The Phoenix Reporter

A Compendium of Insightful Information for Our Phoenix Community – Vol. 2

Welcome to this issue of The Phoenix® Reporter. In this e-newsletter we will share informative educational content along with practical, implementable resources with our Phoenix user community.

In this issue:

  1. Using Integrated Distributed Delay Differential Equations to Model Delays in PK/PD Systems
  2. CDISC PK Data Preparation
  3. Feedback from the Phoenix Community: Our Visits with the FDA
  4. Nurturing Future Pharmacometricians

Using Integrated Distributed Delay Differential Equations to Model Delays in PK/PD Systems

Pharmacologic delays are ubiquitous in PK/PD studies, especially in therapeutic areas such as oncology, diabetes, and arthritis where outcomes are not observed for days to months after drug administration. Response delays are partly due to absorption delays arising from the time it takes for the drug to be transported from the depot site to the central compartment after drug administration. In other cases, drugs administered as pro-drugs, must be metabolized to the active drug. In both these cases, the drug effect may be delayed with respect to the parent drug concentration in the central compartment.

Transit compartment models (TCMs), described by systems of ordinary differential equations (ODEs), have been widely used to describe delayed outcomes, however present some disadvantages: (1) TCMs require a large amount of differential equations to fit the data, (2) one needs to manually find proper values for the number of compartments, and (3) they do not adequately describe complex features.

Advantages of Using Delay Differential versus Ordinary Delay Equations in Population PK/PD Modeling

When ordinary differential equations are used in PK/PD modeling, the future state of a system is totally determined by its present value. However this approach does not capture reality – in PK/PD the measured response of an orally administered drug is frequently delayed and thus the future state needs to be determined not only by its present value(s) but also by its past value(s). Delay Differential Equations (DDEs), which are ODEs that incorporate a delay, provide an alternate, more flexible approach to generate more complex dynamics than their corresponding ODEs, thereby eliminating the disadvantages associated with TCMs. DDEs, which can be either discrete or distributed, are extensions of ODEs, complement TCMs and other models, and provide a more general and simpler way to model delayed outcomes including absorption, distribution, PK/PD link, and drug response.

DDEs offer numerous advantages over TCMs:

  • Only one simple equation is needed versus the large number of differential equations to model delayed outcomes using TCMs
  • DDE’s are more efficient and less error-prone
  • They provide more flexibility for population analysis than TCMs
  • Capture dynamics better than TCMs

Distributed DDEs can be used to model absorption delays and delayed drug effects in a realistic manner. The distributed delay includes the discrete delay approach as a special case, however also incorporates a wide array of PK/PD models including TCMs, typical absorption models, and a number of atypical (or irregular) absorption models.

Integrated Model Delay Function in Phoenix 7.0

Phoenix NLME 7.0 is the first PK/PD modeling engine to offer integration of a Discrete Delay Differential Equation within the Phoenix Modeling language (PML). In NLME 7.0 you can add a discrete delay function with a single PML command avoiding inefficient workarounds and approximations, and without the need to add complex lines of code.The webinar Modeling Delayed Outcomes in PK Studies Using Delay Differential Equations, provides an overview of the discrete DDE function in Phoenix 7.0. With the launch of Phoenix 8 later this year, we will introduce an integrated Distributed Delay Differential Equation. To learn more about distributed delays in Phoenix 8, make sure to view our recent webinar, Modeling PK/PD Systems with Distributed Delays, given by Dr. Wojciech Krzyzanski from SUNY Buffalo. Be sure to visit the Resources section of this newsletter to gain more information on delay differential equations and their importance in pharmacometrics.

CDISC PK Data Preparation

The US Food and Drug Administration (FDA) and other regulatory agencies have implemented electronic submission guidelines using standards developed by the Clinical Data Interchange Standards Consortium (CDISC). CDISC Study Data Tabulation Model (SDTM) and Standard Exchange for Non-clinical Data (SEND) are examples of study data standards required by the FDA for electronic submission of tabulation data. These standards support the acquisition, exchange, submission, and archiving of clinical (SDTM) and non-clinical (SEND) study data sets.

Understanding and complying with CDISC data standards is critical to satisfying electronic regulatory data submission requirements. Submissions that do not comply with CDISC requirements could delay the regulatory review process. Moreover, having data in a standard format provides numerous benefits to pharma and CROs by facilitating easier and faster collaboration on projects and by accelerating the review and approval process by regulatory agencies.

