Covariate modeling in pharmacometrics: General points for consideration.

Modeling the relationships between covariates and pharmacometric model parameters is a central feature of pharmacometric analyses. The information obtained from covariate modeling may be used for dose selection, dose individualization, or the planning of clinical studies in different population subgroups. The pharmacometric literature has amassed a diverse, complex, and evolving collection of methodologies and interpretive guidance related to covariate modeling. With the number and complexity of technologies increasing, a need for an overview of the state of the art has emerged. In this article the International Society of Pharmacometrics (ISoP) Standards and Best Practices Committee presents perspectives on best practices for planning, executing, reporting, and interpreting covariate analyses to guide pharmacometrics decision making in academic, industry, and regulatory settings.

Exposure-response relationships of etrolizumab in patients with moderately-to-severely active ulcerative colitis.

Etrolizumab is an IgG1-humanized monoclonal anti-ß7 integrin antibody. Phase III trials with induction and/or maintenance phases were conducted in patients with moderately-to-severely active ulcerative colitis (UC) who were either previously treated with tumor necrosis factor (TNF) inhibitors (HICKORY) or were TNF inhibitor naïve (HIBISCUS I/II, LAUREL, and GARDENIA). A total of eight exposure-response analyses were conducted for two clinical outcomes (remission and endoscopic improvement) at the end of induction for studies HIBISCUS I/II (combined) and HICKORY and at the end of maintenance for studies HICKORY and LAUREL. Trough concentration at week 4 (Ctrough,wk4 ) of induction was selected as the exposure metric. Exposure-response (ER) modeling was conducted using logistic regression. A full covariate model was used to examine the impact of covariates on clinical outcomes. Linear models with a single intercept for placebo and active treatments adequately described the data for all eight analyses. The etrolizumab exposure-response slope was significant (p < 0.05) for seven of the eight analyses. Baseline Mayo Clinic Score (MCS) was the only statistically significant covariate that impacted induction remission and endoscopic improvement. No statistically significant covariate was identified to impact maintenance outcomes except for baseline fecal calprotectin on endoscopic improvement for LAUREL study. A statistically significant positive ER relationship was identified for most of the clinical outcomes tested, reflecting a better treatment effect in patients with UC with higher etrolizumab Ctrough,wk4 of induction. Baseline MCS was the only other significant covariate impacting induction efficacy. Besides Ctrough,wk4 of induction, no consistent covariate was identified to impact maintenance efficacy.

Population pharmacokinetic analysis of etrolizumab in patients with moderately-to-severely active ulcerative colitis.

Etrolizumab is an IgG1-humanized monoclonal antibody that specifically targets the ß7 subunit of α4ß7 and α4Eß7 integrins, and it has been evaluated for the treatment of moderately-to-severely active ulcerative colitis (UC). Population pharmacokinetic (PK) analysis was performed to characterize etrolizumab PK properties in patients with moderately-to-severely active UC and evaluate covariate impacts on exposure. The population PK model was developed based on etrolizumab serum concentrations from patients with moderately-to-severely active UC enrolled in six studies (one phase I, one phase II, and four phase III) and validated using another phase III clinical trial. Stepwise covariate modeling was used to evaluate the impact of 23 prespecified covariates. Etrolizumab PK was best described by a two-compartment model with first-order absorption, with clearance decreasing over time. Population typical values were 0.260 L/day for clearance (CL) during the first dosing internal, 2.61 L for central volume, 71.2% for bioavailability, and 0.193/day for absorption rate. CL reduced over the study duration, the typical maximum reduction was 26% with an onset half-life of 4.8 weeks. Consequently, the predicted mean terminal half-life was shorter after a single dose (13.0 days) compared to that at steady-state (17.1 days). Baseline body weight and albumin were the most impactful covariates for etrolizumab exposure. Final population PK model well characterized the PK properties of etrolizumab in patients with moderately-to-severely active UC and identified influential covariate effects.

Population Pharmacokinetics and Exposure-Response Relationships of Astegolimab in Patients With Severe Asthma.

