Performance of three estimation methods in repeated time-to-event modeling

Practical Applications of a Nausea and Vomiting Model in the Clinical Development of Additional Doses of Dulaglutide

Dulaglutide 3.0 and 4.5 mg weekly doses were approved for additional glycemic control in adult patients with type 2 diabetes inadequately controlled with metformin and 0.75 or 1.5 mg weekly doses of dulaglutide. Effects such as nausea and vomiting are commonly reported with dulaglutide and other glucagon-like peptide-1 receptor agonist therapies. Based on a pharmacokinetic/pharmacodynamic model-informed approach, a stepwise dose-escalation scheme with 4-week intervals between dose increments was suggested to mitigate gastrointestinal events for dulaglutide. These gastrointestinal events are dose dependent and attenuate over time with repeated dosing. A Markov chain Monte Carlo pharmacokinetic/pharmacodynamic joint model was developed using AWARD-11 data (N = 1842) to optimize dulaglutide dose escalation to 3.0 and 4.5 mg to mitigate gastrointestinal events. Model simulations evaluated probabilities of nausea and vomiting events for various dosing scenarios in patients needing higher doses for additional glycemic control. The model indicated that patients may dose escalate from 1.5 to 3.0 mg, then 4.5 mg weekly after at least 4 weeks on each dose. No clinically meaningful differences in nausea or vomiting events were expected when patients escalated to 3.0 or 4.5 mg following initiation at 0.75 or 1.5 mg dulaglutide. Based on the findings of this model, a minimum 4-week duration at each dose before escalation was appropriate to reduce gastrointestinal events of dulaglutide, consistent with observed gastrointestinal events data from the AWARD-11 study and supporting the currently recommended dose-escalation regimen of dulaglutide doses of 3.0 and 4.5 mg for additional glycemic control.

A simple time-to-event model with NONMEM featuring right-censoring

In healthcare situations, time-to-event (TTE) data are common outcomes. A parametric approach is often employed to handle TTE data because it is possible to easily visualize different scenarios via simulation. Not all pharmacometricians are familiar with the use of non-linear mixed effects models (NONMEMs) to deal with TTE data. Therefore, this tutorial simply explains how to analyze TTE data using NONMEM. We show how to write the code and evaluate the model. We also provide an example of a hands-on model for training.

Predicting Unacceptable Pain in Cardiac Surgery Patients Receiving Morphine Maintenance and Rescue Doses: A Model-Based Pharmacokinetic-Pharmacodynamic Analysis

BACKGROUND

Optimal analgesic treatment following cardiac surgery is crucial for both patient comfort and successful postoperative recovery. While knowledge of both the pharmacokinetics and pharmacodynamics of analgesics is required to predict optimal drug dosing, models quantifying the pharmacodynamics are scarce. Here, we quantify the pharmacodynamics of morphine by modeling the need for rescue morphine to treat unacceptable pain in 118 patients after cardiac surgery.

METHODS

The rescue morphine event data were analyzed with repeated time-to-event (RTTE) modeling using NONMEM. Postoperative pain titration protocol consisted of continuous morphine infusions (median duration 20.5 hours) with paracetamol 4 times daily and rescue morphine in case of unacceptable pain (numerical rating scale ≥4).

RESULTS

Patients had a median age of 73 years (interquartile range [IQR]: 63-77) and median bodyweight of 80 kg (IQR: 72-90 kg). Most patients (55%) required at least 1 rescue morphine dose. The hazard for rescue morphine following cardiac surgery was found to be significantly influenced by time after surgery, a day/night cycle with a peak at 23:00 (95% confidence interval [CI], 19:35-02:03) each day, and an effect of morphine concentration with 50% hazard reduction at 9.3 ng·mL-1 (95% CI, 6.7-16).

CONCLUSIONS

The pharmacodynamics of morphine after cardiac surgery was successfully quantified using RTTE modeling. Future studies can be used to expand the model to better predict morphine's pharmacodynamics on the individual level and to include the pharmacodynamics of other analgesics so that improved postoperative pain treatment protocols can be developed.

The effect of aging on infliximab exposure and response in patients with inflammatory bowel diseases

AIMS

Controversies regarding infliximab treatment in elderly patients with inflammatory bowel diseases remain. We evaluated the effect of patient's age on infliximab exposure, efficacy and safety.

METHODS

Retrospective case-control data of patients receiving infliximab induction treatment were analysed. A population pharmacokinetic model was developed to estimate individual pharmacokinetic parameters. A logistic regression model was used to investigate the effect of exposure on endoscopic remission. Repeated time-to-event models were developed to describe the hazard of safety events over time.

