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Hemophilia is an inherited bleeding disorder caused by a deficiency in a specific clotting factor. This results in spontaneous bleeding episodes and eventual arthropathy. The mainstay of hemophilia treatment is prophylactic replacement of the missing factor, but an optimal regimen remains to be determined. Rather, individualized prophylaxis has been suggested to improve both patient safety and resource utilization. However, uptake of this approach has been hampered by the demanding sampling schedules and complex calculations required to obtain individual estimates of pharmacokinetic (PK) parameters. The use of population pharmacokinetics (PopPK) can alleviate this burden by reducing the number of plasma samples required for accurate estimation, but few tools incorporating this approach are readily available to clinicians.
The Web-accessible Population Pharmacokinetic Service - Hemophilia (WAPPS-Hemo) project aims to bridge this gap by providing a Web-accessible service for the reliable estimation of individual PK parameters from only a few patient samples. This service is predicated on the development of validated brand-specific PopPK models.
We describe the data analysis plan for the development and evaluation of each PopPK model to be incorporated into the WAPPS-Hemo platform. The data sources and structure of the dataset are discussed first, followed by the procedures for handling both data below limit of quantification (BLQ) and absence of such BLQ data. Next, we outline the strategies for building the appropriate structural and covariate models, including the possible need for a process algorithm when PK behavior varies between subjects or significant covariates are not provided. Prior to use in a prospective manner, the models will undergo extensive evaluation using a variety of techniques such as diagnostic plots, bootstrap analysis and cross-validation. Finally, we describe the incorporation of a validated PopPK model into the Bayesian post hoc model to produce individualized estimates of PK parameters.
Dense PK data has been collected for more than 20 brands of factor concentrate from both industry-sponsored and investigator-driven studies. The model development process is underway for the majority of molecules, with refinement and validation to be completed in 2017. Further, the WAPPS-Hemo co-investigator network has contributed more than 300 PK assessments for use in model development and evaluation. This constitutes the largest repository of this type of PK data globally.
The WAPPS-Hemo service aims to eliminate barriers to the uptake of individualized PK-tailored hemophilia treatment. By incorporating this tool into routine practice, clinicians can implement a personalized dosing strategy without performing rigorous sampling or complex calculations. This service is centred on validated models developed according to the robust approach to PopPK modeling described herein.
ClinicalTrials.gov NCT02061072; https://clinicaltrials.gov/ct2/show/NCT02061072 (Archived by WebCite at http://www.webcitation.org/6mRIXJh55)
Hemophilia is an inherited bleeding disorder caused by a deficiency in clotting factor VIII (FVIII, hemophilia A) or factor IX (FIX, hemophilia B). FVIII and FIX are key constituents in the coagulation cascade, which produces fibrin clots in response to blood vessel injury [
Modern hemophilia treatment consists of replacement of the deficient factor [
Despite its proven clinical benefit, an optimal dosing strategy for prophylaxis has yet to be determined. Evidence suggests that treatment should be individualized for best results, both from a therapeutic and economic perspective [
One opportunity to overcome some of the limitations and barriers discussed above is offered by population pharmacokinetic (PopPK) modeling. Indeed, PopPK studies can make use of both rich and sparse sampling, which allows for a larger and more heterogeneous group of participants (eg, pediatric, elderly, and critical care patients) to be included due to less demanding sampling schedules [
In response, the Web-Accessible Population Pharmacokinetic Service - Hemophilia (WAPPS-Hemo, NCT02061072) project was launched in April 2013 at McMaster University, Hamilton, Ontario, Canada. A detailed description of the project methodology, objectives and progress is published separately [
This report outlines the methods used for the development of brand-specific PopPK models, which form the knowledge base of the WAPPS-Hemo Bayesian individual forecast platform.