Astegolimab is a fully human immunoglobulin G2 monoclonal antibody that binds to the ST2 receptor and blocks the interleukin-33 signaling. It was evaluated in patients with uncontrolled severe asthma in the phase 2b study (Zenyatta) at doses of 70, 210, and 490 mg subcutaneously every 4 weeks for 52 weeks. This work aimed to characterize astegolimab pharmacokinetics, identify influential covariates contributing to its interindividual variability, and make a descriptive assessment of the exposure-response relationships. A population pharmacokinetic model was developed using data from 368 patients in the Zenyatta study. Predicted average steady-state concentration was used in the subsequent exposure-response analyses, which evaluated efficacy (asthma exacerbation rate) and biomarker end points including forced expiratory volume in 1 second, fraction exhaled nitric oxide, blood eosinophils, and soluble ST2. A 2-compartment disposition model with first-order elimination and first-order absorption best described the astegolimab pharmacokinetics. The relative bioavailability for the 70-mg dose was 15.3% lower. Baseline body weight, estimated glomerular filtration rate, and eosinophils were statistically correlated with pharmacokinetic parameters, but only body weight had a clinically meaningful influence on the steady-state exposure (ratios exceeding 0.8-1.25). The exposure-response of efficacy and biomarkers were generally flat with a weak trend in favor of the highest dose/exposure. This study characterized astegolimab pharmacokinetics in patients with asthma and showed typical pharmacokinetic behavior as a monoclonal antibody-based drug. The exposure-response analyses suggested the highest dose tested in the Zenyatta study (490 mg every 4 weeks) performed close to the maximum effect, and no additional response may be expected above it.

Population repeated time-to-event analysis of exacerbations in asthma patients: A novel approach for predicting asthma exacerbations based on biomarkers, spirometry, and diaries/questionnaires.

Identification of covariates, including biomarkers, spirometry, and diaries/questionnaires, that predict asthma exacerbations would allow better clinical predictions, shorter phase II trials and inform decisions on phase III design, and/or initiation (go/no-go). The objective of this work was to characterize asthma-exacerbation hazard as a function of baseline and time-varying covariates. A repeated time-to-event (RTTE) model for exacerbations was developed using data from a 52-week phase IIb trial, including 502 patients with asthma randomized to placebo or 70 mg, 210 mg, or 490 mg astegolimab every 4 weeks. Covariate analysis was performed for 20 baseline covariates using the full random effects modeling approach, followed by time-varying covariate analysis of nine covariates using the stepwise covariate model (SCM) building procedure. Following the SCM, an astegolimab treatment effect was explored. Diary-based symptom score (difference in objective function value [dOFV] of -83.7) and rescue medication use (dOFV = -33.5), and forced expiratory volume in 1 s (dOFV = -14.9) were identified as significant time-varying covariates. Of note, time-varying covariates become more useful with more frequent measurements, which should favor the daily diary scores over others. The most influential baseline covariates were exacerbation history and diary-based symptom score (i.e., symptom score was important as both time-varying and baseline covariate). A (nonsignificant) astegolimab treatment effect was included in the final model because the limited data set did not allow concluding the remaining effect size as irrelevant. Without time-varying covariates, the treatment effect was statistically significant (p < 0.01). This work demonstrated the utility of a population RTTE approach to characterize exacerbation hazard in patients with severe asthma.

Translating Pharmacometrics to a Pharmacoeconomic Model of COPD.

BACKGROUND: A model-based meta-analysis (MBMA) is a type of meta-regression that uses nonlinear mixed-effects models estimated on trial-level data to relate patient and trial characteristics, dosing, biomarkers, and outcomes of treatment. OBJECTIVES: To use a pharmacometric MBMA within a pharmacoeconomic model of chronic obstructive pulmonary disease (COPD). METHODS: A Markov microsimulation model was developed to estimate monthly changes in the key disease severity metrics of COPD (forced expiratory volume in 1 second [FEV1] and exacerbations) to compare a hypothetical drug that increases FEV1 to usual care. The MBMA was used to predict a baseline exacerbation rate in a group of actual trial patients, given their known baseline FEV1. The hypothetical drug increased FEV1, thereby decreasing individuals' predicted exacerbation rates. Individual patient simulations allowed stochastic changes in monthly FEV1 decline. RESULTS: In a sample of 1097 trial patients with a mean FEV1 of 50%, the MBMA predicted 0.93 exacerbations per year on average. The exacerbation rate ranged from 0.52 to 1.3 per year across moderate and severe patient subgroups. A hypothetical anti-inflammatory drug that increased FEV1 by 50 ml decreased exacerbations by 26%. Given a simplified estimation of costs and quality-adjusted life-years (QALYs) associated with COPD, a drug with a 50-ml increase priced at €35/mo had an incremental cost-effectiveness ratio ranging from €13,000/QALY to approximately €207,000/QALY across patient severity subgroups. CONCLUSIONS: The synergistic aspects of MBMA and pharmacoeconomic modeling are highlighted in this hypothetical example. Markov microsimulation modeling allows the finer predictions of MBMA to inform parameters. Such an approach has utility in both early-phase cost-effectiveness estimations and trial design.