CDISC PK Data Preparation

CDISC PK data is organized into domains for demographic (DM) and exposure information (EX), PK concentration data (PC), and PK parameters (PP). The data is structured using SDTM, the general model for representing clinical research study tabulation data, which is then transported via the Operational Data Model (ODM). This approach enables data reporting consistency across the review and submission cycle.

Certara’s Tools and Services for CDISC PK Data Preparation

Understanding CDISC data standards, while time-consuming and cumbersome, is a critical task required for achieving compliance of electronic regulatory submissions. As a CDISC-Registered Solutions provider, Certara provides an end-to-end solution to streamline CDISC PK data preparation, analysis, and submittal.

Phoenix CDISC SDTM and SEND Workflow Templates prepare non-compartmental analysis (NCA) data into the CDISC-ready formats required for electronic submittal. Once NCA is completed in Phoenix WinNonlin™, the SDTM and SEND Workflow Templates automate the creation of the Pharmacokinetic Parameters (PP) and Pharmacokinetic Concentration Data (PC) domains in the required SDTM or SEND format.

Phoenix CDISC Navigator provides a user-friendly interface that seamlessly imports CDISC data into an analysis-ready format, and then exports CDISC-formatted PK parameters for regulatory submission. It is ideal for scientists who perform non-compartmental PK analysis in Phoenix WinNonlin.

Certara Strategic Consulting provides a range of pharmacometric services, tailored to the specific needs of each client, ensuring that the modeling & simulation deliverables are embedded in the overall development workflow to optimize the impact of the work.

Implementing CDISC data standards is critical for complying with electronic regulatory data submission requirements. Standardizing data facilitates collaboration between sponsors and CROs on projects and accelerates the review and approval process by regulatory agencies. Moreover, sponsors and CROs obtain more effective knowledge transfer between databases and robust regulatory electronic submission protocols.

Certara’s tools and services streamline routine data preparation for CDISC-ready submission, provide NCA-ready analysis of CDISC-formatted data in Phoenix, and remove the error-prone and time-consuming task of manual CDISC data conversion.

Download our white paper to learn more about the CDISC guidelines for electronic regulatory submittal of clinical and non-clinical study data, and be sure to visit the Resources section of this newsletter.

Feedback from the Phoenix Community: Our Visits with the FDA

Certara recently completed a week long set of meetings with the FDA, where we met with over 300 FDA reviewers from 7 of the 11 FDA centers that use Phoenix.

Here’s a few topics that took center-stage during our visits:

Q: How can we create Phoenix workflow templates that are reusable across different studies with varying numbers of parameters, such as treatments, analytes, matrices, and doses?

A: Creating workflow templates in Phoenix—containing a single object (like an XY plot) or multiple objects (eg, an entire workflow or set of objects)—is an effective way to increase your productivity. An example of a workflow template that is of particular interest for generic drug development is one that can be used for reference-scaled average bioequivalence (RSABE) methodology, which is increasingly used to demonstrate bioequivalence for Highly Variable Drugs and Drug Products (HVDs/HVDPs). For more information on workflow templates, be sure to check out our blog posts on how to create a Phoenix workflow template and how to use the Phoenix RSABE templates. If a more complex automated template is required, learn about implementing custom solutions using our Phoenix Technology Services.

Q: What is the advantage of using the QRPEM engine for Population PK/PD (Pop PK/PD) analysis that was introduced in the latest version of NLME 7.0?

A: The Quasi-random Parametric Expectation Maximization (QRPEM) algorithm is the most advanced and fastest accurate likelihood expectation maximization (EM) algorithm available, ideal for converging complex models such as those used in Pop PK/PD modeling. QRPEM addresses problems typically encountered in the Pop PK/PD NLME domain, resulting in the ability to achieve N-1 behavior, and greatly improves computational efficiency for models where fixed effects cannot be driven by a simple EM update based on the estimated mean and covariance matrix of the posterior distributions for each subject. Download our white paper for a comprehensive overview of the NLME QRPEM algorithm.

Q: How easy is it to set up a grid?

A: To improve performance of computationally intensive algorithms, parallel computing functionality was introduced in Phoenix NLME 7.0. Check out a recent webinar that provides an overview on how to set up grid computing in NLME 7.0, or our blog post on how to access grid computing from your desktop. Be sure to be on the lookout for our next issue of The Phoenix Reporter were we will review new functionality for grid computing.