In the framework of the population pharmacokinetic (PopPK) approach, estimating reliable outcomes by the Web-Accessible Population Pharmacokinetic Service - Hemophilia (WAPPS-Hemo) service requires that underlying PopPK models are well developed using a sufficiently large population of individuals. The WAPPS-Hemo project has assembled a vast database of clotting factors VIII and IX pharmacokinetic (PK) data across numerous brands and this represents the largest repository of this type of data globally. The repository includes PK data from industry sponsors and independent investigators; furthermore, clinical sites contributing data to the WAPPS-Hemo repository for individual estimation agreed upon subsequent use of those data for modeling. Indeed, onboarding of clinical sites requires that each participating site enters the network by signing a data transfer agreement where the site commits to data provision and takes responsibility for clinical use of the results. The principal investigator of WAPPS-Hemo, Dr Alfonso Iorio, agrees to share ownership of the database and authorship on any publication stemming from the project. Clinicians contribute to the repository by submitting to the website as few as 3 to 4 factor levels per patient along with demographic information. The appropriate PopPK control file is selected for the brand of factor concentrate identified in the patient data file. The online PopPK engine automatically estimates the relevant individual PK parameters. Following expert validation, a patient report is generated and sent to the clinician that includes the time when the factor level reaches a specified value, for example 0.05, 0.02 or 0.01 international units (IU) per mL, along with credibility intervals.
The Web-Accessible Population Pharmacokinetic Service - Hemophilia (WAPPS-Hemo) platform uses brand-specific population pharmacokinetic models and submitted patient data to generate reports of individual pharmacokinetic profiles and estimates.
The primary objective of this report is to outline the methods for developing PopPK models on dense FVIII and FIX data obtained from the Data Sources to better understand the relationship between blood plasma concentration and time for each molecule investigated. PopPK model estimates will be entered as priors in subsequent Bayesian post hoc analyses to predict the most reliable function between blood plasma concentration and time for patients with sparse data. This function will be used to inform clinicians when the next dose of a particular FVIII or FIX molecule should be administered.
Dense individual PK data on 878 participants using 21 different molecules from 17 different sources have been collected as part of industry-sponsored or investigator-driven studies. Most of the data in the derivation cohort are provided as both clotting and chromogenic assay results, but we plan to model exclusively with data from clotting assays, as the data received from participating clinical sites is almost uniquely of this type. Characteristics of some of the dense data that has been obtained for the WAPPS-Hemo project are summarized in
Summary of some dense data used for initial population modeling.
Brand | Type | N^{a} | Age, years | Weight, kg | Hematocrit included | vWF^{b} level included | Blood type included |
Advate | FVIII^{c} recombinant | 25 | 15-62 | 53.8-127.4 | No | Yes | No |
Alprolix | FIX^{d} recombinant | 129 | 12.1-71.5 | 45.0-186.7 | Yes | No | No |
Benefix | FIX recombinant | 80 | 4.3-58.5 | 17.9-186.7 | Yes | No | No |
Eloctate | FVIII recombinant | 167 | 12-65 | 42.0-129.2 | No | Yes | Yes |
Kogenate | FVIII recombinant | 40 | 13.0-56.1 | 47.4-124.2 | No | No | No |
Kovaltry | FVIII recombinant | 23 | 12-51 | 46.3-124.2 | No | No | No |
Xyntha | FVIII recombinant | 30 | 14-57 | 50.7-117.2 | No | No | No |
^{a}N: number of participants.
^{b}vWF: von Willebrand factor.
^{c}FVIII: clotting factor FVIII.
^{d}FIX: clotting factor FIX.
Rich data used for PopPK modeling are provided by the data sources. These data will be received in various software packages and in a variety of formats, so they will be re-formatted into a standard comma-separated values (CSV) file for input into the PopPK modeling software, NONMEM (v 7.3.0; ICON Development Systems, Ellicott City, MD, US). Where possible, the dataset will consist of the variables shown in
The record for each patient is organized as follows. The first record is used to read in the pre-dose amount, which accounts for the patient’s endogenous factor level and any residual factor from a previous dose, if measured. The TIMEH entry for the first record is set to zero, and this is the reference point for the time for all subsequent records in the dataset. The first record also contains the BASELINE value, which corresponds to the patient’s endogenous factor level. If a baseline level of the factor was measured, the measured value is entered; if not, a baseline value of 0.005 IU/mL (0.5% of normal factor activity) is assumed.
The second record is used to read in the dose administered (AMT). For this entry, the TIMEH column contains the time (in hours) that was required to administer the dose (eg, 0.1666 for a 10-minute administration). The amount and time are used to calculate the rate (RATE=AMT/TIMEH). For all subsequent records, AMT and RATE are set equal to zero.
