nausea event rate at 600 μg (25%) and a shorter titration interval (8 weeks) to reach the therapeutic dose. The model can be utilized to optimize starting dose and titration schemes for other therapeutics in clinical trials to achieve an optimal risk-benefit balance and reach the therapeutic dose with minimal titration steps.

A comprehensive regulatory and industry review of modeling and simulation practices in oncology clinical drug development

Exposure-response (E-R) analyses are an integral component in the development of oncology products. Characterizing the relationship between drug exposure metrics and response allows the sponsor to use modeling and simulation to address both internal and external drug development questions (e.g., optimal dose, frequency of administration, dose adjustments for special populations). This white paper is the output of an industry-government collaboration among scientists with broad experience in E-R modeling as part of regulatory submissions. The goal of this white paper is to provide guidance on what the preferred methods for E-R analysis in oncology clinical drug development are and what metrics of exposure should be considered.

Bridging Fixed Dose to Body Weight-based Regimen of Adalimumab in Paediatric Ulcerative Colitis Using a Pharmacometric Modelling Approach: Case Study with the Phase 3 ENVISION I Trial

BACKGROUND AND AIMS

The Phase 3 study ENVISION I demonstrated efficacy and safety of adalimumab in paediatric patients with moderate to severe ulcerative colitis. The protocol-specified high-dose adalimumab regimen was numerically more efficacious than the standard-dose regimen. The objective of this work was to bridge a fixed-dosing regimen to the protocol-specified high-induction/high-maintenance, body weight-based dosing regimen studied in ENVISION I, using a pharmacometrics modelling and simulation approach.

METHODS

A stepwise strategy was implemented, including developing an adalimumab paediatric population pharmacokinetic model; using this model to determine a fixed-dosing regimen in paediatric ulcerative colitis patients which achieves similar concentrations to those observed in ENVISION I patients; determining adalimumab exposure-response relationship using population pharmacokinetic/pharmacodynamic model and data from ENVISION I; simulating clinical remission rate in paediatric ulcerative colitis patients using the Markov exposure-response model and the dosing regimen determined to provide similar efficacy to that observed in ENVISION I.

RESULTS

Both developed population pharmacokinetic and pharmacokinetic/pharmacodynamic models adequately described the observed data. Adalimumab exposure was identified as a significant predictor of clinical remission at Week 8 based on logistic regression [p <0.01]. Simulated efficacy suggested that the fixed-dosing regimen performs similarly to the more efficacious dosing regimen used in ENVISION I, by providing comparable clinical remission per Partial Mayo Score response rates over time. No relationship between adalimumab exposure and adverse events was identified.

CONCLUSIONS

The population pharmacokinetic/pharmacodynamic model supports the appropriateness of the use of the fixed-dosing regimen in the paediatric ulcerative colitis population.

Effect of Elagolix Exposure on Clinical Efficacy End Points in Phase III Trials in Women With Endometriosis-Associated Pain: An Application of Markov Model

Elagolix is an oral gonadotropin‐releasing hormone antagonist approved by the US Food and Drug Administration (FDA) for the management of moderate‐to‐severe pain associated with endometriosis and in combination with estradiol/norethindrone acetate approved for the management of heavy menstrual bleeding associated with uterine leiomyomas (fibroids) in premenopausal women. The objective of this work was to characterize the relationships between elagolix exposures and clinical efficacy response rates for dysmenorrhea (DYS) and nonmenstrual pelvic pain (NMPP) in premenopausal women enrolled in the pivotal phase III studies with moderate‐to‐severe pain associated with endometriosis. Relationships between elagolix average concentrations (C_avg) and efficacy responses (DYS and NMPP) were characterized using a nonlinear mixed‐effects discrete‐time first order Markov modeling approach. Only age was statistically significant for NMPP but not considered clinically relevant. This work indicates that the selection of elagolix dose is not determined based on tested patient demographics, baseline, or endometriosis disease severity measures in covariate analysis. In other words, the work suggests no preference of one regimen over the other to treat endometriosis‐associated pain (DYS or NMPP) for any patient subpopulation based on tested covariate groups.