A pharmacokinetic comparison of anrukinzumab, an anti- IL-13 monoclonal antibody, among healthy volunteers, asthma and ulcerative colitis patients.

AIMS: Anrukinzumab is an anti-IL13 monoclonal antibody. The goals of this study are to characterize the pharmacokinetics of anrukinzumab in healthy volunteers and different disease states and to identify covariates. METHODS: A population pharmacokinetic (PK) model was developed in NONMEM, using data from five clinical studies including healthy volunteers, asthma and ulcerative colitis (UC) patients. Different dosing regimens including different routes of administration were also included in the data. RESULTS: The PK of anrukinzumab were described by a two compartment model with first order absorption and elimination. The population estimates (relative standard error) of the volumes of distribution in the central (Vc ) and peripheral (Vp ) compartments were 3.8 (4.6%) and 2.2 l (8.7%), respectively. In non-UC patients, the population estimate of the systemic clearance (CL) and inter-compartmental CL was 0.00732 l h(-1) (4.9%) and 0.0224 l h(-1) (15.4%). For subcutaneous administration, the absorption rate constant was 0.012 h(-1) (6.6%) and bioavailability was nearly 100% in healthy and mild to moderate asthma patients. Both V and CL increased with body weight. CL (but not V) decreased with increasing baseline albumin concentrations. UC patients had an increased CL of 72.3% (10.5%), after correction for differences in body weight and albumin. Moderate to severe asthma patients had decreased bioavailability compared with other populations. CONCLUSIONS: Anrukinzumab's PK behave like a typical antibody. UC patients were identified to have a faster CL of anrukinzumab than healthy volunteers and asthma patients. This finding suggests a higher dose level may be required for this population.

Characterizing systemic exposure of inhaled drugs: application to the long-acting ß2-agonist PF-00610355.

BACKGROUND AND OBJECTIVES: PF-00610355 is an orally inhaled long-acting ß2-adrenoreceptor agonist that is being developed for the once-daily treatment of chronic obstructive pulmonary disease (COPD). The pharmacological effect is exerted in the lungs. However, systemic exposure of PF-00610355 is expected to be responsible for certain drug-related adverse effects. This analysis characterizes PF-00610355 using an integrated analysis of systemic exposure, across trials and patient populations. METHODS: A total of 6,107 samples of PF-00610355 plasma concentration, collected in 264 subjects from eight studies in healthy volunteers, asthma, and COPD patients, were analyzed using non-linear mixed-effects models. Model-based mean (95 % CI) exposure profiles for a range of PF-00610355 doses in COPD patients were simulated. RESULTS: PF-00610355 exposure profiles were described by a three-compartment disposition model with first-order absorption through a transit compartment. Patient status, inhalation device, and demographic factors were found to influence systemic drug exposure. Relative fine particle dose had a minor effect, whereas no effect of baseline lung function on the systemic exposure was found. An implicit method to address pharmacokinetic variability between occasions of drug intake yielded similar results as the established explicit method, yet in a much more efficient way. CONCLUSION: The estimated systemic pre-dose and maximum PF-00610355 plasma concentration was 23 and 38 % in COPD patients compared to healthy volunteers, respectively. The analysis illustrated the value of an integrated pharmacokinetic analysis to address specific challenges in the clinical development of long-/ultra-long-acting ß2-agonists and inhaled compounds in general, both in relation to selecting a safe starting dose in patients, but also in understanding exposure and systemic safety information across different patient populations and different inhalation devices/formulations.

Predicted heart rate effect of inhaled PF-00610355, a long acting ß-adrenoceptor agonist, in volunteers and patients with chronic obstructive pulmonary disease.

AIM: To assess the cardiovascular effects of a new inhaled long-acting ß-adrenoceptor agonist PF-00610355 in COPD patients. METHODS: Thirteen thousand and sixty-two heart rate measurements collected in 10 clinical studies from 579 healthy volunteers, asthma and COPD patients were analyzed. The relationship between heart rate profiles and predicted plasma concentration profiles, patient status, demographics and concomitant medication was evaluated using non-linear mixed-effects models. The median heart rate increase in COPD patients for doses of PF-00610355 up to 280 µg once daily was simulated with the final pharmacokinetic/pharmacodynamic (PKPD) model. RESULTS: An Emax model accounting for delayed on-and off-set of the PF-00610355-induced change in heart rate was developed. The predicted potency in COPD patients was three-fold lower compared with healthy volunteers, while no difference in maximum drug effect was identified. Simulations suggested a maximum placebo-corrected increase of 2.7 (0.90-4.82) beats min(-1) in COPD patients for a PF-00610355 dose of 280 µg once daily, with 19% subjects experiencing a heart rate increase of more than 20 beats min(-1) compared with 8% in the placebo group. CONCLUSIONS: This PKPD analysis supports the clinical observation that no relevant effects of PF-00610355 on heart rate in COPD patients should be expected for doses up to 280 µg once daily.