The third record contains the first valid observation of the plasma concentration and subsequent records contain subsequent valid observations of the plasma concentration. The one exception to this is records following a valid observation that refer to samples that are below the limit of quantification (BLQ). Because the information from these different events (eg, PREDOSE, BASELINE, concentration observations, and BLQ events) needs to be handled in different ways, indicator variables MDV3 and MDV5 are included to designate how each entry should be used.
Typical variables in NONMEM datasets.
Variable | Description | Units | |
CID | Patient identification number | Positive integer | |
OCC | Dose occasion | Positive integer | |
TIMEH | Time for each concentration measurement from start of bolus | Hours or fraction of hours (minimum of 4 decimal places) | |
AMT | Total dose | IU^{a} | |
RATE | Rate of entry of drug: AMT/TIMEH | IU/h | |
DV | Plasma concentration of valid observation or BLQ^{b} | IU/L | |
AGE | Age | Positive integer, years | |
BW | Weight | Positive integer, kilograms | |
EVID | Event identification variable | Positive integer (0=valid observation, 1= dose, 3=BLQ observation) | |
DOSE | AMT/BW | Positive number, IU/kg | |
PREDOSE | Plasma concentration at time of start of bolus | Zero or positive integer if measured, –1 if not measured (IU/L) | |
MDV5 | Missing dependent variable | 0=valid observation; 1=dose or BLQ observation; MDV5=MDV when no BLQ | |
BASELINE | Endogenous plasma concentration | Positive integer if known, –1 if not known, IU/L | |
BLQ | Below limit of quantification | ≤ 0=non BLQ measurement, positive integer=BLQ value, IU/L | |
MDV3 | Missing dependent variable | 0=valid observation or BLQ; 1=dose; MDV3=MDV when BLQ is present | |
HT | Height | Positive integer, centimeter | |
VWF | von Willebrand factor | Percentage | |
RACE | Race | Positive integer (1=White, 2=Black, 3=…) | |
BTYPE | Blood type | Positive integer (1=A, 2=B, 3=AB, 4=O) | |
HCT | Hematocrit | Percentage |
^{a}IU: international unit.
^{b}BLQ: below the limit of quantification.
Prior to analyzing the data, the integrity of the data will be scrutinized to identify potential data errors. Errors can exist for a number of reasons. For example, following a dose, plasma concentrations typically decline with time so if a plasma concentration for a record is higher than the plasma concentration for a previous record, that record will be flagged to be checked. If any data are missing they will be flagged to be checked. Similarly, outlying covariate values for continuous variables (eg, AGE, BW, or HT) will be flagged to be checked. Any categorical variable that has a value that is not expected will be flagged to be checked. Duplicate records within a patient’s data will also be flagged.
All potentially erroneous data will be reported and discussed. If a resolution to the error is forthcoming, it will be documented and the appropriate changes will be made to the dataset. If no resolution is found, the error will be documented and the data will be excluded from subsequent analyses.
Nonlinear mixed effects modeling and Bayesian post hoc estimations will be completed in NONMEM and PDx-Pop (v 5.10; ICON Development Systems, Ellicott City, MD, US). PopPK modeling will be performed using the first order conditional estimation with interaction (FOCEI) method. The ADVAN and TRANS subroutines for each model, which specify the model structure and parameterization, respectively, are shown in
NONMEM subroutines used to implement kinetic equations for linear models following intravenous administration.