Analysis of Longitudinal-Ordered Categorical Data for Muscle Spasm Adverse Event of Vismodegib: Comparison Between Different Pharmacometric Models

Longitudinal‐ordered categorical data, common in clinical trials, can be effectively analyzed with nonlinear mixed effect models. In this article, we systematically evaluated the performance of three different models in longitudinal muscle spasm adverse event (AE) data obtained from a clinical trial for vismodegib: a proportional odds (PO) model, a discrete‐time Markov model, and a continuous‐time Markov model. All models developed based on weekly spaced data can reasonably capture the proportion of AE grade over time; however, the PO model overpredicted the transition frequency between grades and the cumulative probability of AEs. The influence of data frequency (daily, weekly, or unevenly spaced) was also investigated. The PO model performance reduced with increased data frequency, and the discrete‐time Markov model failed to describe unevenly spaced data, but the continuous‐time Markov model performed consistently well. Clinical trial simulations were conducted to illustrate the muscle spasm resolution time profile during the 8‐week dose interruption period after 12 weeks of continuous treatment.

Assessment of Demographic and Socio-Behavioral Factors on Adherence to HIV Pre-Exposure Prophylaxis Using a Markov Modeling Approach

Purpose: Adherence is important for the effectiveness of human immunodeficiency virus (HIV) preexposure prophylaxis (PrEP). The objective of the current work is to assess the impact of multiple demographic and socio-behavioral factors on the adherence to tenofovir-based PrEP among HIV serodiscordant couples in East Africa using Markov mixed-effects modeling approach.

Methods: The Partners Demonstration Project was a prospective, open-label, implementation science-driven study of HIV PrEP among heterosexual HIV serodiscordant couples in Kenya and Uganda. The uninfected partner received oral PrEP according to the “bridge to antiretroviral therapy [ART]” strategy (i.e., until the infected partner had been on ART for ≥6 months). Adherence was monitored electronically; demographic and socio-behavioral data were collected during study visits. Analyzed data reflect 12 months of follow-up per participant. A two-state, first-order, discrete time Markov model was developed with longitudinal adherence data characterized by “dose taking (1)” and “dose missing (0).” Covariate effects were linearly added in the logit domain of transition probability parameters (P01 and P10) in the model. The full covariate model was initially developed, followed by backward elimination process to reduce the model. All significant covariates reported by a prior primary statistical analysis of the same data were included in the full covariate model.

Results: The model included data from 920 participants, who were predominantly male (65%). Significant covariates associated with higher adherence were 25 years or older [odds ratio (OR) for P10, 0.61], female sex (OR for P10, 0.67), participant wanting the relationship with the partner to succeed (OR for P10, 0.79; OR for P01, 1.45), and sex with partner either with 100% or <100% condom use compared to those reported no sex (OR for P10, 0.84; OR for P01, 1.21). Significant covariates associated with lower adherence were partner on ART >6 months (OR for P01, 0.86; OR for P10, 1.34), subject in the study for >6 months (OR for P01, 0.8; OR for P10, 1.25), and problematic alcohol use (OR for P01, 0.63; OR for P10, 1.16).

Conclusion: The developed Markov model provides a mechanistic understanding of relationship between demographic, socio-behavioral covariates, and PrEP adherence, by indicating the pattern of adherence influenced by each factor over time. Such data can be used for further intervention development to promote PrEP adherence.

Neoadjuvant therapy for locally advanced gastric cancer patients. A population pharmacodynamic modeling

Background

Perioperative chemotherapy (CT) or neoadjuvant chemoradiotherapy (CRT) in patients with locally advanced gastric (GC) or gastroesophageal junction cancer (GEJC) has been shown to improve survival compared to an exclusive surgical approach. However, most patients retain a poor prognosis due to important relapse rates. Population pharmacokinetic-pharmacodynamic (PK/PD) modeling may allow identifying at risk-patients. We aimed to develop a mechanistic PK/PD model to characterize the relationship between the type of neoadjuvant therapy, histopathologic response and survival times in locally advanced GC and GEJC patients.

Methods

Patients with locally advanced GC and GEJC treated with neoadjuvant CT with or without preoperative CRT were analyzed. Clinical response was assessed by CT-scan and EUS. Pathologic response was defined as a reduction on pTNM stage compared to baseline cTNM. Metastasis development risk and overall survival (OS) were described using the population approach with NONMEM 7.3. Model evaluation was performed through predictive checks.

Results

A low correlation was observed between clinical and pathologic TNM stage for both T (R = 0.32) and N (R = 0.19) categories. A low correlation between clinical and pathologic response was noticed (R = -0.29). The OS model adequately described the observed survival rates. Disease recurrence, cTNM stage ≥3 and linitis plastica absence, were correlated to a higher risk of death.