RESULTS

A total of 104 patients (46 elderly, ≥65 years) were included. A two-compartment population pharmacokinetic model with linear elimination adequately described the data. Infliximab clearance decreased with older age, higher serum albumin, lower fat-free mass, lower C-reactive protein and absence of immunogenicity. Yet, infliximab exposure was not significantly different between elderly and nonelderly. Regardless of age, an infliximab trough concentration at week (w)14 of 15.6 mg/L was associated with a 50% probability of attaining endoscopic remission between w6 and w22. Infliximab exposure during induction treatment was not a risk factor of (severe) adverse events. The hazard of severe adverse events and malignancy increased by 2% and 7%, respectively, with increasing year of age. Concomitant immunomodulator use increased the hazard of infection by 958%, regardless of age.

CONCLUSIONS

Elderly patients attained infliximab exposure and endoscopic remission similarly to nonelderly patients. Therefore, the same infliximab trough concentration target can be used in therapeutic drug monitoring. The hazards of severe adverse events and malignancy increased with age, but not with infliximab exposure.

Topiramate pharmacokinetics in neonates undergoing therapeutic hypothermia and proposal of an optimised dosing schedule

AIM

The adequate dosing of topiramate in neonates undergoing therapeutic hypothermia has not been established. The aim of this study was to design a dosing schedule capable of providing topiramate serum concentrations within the accepted therapeutic range.

METHODS

Neonates (n = 52) with hypoxic ischaemic encephalopathy and subjected to therapeutic hypothermia were dosed with topiramate, 5 mg/kg on day one and 3 mg/kg on days two to five, to decrease seizure events. A total of 451 topiramate serum concentrations obtained in the patients were used to develop a population pharmacokinetic model using a non-linear mixed-effects modelling approach.

RESULTS

A one-compartment model with first-order absorption and two different clearance terms, one for the cooling period and another for the post-warming period, were used to describe the concentration-time topiramate data. The probability of no-seizure events could not be related to topiramate concentrations, which was attributed to excessively low topiramate concentrations. A modified dosage schedule was designed with the aim of obtaining more than 90% of patients with topiramate concentrations within the therapeutic range after the first dose.

CONCLUSION

The dosage schedule of topiramate in these patients should be modified with the aim of decreasing the frequency of seizure events.

Relationship between factor VIII activity, bleeds and individual characteristics in severe hemophilia A patients

Pharmacokinetic-based prophylaxis of replacement factor VIII (FVIII) products has been encouraged in recent years, but the relationship between exposure (factor VIII activity) and response (bleeding frequency) remains unclear. The aim of this study was to characterize the relationship between FVIII dose, plasma FVIII activity, and bleeding patterns and individual characteristics in severe hemophilia A patients. Pooled pharmacokinetic and bleeding data during prophylactic treatment with BAY 81-8973 (octocog alfa) were obtained from the three LEOPOLD trials. The population pharmacokinetics of FVIII activity and longitudinal bleeding frequency, as well as bleeding severity, were described using non-linear mixed effects modeling in NONMEM. In total, 183 patients [median age 22 years (range, 1-61); weight 60 kg (11-124)] contributed with 1,535 plasma FVIII activity observations, 633 bleeds and 11 patient/study characteristics [median observation period 12 months (3.1-13.1)]. A parametric repeated time-to-categorical bleed model, guided by plasma FVIII activity from a 2-compartment population pharmacokinetic model, described the time to the occurrence of bleeds and their severity. Bleeding probability decreased with time of study, and a bleed was not found to affect the time of the next bleed. Several covariate effects were identified, including the bleeding history in the 12-month pre-study period increasing the bleeding hazard. However, unexplained inter-patient variability in the phenotypic bleeding pattern remained large (111%CV). Further studies to translate the model into a tool for dose individualization that considers the individual bleeding risk are required. Research was based on a post-hoc analysis of the LEOPOLD studies registered at clinicaltrials.gov identifiers: 01029340, 01233258 and 01311648.