Model | ADVAN subroutine | TRANS subroutine |
1-compartment | ADVAN1 | TRANS2: CL, V |
2-compartment | ADVAN3 | TRANS4: CL, V1, Q, V2 |
3-compartment | ADVAN11 | TRANS4: CL, V1, Q2, V2, Q3, V3 |
Severe hemophilia patients have, by definition, an endogenous coagulation factor level below 0.01 IU/mL, which is also often cited as the limit of quantification (LOQ) for coagulation activity assays [
The first step in model development will be a naïve pooled analysis, which allows for preliminary exploration of model structure and mean estimates of PK parameters. Further definition of the model structure (ie, number of compartments) will be determined using a combination of graphical techniques and numerical goodness-of-fit measures. Models will be evaluated using an objective function value based on a summation of the residual error. One model is considered to be superior to a similar hierarchically well-formulated model with one more degrees of freedom if the objective function decreases by 3.84 units or more, based on the assumption of a chi squared (χ^{2}) distribution. Models will also be evaluated using diagnostic plots (
Observed values vs individual/population predicted values
Conditional weight residuals (CWRES) vs predicted values
CWRES vs time
Observed and predicted values vs time
Normal QQ-plots
CWRES histogram
Eta histograms
Population covariate plots
In the event that it is difficult to determine which structure best characterizes the data, it may be helpful to fit each subject individually to explore the reasons for unexplained variability. For example, some factor concentrates may exhibit different structures between patients, which may in turn require estimates to be derived from both models followed by a comparison of the effects on population estimates and individual dosing decisions; as a rule of thumb, we will always take the most conservative approach.
The goal of PopPK is to describe the concentration-time profile for each subject using a series of mathematical equations in a hierarchical manner (
The appropriate structure for the residual unexplained variability (RUV, ε) will be determined using graphical goodness-of-fit plots (including histograms of the residuals, normal QQ plots, and plots of the residuals vs predicted values) and numerical measures (such as objective function value and shrinkage). Possible models for the RUV are shown in
From a population of participants, an estimate of the typical value of the relevant PK parameters can be obtained. A new parameter, η, can then be used to describe how an individual’s parameter deviates from the typical value (ie, the BSV,
The BSV (
Initially, BSV will be included on all PK parameters, and the necessity of all these terms will be investigated both graphically and using formal hypothesis tests. Once the significant random effects have been identified, the structure of the variance-covariance matrix (ω^{2}) can be explored. All prior model development assumes a diagonal variance-covariance matrix (ie, no correlation between random effects). Comparing models with diagonal and unstructured variance-covariance matrices will test for the correlation between random effects.
Illustration of the various components of the base model for a one-compartment model with exponential between subject variability and proportional residual unexplained variability.
Equations for defining different aspects of the population pharmacokinetic models including residual unexplained error (1-4), between subject variability (5-6), and covariates (7-10).
In order to minimize the unexplained portion of the BSV, covariates will be added to the model. Potential covariate relationships will first be explored by examining plots of the included
All model-building datasets include age and weight as parameters, but data for certain brands of factor concentrate could also include height, hematocrit, von Willebrand factor level and blood group as possible covariates. Where available, these covariates can be tested in model development and, if fitting the above criteria for retention, be included in the final model. However, the choice of model would need to take into account the fact that clinicians using WAPPS-Hemo for individual PK estimations are required to include age and weight when requesting PK estimates from the WAPPS-Hemo platform, whereas inclusion of other covariates listed above is optional. Therefore, it is possible that a covariate may significantly influence the PK of a molecule, but may not be recorded at the clinical site. In order to reconcile significant covariates and available information, multiple models may be produced for a single molecule and a process algorithm for determining which model to use in a given situation will be incorporated into the WAPPS-Hemo platform. The decision tree may also incorporate different structural models for molecules that behave differently between subjects, and the model that provides the most precise estimates will be selected. In all cases, the clinician will receive a single report corresponding to whichever model was chosen for the data provided.
The first step in model evaluation includes the use of the diagnostic plots outlined above to ensure that all model assumptions are being met (eg, independent and normally distributed residual error, normally distributed random effects). Also, metrics such as the condition number and the variance inflation factor may be used to assess collinearity. A bootstrap analysis will also be performed to ensure that the model is stable and provides precise estimates for all parameters.