Conclusion

Our model adequately described clinical response profiles, though pathologic response could not be predicted. Although the risk of disease recurrence and survival were linked, the identification of alternative approaches aimed to tailor therapeutic strategies to the individual patient risk warrants further research.

Modeling Exposure-Driven Adverse Event Time Courses in Oncology Exemplified by Afatinib

Models were developed to characterize the relationship between afatinib exposure and diarrhea and rash/acne adverse event (AE) trajectories, and their predictive ability was assessed. Based on pooled data from seven phase II/III clinical studies including 998 patients, mixed-effects models for ordered categorical data were applied to describe daily AE severity. Clinical trial simulation aided by trial execution models was used for internal and external model evaluation. The final exposure-safety model consisted of longitudinal logistic regression models with first-order Markov elements for both AEs. Drug exposure was included as daily area under the concentration-time curve (AUC), and drug effects on the AEs were correlated. Clinical trial simulation allowed adequate prediction of maximum AE grades and AE severity time courses but overestimated the proportion of AE-dependent dose reductions and discontinuations. Both diarrhea and rash/acne were correlated with afatinib exposure. The developed modeling framework allows a prospective comparison of dosing strategies and study designs with respect to safety.

The impact of tacrolimus exposure on extrarenal adverse effects in adult renal transplant recipients

AIMS

Tacrolimus has been associated with notable extrarenal adverse effects (AEs), which are unpredictable and impact patient morbidity. The association between model-predicted tacrolimus exposure metrics and standardized extrarenal AEs in stable renal transplant recipients was investigated and a limited sampling strategy (LSS) was developed to predict steady-state tacrolimus area under the curve over a 12-h dosing period (AUC_ss,0-12h ).

METHODS

All recipients receiving tacrolimus and mycophenolic acid ≥6 months completed a 12-h cross-sectional observational pharmacokinetic-pharmacodynamic study. Patients were evaluated for the presence of individual and composite gastrointestinal, neurological, and aesthetic AEs during the study visit. The associations between AEs and tacrolimus exposure metrics generated from a published population pharmacokinetic model were investigated using a logistic regression analysis in NONMEM 7.3. An LSS was determined using a Bayesian estimation method with the same patients.

RESULTS

Dose-normalized tacrolimus AUC_ss,0-12h and apparent clearance were independently associated with diarrhoea, dyspepsia, insomnia and neurological AE ratio. Dose-normalized tacrolimus maximum concentration was significantly correlated with skin changes and acne. No AE associations were found with trough concentrations. Using limited sampling at 0, 2h; 0, 1, 4h; and 0, 1, 2, 4h provided a precise and unbiased prediction of tacrolimus AUC (root mean squared prediction error < 10%), which was not well characterized using trough concentrations only (root mean squared prediction error >15%).

CONCLUSIONS

Several AEs (i.e. diarrhoea, dyspepsia, insomnia and neurological AE ratio) were associated with tacrolimus dose normalized AUC_ss,0-12h and clearance. Skin changes and acne were associated with dose-normalized maximum concentrations. To facilitate clinical implementation, a LSS was developed to predict AUC_ss,0-12h values using sparse patient data to efficiently assess projected immunosuppressive exposure and potentially minimize AE manifestations.

A Minimal Continuous-Time Markov Pharmacometric Model

In this work, an alternative model to discrete-time Markov model (DTMM) or standard continuous-time Markov model (CTMM) for analyzing ordered categorical data with Markov properties is presented: the minimal CTMM (mCTMM). Through a CTMM reparameterization and under the assumption that the transition rate between two consecutive states is independent on the state, the Markov property is expressed through a single parameter, the mean equilibration time, and the steady-state probabilities are described by a proportional odds (PO) model. The mCTMM performance was evaluated and compared to the PO model (ignoring Markov features) and to published Markov models using three real data examples: the four-state fatigue and hand-foot syndrome data in cancer patients initially described by DTMM and the 11-state Likert pain score data in diabetic patients previously analyzed with a count model including Markovian transition probability inflation. The mCTMM better described the data than the PO model, and adequately predicted the average number of transitions per patient and the maximum achieved scores in all examples. As expected, mCTMM could not describe the data as well as more flexible DTMM but required fewer estimated parameters. The mCTMM better fitted Likert data than the count model. The mCTMM enables to explore the effect of potential predictive factors such as drug exposure and covariates, on ordered categorical data, while accounting for Markov features, in cases where DTMM and/or standard CTMM is not applicable or conveniently implemented, e.g., non-uniform time intervals between observations or large number of categories.

