Accelerating the Rate of Adoption of New Pharmacometrics Platforms Using Formal Tools For Model Interconversion
Rich Haney
Cellular Statistics, LLC
Objectives: The FDA can accelerate the rate of approval of new drugs by accelerating the rate of adoption in industry of new pharmacometrics platforms. In support of that overall effort, we have written tools that convert NMTRAN models to and from forms that can be used by the new platforms. Doing this can allow the FDA and industry to test the new platforms using the very large numbers of existing models now in NMTRAN, WinNonlin, and other forms.
Methods:
Practical Methods: We use PERL and Maple to convert NMTRAN, WinBUGS, Monolix, and WinNonlin models to algebraic, language-independent forms that make extensive use of polynomials and differential polynomials[1,2] We then use PERL to convert these back to language-specific representations. We store all intermediate and final results of translations ( as well as all results of NONMEM, Monolix and other runs) in a MySQL database. We use C# and web-based methods to let users browse and edit models easily.
Formal Methods: Various fixed effects and NLME approaches can sometimes be “embedded” within one another in simple ways; they can also be related in ways that are more complex. We characterize such relationships using algebraic methods. In this context, pairs of translations (such as from NMTRAN to WinBUGS and back) define (a.) "back-and-forth" or "up-and-down" operators in model theory, (b.) monads in universal algebra, and (c.) pairs of adjunctions in category theory. We consider ourselves successful when we can pass our various practical tests but still obey about 10-15 “nitpicking” algebraic rules inherent to our algebraic perspective as a whole.
Results: So far we have tried to convert 250 models back and forth among NONMEM, WinBUGS, Monolix, and other forms. Of these, 63 pairs of translations work well in practice and can be characterized nicely formally. Another 95 work “informally”. 92 do not work yet. ( We hope to about 400 completely working by June.)
Many of our models involve categorical data models. For these, use of toric polynomials[1,2,3,4] as the intermediate representations when translating between NONMEM and WinBUGS works well, but we should add that we may have been able to do this step just as well using a simpler approach.
We converted WinBUGS and other models to annotated, “regularized” NMTRAN forms. These conform to various rules (e.g., variables can only be on left-hand sides of equations once.)
We could not handle Monolix "For" lops, NMTRAN "DO WHILE" statements, pure FORTRAN code, and other NONMEM features and options.
Conclusion: The overall approach, whether formal or informal (or done by ourselves or others ) will accelerate the adoption of new pharmacometrics platforms in the future.[5,6]
References:
[1] Seth Sullivant, 2006, "Statistical Models are Algebraic Varieties", www.math.harvard.edu/~seths/lecture1.pdf
[2] Lior Pachter and Stumfels, "Algebraic Statistics for Computational Biology", 2005
[3] Fabio Rapallo, "Toric statistical models: parametric and binomial representations", AISM (2007) 59:727–740
[4] Rich Haney, "Toric models for categorical data in Pop PK/PD: Are They Useful or Not"?", to be posted summer 2008 at site of www.cellularStatistics.com
[5] Our belief is that our approaches will be complementary ( formally speaking, "adjoint") to those of language-based approaches, e.g., Mike Dunlavey's PML language[5] and future standards by the NLMEc. See, for example, Mike Dunlavey, "Next generation Modeling Language", PAGE 16 (2007) Abstr 1076 [www.page-meeting.org/?abstract=1076]
[6]For a summary of some of own ( formal ) approaches overall, please see http://openservices.sourceforge.net/