Next, the models will be evaluated using cross-validation techniques with the rich data. Either the holdout method or a
Following evaluation with rich data, the models will be validated using sparsely sampled data to ensure that they perform adequately with the type of data that will be provided by clinicians using the WAPPS-Hemo platform. Validation with sparse data presents some challenges, since the typical methods discussed above cannot be employed. However, a number of strategies for evaluating models using sparse data have been reported. These include using a subset of a complete sampling scheme to compare performance [
Bayesian estimations will also be performed in NONMEM, using the parameter estimates from the PopPK models as informative priors for the relevant PK parameters (eg, volume of distribution, clearance). This step will use the same model structures and estimation methods as previously described, and will handle the presence or absence of PREDOSE, BASELINE, and BLQ values in the same manner as outlined above. From the output files, the time from dose initiation to various concentrations (eg, 0.05, 0.02 or 0.01 IU/mL) or the concentration at different times (eg, 24, 48, and 72 h) can be reported with the accompanying 95% credibility intervals. The times reported to the clinician will be the times at which the lower boundary of the 95% credibility interval for concentration first reaches each of these three concentration thresholds (
We have opted to use the credibility interval as the most efficient and understandable way to report the amount of “shrinkage” of the patient data to the population model. The interval will be larger or smaller depending upon the amount of information that is used either from the population (ie, larger band where most values within the population are possible for the patient) or the individual (ie, smaller band where more rich patient data reduces variability). The Bayesian approach used allows this variability to vary across different segments of the curve, being large where no or little information is provided and small where informative points are provided.
A comprehensive PopPK report will be assembled for each brand-specific model that is developed, according to the Food and Drug Administration (FDA) guidance on PopPK reporting [
Factor concentration as a function of time (symbols: patient data, black line: predicted individual pharmacokinetic profile) where time to the lower 95% credibility interval bound for each of the 0.05 (green line), 0.02 (blue line) or 0.01 (red line) IU/mL thresholds is reported to the clinician. Time 0 represents time of dose initiation.
Summary
Introduction
Objectives, Hypotheses and Assumptions
Materials and Methods
Assay
Data
Data Analysis Methods
Results
Discussion
Application of Results
Appendix
Dense PK data has been collected for more than 20 brands of factor concentrate. Models have been developed for all but three molecules, and we expect to receive data for one additional molecule in early 2017. All models will undergo further refinement and validation, and be submitted for publication in 2017. From the WAPPS-Hemo co-investigator network, we have collected 300 PK assessments to date and expect to reach the 500-assessment mark by early 2017.
The main risk associated with the use of the WAPPS-Hemo service is the possibility that the specific patient is outside of the covariate space used to build the models. In such cases, the individual estimated PK parameters may be imprecise or essentially “wrong” and could result in suboptimal treatment decisions. In light of this, we plan to implement risk minimization procedures. First, we provide both average estimates as well as their associated credibility intervals. In cases where the patient is outside of the model development space, we expect the intervals to be large such that clinical usage of the predictions is discouraged. Second, each forecasted PK is reviewed individually by an expert and appropriate warnings will be added as needed. Third, as a general policy for WAPPS-Hemo users, we recommend that the PK prediction is used as a tool to speed up treatment optimization. To this end, we recommend prospective testing with sampling around specific times that would be valuable in decreasing uncertainty.
One of the main goals of the WAPPS-Hemo program is to eliminate barriers to the uptake of an individualized PopPK-driven approach to hemophilia treatment. By adopting this tool, clinicians require fewer blood samples and circumvent the complex calculations usually needed to implement a tailored dosing strategy. However, the current output report may be a potential hindrance. Although the report contains times to critical factor levels as well as concentrations at convenient time points, these results only pertain to the dose that was administered. A proposed clinical module will allow clinicians to input two parameters among dose, frequency, and desired factor level to calculate the third. This additional functionality will allow those that treat hemophilia to evaluate the theoretical effect of changing dose and frequency on future plasma levels in real time without having to submit multiple profiles through the WAPPS-Hemo platform.
In summary, the WAPPS-Hemo service is predicated on valid PopPK models. This report focuses on describing the process for model development and evaluation, which all brand-specific models will undergo. Rich data has been, and continues to be, the main source of data for model development. However, as clinical sites contribute sparse data to the repository, a greater breadth of PK data and covariates will allow for continuous quality improvements in the models.