Exposure-Response Model of Subcutaneous C1-Inhibitor Concentrate to Estimate the Risk of Attacks in Patients With Hereditary Angioedema

Subcutaneous C1‐inhibitor (HAEGARDA, CSL Behring), is a US Food and Drug Administration (FDA)‐approved, highly concentrated formulation of a plasma‐derived C1‐esterase inhibitor (C1‐INH), which, in the phase III Clinical Studies for Optimal Management in Preventing Angioedema with Low‐Volume Subcutaneous C1‐inhibitor Replacement Therapy (COMPACT) trial, reduced the incidence of hereditary angioedema (HAE) attacks when given prophylactically. Data from the COMPACT trial were used to develop a repeated time‐to‐event model to characterize the timing and frequency of HAE attacks as a function of C1‐INH activity, and then develop an exposure–response model to assess the relationship between C1‐INH functional activity levels (C1‐INH(f)) and the risk of an attack. The C1‐INH(f) values of 33.1%, 40.3%, and 63.1% were predicted to correspond with 50%, 70%, and 90% reductions in the HAE attack risk, respectively, relative to no therapy. Based on trough C1‐INH(f) values for the 40 IU/kg (40.2%) and 60 IU/kg (48.0%) C1‐INH (SC) doses, the model predicted that 50% and 67% of the population, respectively, would see at least a 70% decrease in the risk of an attack.

Performance comparison of first-order conditional estimation with interaction and Bayesian estimation methods for estimating the population parameters and its distribution from data sets with a low number of subjects

Background

Exploratory preclinical, as well as clinical trials, may involve a small number of patients, making it difficult to calculate and analyze the pharmacokinetic (PK) parameters, especially if the PK parameters show very high inter-individual variability (IIV). In this study, the performance of a classical first-order conditional estimation with interaction (FOCE-I) and expectation maximization (EM)-based Markov chain Monte Carlo Bayesian (BAYES) estimation methods were compared for estimating the population parameters and its distribution from data sets having a low number of subjects.

Methods

In this study, 100 data sets were simulated with eight sampling points for each subject and with six different levels of IIV (5%, 10%, 20%, 30%, 50%, and 80%) in their PK parameter distribution. A stochastic simulation and estimation (SSE) study was performed to simultaneously simulate data sets and estimate the parameters using four different methods: FOCE-I only, BAYES(C) (FOCE-I and BAYES composite method), BAYES(F) (BAYES with all true initial parameters and fixed ω²), and BAYES only. Relative root mean squared error (rRMSE) and relative estimation error (REE) were used to analyze the differences between true and estimated values. A case study was performed with a clinical data of theophylline available in NONMEM distribution media. NONMEM software assisted by Pirana, PsN, and Xpose was used to estimate population PK parameters, and R program was used to analyze and plot the results.

Results

The rRMSE and REE values of all parameter (fixed effect and random effect) estimates showed that all four methods performed equally at the lower IIV levels, while the FOCE-I method performed better than other EM-based methods at higher IIV levels (greater than 30%). In general, estimates of random-effect parameters showed significant bias and imprecision, irrespective of the estimation method used and the level of IIV. Similar performance of the estimation methods was observed with theophylline dataset.

Conclusions

The classical FOCE-I method appeared to estimate the PK parameters more reliably than the BAYES method when using a simple model and data containing only a few subjects. EM-based estimation methods can be considered for adapting to the specific needs of a modeling project at later steps of modeling.

Electronic supplementary material

The online version of this article (10.1186/s12874-017-0427-0) contains supplementary material, which is available to authorized users.

Population Pharmacokinetics of Selumetinib and Its Metabolite N-desmethyl-selumetinib in Adult Patients With Advanced Solid Tumors and Children With Low-Grade Gliomas

Selumetinib (AZD6244, ARRY‐142886), a mitogen activated protein kinases (MEK1 and 2) inhibitor, has been granted orphan drug designation for differentiated thyroid cancer. The primary aim of this analysis was to characterize the population pharmacokinetics of selumetinib and its active metabolite N‐desmethyl‐selumetinib in patients with cancer. Concentration–time data from adult and pediatric clinical trials were pooled to develop a population pharmacokinetic model using a sequential approach where selumetinib and N‐desmethyl‐selumetinib data were modeled separately. A sequential zero‐ and first‐order absorption with lag time with a two‐compartment model for selumetinib and a two‐compartment model for N‐desmethyl‐selumetinib best described the concentration–time data. Intrapatient variability in absorption was higher than interpatient variability. The apparent drug clearance (CL/F) from the central compartment was 13.5 L/hr (RSE 4.9%). Significant covariates for CL/F were age, alanine aminotransferase, and body surface area. This study confirms that flat dosing is appropriate in adults, whereas body‐surface area based dosing should be used in pediatric patients.