Longitudinal FEV1 dose-response model for inhaled PF-00610355 and salmeterol in patients with chronic obstructive pulmonary disease.

The objective of this work was to characterize the dose-response relationship between two inhaled long-acting beta agonists (PF-00610355 and salmeterol) and the forced expiratory volume in one second (FEV1) in order to inform dosing recommendations for future clinical trials in patients with chronic obstructive pulmonary disease (COPD). This meta-analysis of four studies included 8,513 FEV1 measurements from 690 patients with moderate COPD. A longitudinal kinetic-pharmacodynamic (K-PD) model was developed and adequately described changes in FEV1 measurements over time, including circadian patterns within a day, as well as changes in FEV1 measurements elicited from administration of PF-00610355 or salmeterol. The fine-particle dose, the amount of drug present in particles small enough for lung delivery, was used as the exposure measure for PF-00610355. Greater reversibility following administration of a short-acting beta agonist during run-in was associated with increased FEV1 response to long-acting beta agonists (through an increased maximal response, E(max)). Simulations were conducted to better understand the response to PF-00610355 relative to placebo and salmeterol. The results of the simulations show that once daily fine-particle doses of 28.1 µg versus placebo have a moderate probability of providing an average improvement above 100 mL at trough. The 50 µg fine-particle dose, on the other hand, has a greater than 0.78 probability of achieving a 120 mL improvement versus placebo at trough. From an efficacy perspective and assuming a fine-particle fraction of 25 % for the Phase 3 formulation; 100 and 200 µg once daily nominal doses would be of interest to investigate in future Phase 3 trials.

Placebo effect model in asthma clinical studies: longitudinal meta-analysis of forced expiratory volume in 1 second.

OBJECTIVE: Our objective was to describe the time course of the placebo effect in asthma and quantitatively investigate the affective factors of the placebo effect for the placebo response simulation during the asthma clinical study design. METHODS: We conducted a systemic search of public data sources for the study-level forced expiratory volume in 1 second (FEV(1)) to build the placebo effect model for studies by oral or inhaled administrations simultaneously. The administration routes, types of inhalation device, mean patient age, mean male proportion, baseline FEV(1), disease severity, year of publication, inhaled corticosteroid status during the treatment, and dropout rate were tested as covariates. RESULTS: There are 34 literature sources containing 178 mean values for FEV(1) presenting the individual observations from about 3,703 patients. The exponential models adequately described the time course of placebo effect with the typical value of the maximum placebo effect (P(max)) of 0.060 L. Dropout rate incorporated in the residual error model and the disease severity (mild to moderate and moderate to severe) at baseline were covariates that remained in the final model. CONCLUSIONS: The placebo effect is adequately described by an exponential model over time. By incorporating the dropout rate in the residual error model, the estimation precision was improved. The model could predict the placebo response profile in mild to severe asthmatic patients for the asthma clinical study design and could also be a structure model of the placebo effect for the pure drug effect evaluation in the asthma clinical trials.

A model for glucose, insulin, and beta-cell dynamics in subjects with insulin resistance and patients with type 2 diabetes.

Type 2 diabetes mellitus (T2DM) is a progressive, metabolic disorder characterized by reduced insulin sensitivity and loss of beta-cell mass (BCM), resulting in hyperglycemia. Population pharmacokinetic-pharmacodynamic (PKPD) modeling is a valuable method to gain insight into disease and drug action. A semi-mechanistic PKPD model incorporating fasting plasma glucose (FPG), fasting insulin, insulin sensitivity, and BCM in patients at various disease stages was developed. Data from 3 clinical trials (phase II/III) with a peroxisome proliferator-activated receptor agonist, tesaglitazar, were used to develop the model. In this, a modeling framework proposed by Topp et al was expanded to incorporate the effects of treatment and impact of disease, as well as variability between subjects. The model accurately described FPG and fasting insulin data over time. The model included a strong relation between insulin clearance and insulin sensitivity, predicted 40% to 60% lower BCM in T2DM patients, and realistic improvements of BCM and insulin sensitivity with treatment. The treatment response on insulin sensitivity occurs within the first weeks, whereas the positive effects on BCM arise over several months. The semi-mechanistic PKPD model well described the heterogeneous populations, ranging from nondiabetic, insulin-resistant subjects to long-term treated T2DM patients. This model also allows incorporation of clinical-experimental studies and actual observations of BCM.