below the limit of quantification
between subject variability
conditional weight residuals
clotting factor IX
clotting factor FVIII
limit of quantification
pharmacokinetic
population pharmacokinetics
Web-Accessible Population Pharmacokinetic Service - Hemophilia
within subject variability
The authors wish to acknowledge the WAPPS-Hemo co-investigator network for their contributions: Dr Giovanni Balliari, Hemophilia Center, Udine, Italy; Dr Philippe Beurrier, Chu, Angers, France; Dr Cristoph Bidlingmaier, Pediatric Hemophilia Center, Germany; Dr Victor Blanchette, Sick Children’s Hospital, Canada; Dr Jan Blatny, University Hospital Brno, Czech Republic; Dr Kelsey Brose, Saskatchewan Bleeding Disorders Program, Canada; Dr Deborah Brown, Gulf States Hemophilia, USA; Dr Giancarlo Castaman, Careggi University Hospital, Italy; Dr Meera Chitlur, Children's Hospital of Michigan, USA; Dr Pratima Chowdary, KD Haemophilia Centre & Thrombosis Unit, UK; Dr Marjon Cnossen, Erasmus MC-Sophia Children’s Hospital, Rotterdam, Netherlands; Drs Stacy Croteau Ellis J Neufeld, Dana-Farber/Boston Children’s Center for Cancer and Blood Disorders, USA; Dr Amy Dunn, Nationwide Children’s Hospital, Columbus, USA; Dr Magdy El-Ekiabi, Shabrawishi Hospital Blood Bank, Egypt; Dr Barbara Faganel Kotnik, Haemophilia Comprehensive Care Center, Slovenia; Dr Kathelijn Fischer, University Medical Center Utrecht, Netherlands; Dr C Gómez del Castillo, Complexo Hospitalario Universitario, Spain; Dr Daniel Hart, The Royal London Hospital, UK; Dr Cedric Hermans, St-Luc University Hospital, Belgium; Dr Baolai Hua, Peking Union Medical College Hospital, China; Dr Shannon Jackson, Hemophilia Program, St. Paul's Hospital, Canada; Dr Paula James, SE Ontario Regional Inherited Bleeding Disorders Program, Canada; Dr Craig Kessler, Georgetown University Medical Center, USA; Dr Rainer Kobelt, University Children’s Hospital, Switzerland; Dr Kaan Kavakli, Ege Hemophilia Center, Turkey; Ms. Caitlin Montcrieff, Rhode Island Hemostasis and Thrombosis Center, USA; Dr Riitta Lassila, Coagulation Disorders in Helsinki University Hospital, Finland; Drs Adrienne Lee and Man-Chiu Poon, Foothills Medical Centre, Calgary, Canada; Dr Jennifer Lissick, Children's of Minnesota, USA; Dr Johnny Mahlangu, University of the Witwatersrand, South Africa; Dr Emanuela Marchesini, Department of Medicine, Italy; Dr Margarete Ozelo, INCT do Sangue Hemocentro UNICAMP, Brazil; Dr J Carl Panetta, St. Jude’s Hospital, Memphis, USA; Dr Kathelijne Peerlinck, Hemophilia center Leuven, Belgium; Dr Paolo Radossi, Hemophilia and Regional Blood Disease Centre Hematology, Italy; Dr Savita Rangarajan, Southern Hemophilia Network, UK; Dr Mark T Reding, Center for Bleeding and Clotting, Minneapolis MN; Dr Arlette Ruiz-Sàez, Centro Nacional de Hemofilia, Venezuela; Dr Anjali Sharathkumar, University of Iowa Children’s Hospital, USA; Dr MacGregor Steele, Southern Alberta Pediatric Bleeding Disorder Program, Canada; Dr Jayson Stoffman, Bleeding Disorder’s Program, Canada; Dr Jerry Teitel, Toronto & Central Ontario Hemophilia Program, Canada; Dr Alan Tinmouth, Ottawa Regional Adult Bleeding Disorders Program, Canada; Dr Alberto Tosetto, Divisione di Ematologia Ospedale S Bortolo, Italy; Dr Catherine Vezina, Montreal Children's Hospital, Canada; Dr John KM Wu, BC Children’s Hospital, Canada; Dr Guy Young, Hemostasis/Thrombosis program at Children's Hospital, LA, USA.
A Iorio is the principal investigator of the WAPPS project and has received research and consultancy funds from Bayer, Baxalta, Biogen, NovoNordisk, and Pfizer. All funds were granted to McMaster University and no funds were received for this manuscript. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.