Nurturing Future Pharmacometricians

Certara is committed to providing innovative products and consultative services for model-based drug development (MBDD). As a way to serve our community, we are dedicated to shaping the future of healthcare innovation through education, and offer a range of programs that benefit all levels of experience. Attend upcoming webinars or archived webinars, check out the MBDD Roundtable Blog for the latest advances in technology, learn how to build custom PK/PD codes at PML School, get up to speed and take a WinNonlin, NLME or IVIVIC course through Certara University, follow the Support Forum to pose a question or find answers to Phoenix-based questions, or visit our comprehensive Scientific Resource Library for leading edge publications, case studies, posters, and technology-based product literature.

Particularly for those starting out on their career in pharmacometrics, we hold an annual Student Sponsorship that supports travel and accommodation expenses for a selected number of students wishing to attend the Population Approach Group in Europe (PAGE) meeting, held this year in Budapest Hungary June 6-9th. PAGE is a nonprofit organization whose community shares interest in data analysis using the population approach. This year’s sponsorship brought together six PhD and MS candidates whose thesis work focuses on using a variety of PKPB, mechanistic-based modeling, Pop PK, and PK/PD approaches to solve research problems. Read more about these talented young scientists.

PAGE is also an important meeting for our scientists to present their latest work through posters, presentations, workshops and tutorials. See a complete list of our research presented at PAGE or search PAGE for abstract summaries.

For the broader student population, we partner with eminent scientists at designated academic Centers of Excellence around the world. Through our Centers of Excellence Program, Certara is committed to training the next generation of experts in model-based drug development, with a particular focus on pharmacometrics.

Tips of the Trade

The most popular sessions during our Phoenix roadshows, webinars and customer educational sessions are “tips and tricks in Phoenix.” Here’s a tip for Phoenix WinNonlin users to automate the preparation of NCA Data into the SEND format using Phoenix CDISC Workflow Templates. Learn More >


Following is a compendium of scientific articles and information to augment your knowledge on topics highlighted in this issue.

Published Articles

  1. Krzyzanski, W. J. Interpretation of transit compartments pharmacodynamic models as lifespan based indirect response models. Pharmacokinet Pharmacodyn (2011). 38:179-204.
  2. Koch, W. Krzyzanski, J.J. Pérez-Ruixo, and J. Schopp. Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations. J Pharmacokinet Pharmacodyn (2014). 41:291–318.
  3. Mo, G., Gibbons, F., Schroeder, P., and Krzyzanski, W. Lifespan based pharmacokinetic-pharmacodynamic model of tumor growth inhibition by anticancer therapeutics. PLoS ONE 9 (2014). (10): e109747.
  4. Providing regulatory submissions in electronic format: standardized study data. Guidance for the industry. US Department of Health and Human Services Food and Drug Administration. December 2014.
  5. Liu, X., and Wang, Y. Comparing the performance of FOCE and different expectation maximization methods in handling complex population physiologically-based pharmacokinetic models. J Pharmacokinet Pharmacodyn (2016). 43: 359-370.
Blog Posts

Archived Webinars

Community Forum

Become a member of the Phoenix Forum, a site dedicated for our Phoenix software community. In the forum, members can pose questions to our experts and interact with their peers – it is an excellent source to gain and share knowledge, experience and ideas. The forum is also a site to download software, check on licensing, and submit Phoenix software support requests.

Resource Library

Your source for all Certara information including case studies, white papers, blog posts, webinars, articles, posters, brochures, and press releases. Visit the Library >

Information from Certara on topics contained in this issue:

Learn from the Best

Become a “More Valuable Player” by enrolling in a Certara University pharmacometrics course:
8 modeling and simulation course topics
On-site courses given in over 15 cities
On-demand, e-learning course library
See the full schedule >
We've recently introduced a new program of complementary webinar-tutorials on Phoenix Modeling Language (PML). Join our instructors and guest lecturers for this educational webinar series featuring topics submitted to our Phoenix Forum by users interested in developing custom PK/PD models.

Upcoming PML School Presentations
Turnover Model 1: Repeated Dosing
July 13, 2017
10am ET
Presenter: Chris Mehl
Dose-response-time Analysis I-IV
July 27, 2017
10am ET
Presenter: Bernd Wendt
Transduction Modeling: Assessment of Number of Transit Departments
August 10, 2017
10am ET
Presenter: Bernd Wendt
See the full schedule and learn how to access prior tutorials >

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