Non-Bayesian knowledge propagation using model-based analysis of data from multiple clinical studies.

The ultimate goal in drug development is to establish the manner of safe and efficacious administration to patients. To achieve this in an efficient way the information contained in the clinical studies should contribute to the increasing pool of accumulated knowledge. The aim of this simulation study is to investigate different knowledge-propagation strategies when the data is analysed using a model-based approach in NONMEM. Pharmacokinetic studies were simulated according to several scenarios of the underlying model and study design, including a population-optimal design based on analysis of a previous study. Five approaches with different degrees of knowledge propagation were investigated: analysing the studies pooled into one dataset, merging the results from analysing the studies separately, fitting a pre-specified model that has been selected from a previous study on either the most recent study or on the pooled dataset, or naïvely analysing the most recent study without any regards to any previous study. The approaches were evaluated on what model was selected (qualitative knowledge, investigated by stepwise covariate selection within NONMEM) as well as parameter precision (quantitative knowledge) and predictive performance of the model. Pooling all studies into one dataset is the best approach for identifying the correct model and obtaining good predictive performance and merging the results of separate analyses may perform almost as well. Fitting a pre-specified model on new data is fast, without selection bias, and sanctioned for model-based confirmatory analyses. However, fitting the same pre-specified model to all available data is still fast and can be expected to perform better in terms of predictive performance than the unbiased alternative. Using ED-optimal design of sample times and stratification of subjects from different subgroups is a successful strategy which allows sparse sampling and handles prior parameter uncertainty.

The lasso--a novel method for predictive covariate model building in nonlinear mixed effects models.

Covariate models for population pharmacokinetics and pharmacodynamics are often built with a stepwise covariate modelling procedure (SCM). When analysing a small dataset this method may produce a covariate model that suffers from selection bias and poor predictive performance. The lasso is a method suggested to remedy these problems. It may also be faster than SCM and provide a validation of the covariate model. The aim of this study was to implement the lasso for covariate selection within NONMEM and to compare this method to SCM. In the lasso all covariates must be standardised to have zero mean and standard deviation one. Subsequently, the model containing all potential covariate-parameter relations is fitted with a restriction: the sum of the absolute covariate coefficients must be smaller than a value, t. The restriction will force some coefficients towards zero while the others are estimated with shrinkage. This means in practice that when fitting the model the covariate relations are tested for inclusion at the same time as the included relations are estimated. For a given SCM analysis, the model size depends on the P-value required for selection. In the lasso the model size instead depends on the value of t which can be estimated using cross-validation. The lasso was implemented as an automated tool using PsN. The method was compared to SCM in 16 scenarios with different dataset sizes, number of investigated covariates and starting models for the covariate analysis. Hundred replicate datasets were created by resampling from a PK-dataset consisting of 721 stroke patients. The two methods were compared primarily on the ability to predict external data, estimate their own predictive performance (external validation), and on the computer run-time. In all 16 scenarios the lasso predicted external data better than SCM with any of the studied P-values (5%, 1% and 0.1%), but the benefit was negligible for large datasets. The lasso cross-validation provided a precise and nearly unbiased estimate of the actual prediction error. On a single processor, the lasso was faster than SCM. Further, the lasso could run completely in parallel whereas SCM must run in steps. In conclusion, the lasso is superior to SCM in obtaining a predictive covariate model on a small dataset or on small subgroups (e.g. rare genotype). Run in parallel the lasso could be much faster than SCM. Using cross-validation, the lasso provides a validation of the covariate model and does not require the user to specify a P-value for selection.

Power, selection bias and predictive performance of the Population Pharmacokinetic Covariate Model.

Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).

Perl-speaks-NONMEM (PsN)--a Perl module for NONMEM related programming.

The NONMEM program is the most widely used nonlinear regression software in population pharmacokinetic/pharmacodynamic (PK/PD) analyses. In this article we describe a programming library, Perl-speaks-NONMEM (PsN), intended for programmers that aim at using the computational capability of NONMEM in external applications. The library is object oriented and written in the programming language Perl. The classes of the library are built around NONMEM's data, model and output files. The specification of the NONMEM model is easily set or changed through the model and data file classes while the output from a model fit is accessed through the output file class. The classes have methods that help the programmer perform common repetitive tasks, e.g. summarising the output from a NONMEM run, setting the initial estimates of a model based on a previous run or truncating values over a certain threshold in the data file. PsN creates a basis for the development of high-level software using NONMEM as the regression tool.