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ProbOnto Knowledge Base and Ontology of Probability Distributions Maciej J Swat

ProbOnto Knowledge Base and Ontology of Probability Distributions Maciej J Swat. URL: probonto.org. DDMoRe Project. Subtask : develop formats for encoding/exchange of statistical (NLME) models and numerical results as used in pharmacometrics (analysis of sparse clinical data)

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ProbOnto Knowledge Base and Ontology of Probability Distributions Maciej J Swat

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  1. ProbOnto Knowledge Base and Ontology of Probability Distributions Maciej J Swat URL: probonto.org

  2. DDMoRe Project • Subtask: develop formats for encoding/exchange of statistical (NLME) models and numerical results as used in pharmacometrics (analysis of sparse clinical data) • Major results: • PhamacometricsMarkup Language – PharmML • Standard Output – SO

  3. Mathematical formalism of non-linear mixed effect (NLME) models Distributions, or their defining functions, are used in almost every sub-model

  4. Practical application example of ProbOnto in PharmML Problem description: Count data models require the specification of the according PMF (probability mass function), here e.g. for the Zero-inflated Poisson with PMF PMF implemented using ProbOnto –> full interoperability by using the code names of the distribution and its parameters PMF implemented explicitly –> error prone process and limited interoperability

  5. Development timeline

  6. Background • Motivation for ProbOnto was to create an database/ontology of probability distributions for • statistical model encoding • support of model exchange between tools – different tools may support different parameterization of the same distribution • annotation purposes. Many resources available online, as papers/books etc – but no proper ontology existed so far. Existing ontologies were insufficient, see e.g. STATO, PR-OWL. • Until 2015 • when encoding probabilistic uncertainties in PharmML we have been relying on UncertML, which provides means to encode a range of probability distributions (28 in version 2). However it has several limitations: limited scope, missing math support, not extendable • Needed an extension mechanism – additional distributions and parameterisations are required for many standard discrete models and/or Bayesian inference. • Idea –ProbOnto can be helpful in providing a generic extension mechanism of UncertML and can be used in PharmML both • as ontological resource for annotation purposes and • as knowledge base to provide several distribution related function (PDF, CDF, HF, SF, IDF), re-parameterisations and quantities

  7. ProbOnto v2.5 – Features • 150 parametric distributions and alternative parameterisations • 135 discrete and continuous univariates & 1 mixture distribution • 14 discrete & continuous multivariates • 3 empirical distributions (aka samples) • Covers all distributions used the DDMoRe target tools, such as NONMEM, Monolix, BUGS, and many others. • >220 relationships and re-parameterisation formulas. • For each distribution, either PDF or PMF and in many cases also CDF, hazard function (HF) and survival function (SF) • Related quantities: mean, median, mode, variance • Support/range definition • All mathematical functions and quantities are available in • Latex and • additionally R-code is provided for functions • Can be used to annotate statistical models based on supported probability distributions, e.g. their name, parameters, truncation bounds, their defining functions and quantities.

  8. Focus on re-parameterization relationships • Interoperability background: various tools support different parameteri-sations, e.g. log-normal distribution • When moving model from tool to tool –> re-parameterisation is needed • ProbOnto supports the model exchange Figure: Re-parameterization relationships implemented in ProbOnto and their support in target languages/tools.

  9. Re-parameterization example • Consider the situation when one would like to run a model using two different optimal design tools, e.g. • PFIMand PopED.  • The former supports the LN2, the latter LN7 parameterization, respectively. •  re-parameterization is required, otherwise the two tools would produce different results – all these formulas are stored in ProbOnto (in Latex)

  10. LN1…LN7 re-parameterisations screenshots from the ProbOnto specification

  11. ProbOnto v2.5 – coverage of univariates

  12. Example from the spec

  13. ProbOnto v2.5 – relationships between distributions

  14. ProbOnto v2.5 – Protégé screenshots

  15. ProbOnto Team • Pierre Grenon (UCL, UK): knowledge representation, ontological engineering • Sarala Wimalaratne (EMBL-EBI, UK): software development • Maciej J Swat (Simcyp/Certara, UK, previously at EMBL-EBI, UK): team leader, scientific development, database curation & quality assurance

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