BSA and ABCB1 polymorphism affect the pharmacokinetics of sunitinib and its active metabolite in Asian mRCC patients receiving an attenuated sunitinib dosing regimen

PURPOSE

An attenuated dosing (AD) sunitinib regimen of 37.5 mg daily has been suggested to reduce the toxicity reported with the standard dosing regimen to metastatic renal cell carcinoma (mRCC) patients. The aim of this study was to characterize the population pharmacokinetic (PK) properties of sunitinib and SU12662, the active metabolite, in patients receiving the AD regimen and to ascertain significant covariates influencing PK parameters.

METHODS

Thirty-one mRCC patients receiving AD sunitinib regimen were included. Plasma samples were collected on day 29 of each treatment cycle after the start of the therapy. Nonlinear mixed-effects modeling was applied to estimate the population PK properties of sunitinib and SU12662 as well as the effect of covariates on PK parameters. Monte Carlo simulation was also performed to predict the total trough level (TTL) of sunitinib and SU12662.

RESULTS

Sunitinib population means for CL/F and V d /F central were 13.8 L/h and 1720 L, respectively. SU12662 population means for CL/F and V d /F were 42.1 L/h and 1410 L, respectively. Body surface area (BSA) and ABCB1 polymorphism significantly influenced the CL/F variability of sunitinib: CL/F parent = 13.8 × exp((BSA - 1.75) × 2.08 + (ABCB1 genotype - 0.67) × 0.61), ABCB1-0: wild genotype, 1: mutant genotype. The effect size of ABCB1 mutant genotype and BSA greater than 1.75 m(2) in relation to sunitinib clearance was 31.14 % (p = 0.006) and 22.11 % (p = 0.011), respectively, relative to the reference group.

CONCLUSIONS

Adjusting doses of sunitinib according to BSA and ABCB1 polymorphism in Asian mRCC patients may be recommended for sufficient attainment of a target TTL of sunitinib and its metabolite.

Repeated Time-to-event Analysis of Consecutive Analgesic Events in Postoperative Pain

BACKGROUND

Reduction in consumption of opioid rescue medication is often used as an endpoint when investigating analgesic efficacy of drugs by adjunct treatment, but appropriate methods are needed to analyze analgesic consumption in time. Repeated time-to-event (RTTE) modeling is proposed as a way to describe analgesic consumption by analyzing the timing of consecutive analgesic events.

METHODS

Retrospective data were obtained from 63 patients receiving standard analgesic treatment including morphine on request after surgery following hip fracture. Times of analgesic events up to 96 h after surgery were extracted from hospital medical records. Parametric RTTE analysis was performed with exponential, Weibull, or Gompertz distribution of analgesic events using NONMEM, version 7.2 (ICON Development Solutions, USA). The potential influences of night versus day, sex, and age were investigated on the probability.

RESULTS

A Gompertz distribution RTTE model described the data well. The probability of having one or more analgesic events within 24 h was 80% for the first event, 55% for the second event, 31% for the third event, and 18% for fourth or more events for a typical woman of age 80 yr. The probability of analgesic events decreased in time, was reduced to 50% after 3.3 days after surgery, and was significantly lower (32%) during night compared with day.

CONCLUSIONS

RTTE modeling described analgesic consumption data well and could account for time-dependent changes in probability of analgesic events. Thus, RTTE modeling of analgesic events is proposed as a valuable tool when investigating new approaches to pain management such as opioid-sparing analgesia.

Modeling the Anesthetic Effect of Ropivacaine after a Femoral Nerve Block in Orthopedic Patients

Background:

Even though ropivacaine is frequently used during orthopedic surgery, the relationship between plasma concentrations and degree of sensory anesthesia after a peripheral nerve block is currently unknown. The aim of this study was to characterize this relation using population pharmacokinetic–pharmacodynamic modeling.

Methods:

Femoral nerve block was performed by the anterior approach using a single injection (20 ml) of 0.5% ropivacaine hydrochloride in 20 patients scheduled for total knee arthroplasty under spinal anesthesia. Sensory thresholds in response to a gradual increase in transcutaneous electrical stimulation (primary endpoints), loss and recovery of ice-cold sensation, as well as total ropivacaine plasma concentrations were determined up to 4 days after administration of the local anesthetic. Using NONMEM (ICON, USA), sensory block was modeled by assuming an equilibration delay (ke0) between amount in the depot and effect-site compartments.

Results:

Mean effect-site amount producing 90% of the maximum possible effect (AE90) was estimated as 20.2 mg. At 2 × AE90, the sigmoid Emax model predicted a mean onset time of 23.4 min and mean duration of 22.9 h. Interindividual variability (IIV) for AE50 was 49%. Typical ke0 half-life was 34.7 min (IIV = 52%) and steepness parameter 8.7 (IIV = 48%). None of the pharmacodynamic model parameters showed sex, age, or body weight dependency.