Markov Mixed Effects Modeling Using Electronic Adherence Monitoring Records Identifies Influential Covariates to HIV Preexposure Prophylaxis

Adherence is a major factor in the effectiveness of preexposure prophylaxis (PrEP) for HIV prevention. Modeling patterns of adherence helps to identify influential covariates of different types of adherence as well as to enable clinical trial simulation so that appropriate interventions can be developed. We developed a Markov mixed-effects model to understand the covariates influencing adherence patterns to daily oral PrEP. Electronic adherence records (date and time of medication bottle cap opening) from the Partners PrEP ancillary adherence study with a total of 1147 subjects were used. This study included once-daily dosing regimens of placebo, oral tenofovir disoproxil fumarate (TDF), and TDF in combination with emtricitabine (FTC), administered to HIV-uninfected members of serodiscordant couples. One-coin and first- to third-order Markov models were fit to the data using NONMEM^® 7.2. Model selection criteria included objective function value (OFV), Akaike information criterion (AIC), visual predictive checks, and posterior predictive checks. Covariates were included based on forward addition (α = 0.05) and backward elimination (α = 0.001). Markov models better described the data than 1-coin models. A third-order Markov model gave the lowest OFV and AIC, but the simpler first-order model was used for covariate model building because no additional benefit on prediction of target measures was observed for higher-order models. Female sex and older age had a positive impact on adherence, whereas Sundays, sexual abstinence, and sex with a partner other than the study partner had a negative impact on adherence. Our findings suggest adherence interventions should consider the role of these factors.

Pharmacodynamic modeling of adverse effects of anti-cancer drug treatment

Purpose

Adverse effects related to anti-cancer drug treatment influence patient’s quality of life, have an impact on the realized dosing regimen, and can hamper response to treatment. Quantitative models that relate drug exposure to the dynamics of adverse effects have been developed and proven to be very instrumental to optimize dosing schedules. The aims of this review were (i) to provide a perspective of how adverse effects of anti-cancer drugs are modeled and (ii) to report several model structures of adverse effect models that describe relationships between drug concentrations and toxicities.

Methods

Various quantitative pharmacodynamic models that model adverse effects of anti-cancer drug treatment were reviewed.

Results

Quantitative models describing relationships between drug exposure and myelosuppression, cardiotoxicity, and graded adverse effects like fatigue, hand-foot syndrome (HFS), rash, and diarrhea have been presented for different anti-cancer agents, including their clinical applicability.

Conclusions

Mathematical modeling of adverse effects proved to be a helpful tool to improve clinical management and support decision-making (especially in establishment of the optimal dosing regimen) in drug development. The reported models can be used as templates for modeling a variety of anti-cancer-induced adverse effects to further optimize therapy.

Simultaneous Exposure-Response Modeling of ACR20, ACR50, and ACR70 Improvement Scores in Rheumatoid Arthritis Patients Treated With Certolizumab Pegol

The Markovian approach has been proposed to model American College of Rheumatology's (ACR) response (ACR20, ACR50, or ACR70) reported in rheumatoid arthritis clinical trials to account for the dependency of the scores over time. However, dichotomizing the composite ACR assessment discards much information. Here, we propose a new approach for modeling together the three thresholds: a continuous-time Markov exposure–response model was developed, based on data from five placebo-controlled certolizumab pegol clinical trials. This approach allows adequate prediction of individual ACR20/50/70 time-response, even for non-periodic observations. An exposure–response was established over a large range of licensed and unlicensed doses including phase II dose-ranging data. Simulations from the model (50–400 mg every other week) illustrated the range and sustainability of response (ACR20: 56–68%, ACR50: 27–42%, ACR70: 11–22% at week 24) with maximum clinical effect achieved at the recommended maintenance dose of 200 mg every other week.

Dopamine D2 receptor occupancy as a predictor of catalepsy in rats: a pharmacokinetic-pharmacodynamic modeling approach

OBJECTIVES

Dopamine D2 receptor occupancy (D2RO) is the major determinant of efficacy and safety in schizophrenia drug therapy. Excessive D2RO (>80%) is known to cause catalepsy (CAT) in rats and extrapyramidal side effects (EPS) in human. The objective of this study was to use pharmacokinetic and pharmacodynamic modeling tools to relate CAT with D2RO in rats and to compare that with the relationship between D2RO and EPS in humans.