Conclusions:

A population pharmacokinetic/pharmacodynamic model was developed that quantitatively describes the sensory component of a femoral nerve block in orthopedic patients. Further clinical studies will be needed to validate the clinical relevance of this finding.

Evaluation of bias, precision, robustness and runtime for estimation methods in NONMEM 7

NONMEM is the most widely used software for population pharmacokinetic (PK)-pharmacodynamic (PD) analyses. The latest version, NONMEM 7 (NM7), includes several sampling-based estimation methods in addition to the classical methods. In this study, performance of the estimation methods available in NM7 was investigated with respect to bias, precision, robustness and runtime for a diverse set of PD models. Simulations of 500 data sets from each PD model were reanalyzed with the available estimation methods to investigate bias and precision. Simulations of 100 data sets were used to investigate robustness by comparing final estimates obtained after estimations starting from the true parameter values and initial estimates randomly generated using the CHAIN feature in NM7. Average estimation time for each algorithm and each model was calculated from the runtimes reported by NM7. The method giving the lowest bias and highest precision across models was importance sampling, closely followed by FOCE/LAPLACE and stochastic approximation expectation-maximization. The methods relative robustness differed between models and no method showed clear superior performance. FOCE/LAPLACE was the method with the shortest runtime for all models, followed by iterative two-stage. The Bayesian Markov Chain Monte Carlo method, used in this study for point estimation, performed worst in all tested metrics.

Evaluation of estimation methods and power of tests of discrete covariates in repeated time-to-event parametric models: application to Gaucher patients treated by imiglucerase

Analysis of repeated time-to-event data is increasingly performed in pharmacometrics using parametric frailty models. The aims of this simulation study were (1) to assess estimation performance of Stochastic Approximation Expectation Maximization (SAEM) algorithm in MONOLIX, Adaptive Gaussian Quadrature (AGQ), and Laplace algorithm in PROC NLMIXED of SAS and (2) to evaluate properties of test of a dichotomous covariate on occurrence of events. The simulation setting is inspired from an analysis of occurrence of bone events after the initiation of treatment by imiglucerase in patients with Gaucher Disease (GD). We simulated repeated events with an exponential model and various dropout rates: no, low, or high. Several values of baseline hazard model, variability, number of subject, and effect of covariate were studied. For each scenario, 100 datasets were simulated for estimation performance and 500 for test performance. We evaluated estimation performance through relative bias and relative root mean square error (RRMSE). We studied properties of Wald and likelihood ratio test (LRT). We used these methods to analyze occurrence of bone events in patients with GD after starting an enzyme replacement therapy. SAEM with three chains and AGQ algorithms provided good estimates of parameters much better than SAEM with one chain and Laplace which often provided poor estimates. Despite a small number of repeated events, SAEM with three chains and AGQ gave small biases and RRMSE. Type I errors were closed to 5%, and power varied as expected for SAEM with three chains and AGQ. Probability of having at least one event under treatment was 19.1%.

A time-to-event pharmacodynamic model describing treatment response in patients with pulmonary tuberculosis using days to positivity in automated liquid mycobacterial culture

Days to positivity in automated liquid mycobacterial culture have been shown to correlate with mycobacterial load and have been proposed as a useful biomarker for treatment responses in tuberculosis. However, there is currently no quantitative method or model to analyze the change in days to positivity with time on treatment. The objectives of this study were to describe the decline in numbers of mycobacteria in sputum collected once weekly for 8 weeks from patients on treatment for tuberculosis using days to positivity in liquid culture. One hundred forty-four patients with smear-positive pulmonary tuberculosis were recruited from a tuberculosis clinic in Cape Town, South Africa. A nonlinear mixed-effects repeated-time-to-event modeling approach was used to analyze the time-to-positivity data. A biexponential model described the decline in the estimated number of bacteria in patients' sputum samples, while a logistic model with a lag time described the growth of the bacteria in liquid culture. At baseline, the estimated number of rapidly killed bacteria is typically 41 times higher than that of those that are killed slowly. The time to kill half of the rapidly killed bacteria was about 1.8 days, while it was 39 days for slowly killed bacteria. Patients with lung cavitation had higher bacterial loads than patients without lung cavitation. The model successfully described the increase in days to positivity as treatment progressed, differentiating between bacteria that are killed rapidly and those that are killed slowly. Our model can be used to analyze similar data from studies testing new drug regimens.