METHODS

Severity of CAT was assessed in rats at hourly intervals over a period of 8 h after antipsychotic drug treatment. An indirect response model with and without Markov elements was used to explain the relationship of D2RO and CAT.

RESULTS

Both models explained the CAT data well for olanzapine, paliperidone and risperidone. However, only the model with the Markov elements predicted the CAT severity well for clozapine and haloperidol. The relationship between CAT scores in rat and EPS scores in humans was implemented in a quantitative manner. Risk of EPS not exceeding 10% over placebo correlates with less than 86% D2RO and less than 30% probability of CAT events in rats.

CONCLUSION

A quantitative relationship between rat CAT and human EPS was elucidated and may be used in drug discovery to predict the risk of EPS in humans from D2RO and CAT scores measured in rats.

PKPD Modeling of Predictors for Adverse Effects and Overall Survival in Sunitinib-Treated Patients With GIST

A modeling framework relating exposure, biomarkers (vascular endothelial growth factor (VEGF), soluble vascular endothelial growth factor receptor (sVEGFR)-2, -3, soluble stem cell factor receptor (sKIT)), and tumor growth to overall survival (OS) was extended to include adverse effects (myelosuppression, hypertension, fatigue, and hand–foot syndrome (HFS)). Longitudinal pharmacokinetic–pharmacodynamic models of sunitinib were developed based on data from 303 patients with gastrointestinal stromal tumor. Myelosuppression was characterized by a semiphysiological model and hypertension with an indirect response model. Proportional odds models with a first-order Markov model described the incidence and severity of fatigue and HFS. Relative change in sVEGFR-3 was the most effective predictor of the occurrence and severity of myelosuppression, fatigue, and HFS. Hypertension was correlated best with sunitinib exposure. Baseline tumor size, time courses of neutropenia, and relative increase of diastolic blood pressure were identified as predictors of OS. The framework has potential to be used for early monitoring of adverse effects and clinical response, thereby facilitating dose individualization to maximize OS.

First-time-in-human study with GSK1018921, a selective GlyT1 inhibitor: relationship between exposure and dizziness

The pharmacokinetics (PK), safety, and tolerability of GSK1018921, a glycine transporter 1 (GlyT-1) inhibitor, were assessed in this first-time-in-human (FTIH) study. Single oral doses ranging from 0.5 to 280 mg and placebo were administered to 25 healthy subjects in a five-period, two-cohort, crossover study. GSK1018921 showed dose-proportional PK with a terminal half-life of ~17 h. The subjects reported dizziness with a dose-dependent frequency of 22-88% at doses of 70-280 mg. The time course of the dizziness paralleled the PK of the drug, with peak response at 2 h after the dose, consistent with time to maximum plasma concentration (T(max)). The dizziness was resolved by 10-12 h in all subjects. A Markov-chain logistic regression model was implemented in NONMEM to determine the probability of developing dizziness as a function of the plasma concentration of the compound. Frequency, onset (<1 h), and offset (4 h) were well described by the model. Exposure resulting in 80% receptor occupancy is predicted to be well tolerated.

Implementation and evaluation of the SAEM algorithm for longitudinal ordered categorical data with an illustration in pharmacokinetics-pharmacodynamics

Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable.

Pharmacodynamic differentiation of lorazepam sleepiness and dizziness using an ordered categorical measure

Categorical measures of lorazepam sleepiness and dizziness were modeled to identify differences in pharmacodynamic (PD) parameters between these adverse events (AEs). Differences in data-derived PD parameters were compared with relative incidence rates in the drug label (15.7% and 6.9%, respectively). Healthy volunteers (n = 20) received single oral doses of 2 mg lorazepam or placebo in a randomized, double-blind, cross-over fashion. A seven-point categorical scale measuring the intensity of AEs was serially administered over 24 h. The maximum score (MaxS), and area under the effect curve (AUEC) were determined by noncompartmental methods and compared using a paired t-test. Individual scores were modeled using a logistic function implemented in NONMEM. AUEC and MaxS for sleepiness were significantly higher than dizziness (20.35 vs. 9.76, p < 0.01) and (2.35 vs. 1.45, p < 0.01). Model slope estimates were similar for sleepiness and dizziness (0.21 logits x mL/ng vs. 0.19 logits x mL/ng), but baseline logits were significantly higher for sleepiness (-2.81 vs. -4.34 logits). Data-derived PD parameters were in concordance with label incidence rates. The higher intensity of sleepiness may be directly related to baseline (no drug present) while the increase in intensity as a result of drug was relatively similar for both AEs.

Modelling overdispersion and Markovian features in count data

The number of counts (events) per unit of time is a discrete response variable that is generally analyzed with the Poisson distribution (PS) model. The PS model makes two assumptions: the mean number of counts (lambda) is assumed equal to the variance, and counts occurring in non-overlapping intervals are assumed independent. However, many counting outcomes show greater variability than predicted by the PS model, a phenomenon called overdispersion. The purpose of this study was to implement and explore, in the population context, different distribution models accounting for overdispersion and Markov patterns in the analysis of count data. Daily seizures count data obtained from 551 subjects during the 12-week screening phase of a double-blind, placebo-controlled, parallel-group multicenter study performed in epileptic patients with medically refractory partial seizures, were used in the current investigation. The following distribution models were fitted to the data: PS, Zero-Inflated PS (ZIP), Negative Binomial (NB), and Zero-Inflated Negative Binomial (ZINB) models. Markovian features were introduced estimating different lambdas and overdispersion parameters depending on whether the previous day was a seizure or a non-seizure day. All analyses were performed with NONMEM VI. All models were successfully implemented and all overdispersed models improved the fit with respect to the PS model. The NB model resulted in the best description of the data. The inclusion of Markovian features in lambda and in the overdispersion parameter improved the fit significantly (P < 0.001). The plot of the variance versus mean daily seizure count profiles, and the number of transitions, are suggested as model performance tools reflecting the capability to handle overdispersion and Markovian features, respectively.

Quantitative disease, drug, and trial models

Quantitative disease-drug-trial models allow learning from prior experience and summarize the knowledge in a ready to apply format. Employing these models to plan future development is proposed as a powerful solution to improve pharmaceutical R&D productivity. The disease and trial models are, to a large extent, independent of the product, but the drug model is not. The goals are to apply the disease and trial models to future development and regulatory decisions, and publicly share them. We propose working definitions of these models, describe the various subcomponents, provide examples, and discuss the challenges and potential solutions for developing such models. Building useful disease-drug-trial models is a challenging task and cannot be achieved by any single organization. It requires a consorted effort by industry, academic, and regulatory scientists. We also describe the strategic goals of the FDA Pharmacometrics group.

The use of clinical utility assessments in early clinical development

A quickly realizable benefit of model-based drug development is in reducing uncertainty in risk/benefit, comprising individually of safety and effectiveness, two key attributes of a product evaluated for regulatory approval, marketing, and use. In this review, we investigate gaps and opportunities in using fundamental decision analytic principles in drug development and present a quantitative clinical pharmacology framework for the application of such aids for early clinical development decision making. We anticipate that implementation of such emerging tools will enable sufficient scientific understanding of the two attributes to facilitate the early termination of compounds with less than desirable risk/benefit profiles and continuance of compounds with acceptable risk/benefit profiles.

Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004

Model evaluation is an important issue in population analyses. We aimed to perform a systematic review of all population pharmacokinetic and/or pharmacodynamic analyses published between 2002 and 2004 to survey the current methods used to evaluate models and to assess whether those models were adequately evaluated. We selected 324 articles in MEDLINE using defined key words and built a data abstraction form composed of a checklist of items to extract the relevant information from these articles with respect to model evaluation. In the data abstraction form, evaluation methods were divided into three subsections: basic internal methods (goodness-of-fit [GOF] plots, uncertainty in parameter estimates and model sensitivity), advanced internal methods (data splitting, resampling techniques and Monte Carlo simulations) and external model evaluation. Basic internal evaluation was the most frequently described method in the reports: 65% of the models involved GOF evaluation. Standard errors or confidence intervals were reported for 50% of fixed effects but only for 22% of random effects. Advanced internal methods were used in approximately 25% of models: data splitting was more often used than bootstrap and cross-validation; simulations were used in 6% of models to evaluate models by a visual predictive check or by a posterior predictive check. External evaluation was performed in only 7% of models. Using the subjective synthesis of model evaluation for each article, we judged the models to be adequately evaluated in 28% of pharmacokinetic models and 26% of pharmacodynamic models. Basic internal evaluation was preferred to more advanced methods, probably because the former is performed easily with most software. We also noticed that when the aim of modelling was predictive, advanced internal methods or more stringent methods were more often used.