1. Ratio Measurements Overview of modeling approaches in existing ontologies. Note: class hierarchies are shortened in the following Heiner Oberkampf

2. 1.General considerations 2.Ratio related concepts in existing ontologies 3.Example representations 4.Discussion Agenda

3. Distinction of ratios with and without dimensions: mass concentration: “zinc in a solute in g/ml” immunohistochemical staining of tumor cells: “10 % of Ki-67 positive tumor cells” Requirements: Numerator and denominator should be explicit It should be possible to link ratio the to the assay or method used to determine the ratio. Allow comparison of ratios representing the same ratios Prevent comparison of ‘incomparable’ ratios Problems: limit of detectibility: “We might measure nothing because the instrument can't detect that little.” (Alan) Genaral Considerations

4. Ratio related concepts in existing ontologies Ontology placement and definitions

5. Ontology for Biomedical Investigations (OBI) No general definition of ratio. Definititions ratio of collected to emitted light: A measurement datum measuring the amount of light collected s compared to the total amount of emitted light in the detector component of a flow cytometer instrument. The datum has a qualitative role Example of Usage 10 % Logical Definition none specific, only inherited from superclasses

6. Statistics Ontology (STATO) Distinction between dimensional and dimensionless ratios. Definitions ratio: A ratio is a data item which is formed with two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. dimensionless ratio: A ratio where the numerator and denominator are expressed in the same unit. Logical definition ratio := (‘has numerator’ SOME ‘measurement data item’) AND (‘has donominator’ SOME ‘measurement data item’)

7. Ontology of Biological and Clinical Statistics (OBCS) Several ratio related concepts but no general definition. Definitions odds ratio: A data item that refers to the odds that an individual with a specific condition has been exposed to a risk factor divided by the odds that a control has been exposed. The odds ratio is used in case- control studies. The odds ratio provides a reasonable estimate of the relative risk for uncommon conditions. likelyhood ratio: a quantitative confidence value that expresses how many times more likely the data are under one model than the other. ratio scale: A measurement scale that is similar to an interval scale, i.e. a magnitude of a continuous quantity and a unit magnitude of the same kind; the distinguishing feature of a ratio scale is a meaningful zero value that means the absence of whatever is measured. Logical Definitions none

8. Definititions ratio: A dimensionless unit which denotes an amount or magnitude of one quantity relative to another. concentration unit: A unit which represents a standard measurement of how much of a given substance there is mixed with another substance. Logical Definitions ratio: none concentration unit: subclass of (is_unit_of SOME ‘pato:concentration of’) Units Ontology (UO) Ratio as a dimensionless unit and addional definition of ‘concentration unit’.

9. pato:ratio pato:ratio value pato:percentage pato:percentage value pato:absolute ratio pato:absolute ratio value pato:absolute percentage pato:absolute percentage value pato:relative percentage pato:relative percentage value … Ontologies using the deprecated concepts: NIF Dysfunction NIF Cell Neuro Behavior Ontology (NBO) NIF Gross Anatomy Sample processing and separation techniques (SEP) Phenotypic Quality (PATO) Many ratio related concepts, but all deprecated

10. Example Represenations

11. 10% of Ki-67 positive tumor cells Ki-67 is a protein in cells that increases as they prepare to divide into new cells. A staining process can measure the percentage of tumor cells that are positive for Ki-67. The more positive cells there are, the more quickly they are dividing and forming new cells. In breast cancer, a result of less than 10% is considered low, 10-20% is intermediate/borderline, and more than 20% is considered high. Zinc in a solute in g/ml A mass concentration is measured in mass per volume. Examples

12. Example: 10 % of Ki-67 positive tumor cells Alan’s proposal 'Prevalence of Ki-67+ cells in a tumor‘ a quality ; inheres_in a Tumor. 'Ki-67+ cell ratio measurement datum' a scalar measurement datum ; is_specified_output_of [ a ratio calculation ; has_specified_input [ specified_output_of xxx assay ] ; is_quality_measure_of some 'Fraction of Ki-67+ cells in a tumor‘ ; has_value_specification [ has_measurement_unit_label 'Fraction of Ki-67+ cells in a tumor‘ ; specifies_value_of some 'Prevalence of Ki-67+ cells in a tumor‘ ; ]. _:Ki-67+ cell ratio measurement datum obi:has value specification fraction of Ki-67+ cells in a tumor' obi:scalar value specification _:svs “0.1”^^xsd:float obi:has specified value iao:scalar measurement datum :prevalence of Ki-67+ cells in a tumor iao:is quality measurement of pato:quality iao:has measurement unit label tumor _:tumor bfo:inheres in iao:specifies value of Fraction of Ki-67+ cells in a tumor'

13. Example: 10 % of Ki-67 positive tumor cells Using STATO 10% of Ki-67 positve tumor cells = ratio(number of Ki-67 positive tumor cells/number of negative tumor cell) * 100 and indicating that fact by adding a symbol, namely % ratio of Ki-67+ tumor cells = stato:ratio AND stato:has_numerator SOME (stato:count AND is_about SOME ('cell' and has_quality SOME 'Ki-67+')) AND stato:has_denominator SOME (stato:count and is_about SOME('cell' and has_quality SOME 'Ki67- ')) *100 could be read as: percentage calculation: has_specified_input some ratio has_specified_input some 'coefficient and has value value 100 has_specified_output some percentage percentage defined as: percentage subClassOf 'data item' has_numerator some 'measurement data item' has_denominator some 'measurement data item' percentage is_specified_output some 'percentage calculation' percentage is_denoted_by some 'symbol:%‘ or reuse the component you have and rely on that pattern. obi:has value specification' [ a 'obi:scalar value specification' ; 'obi:has specified value' "10"^^xsd:integer ; 'iao:has measurement unit label' 'uo:percentage'. ] ;

14. Example: 10 % of Ki-67 positive tumor cells :prevalence of Ki-67 positive cells in a tumor iao:scalar value specification :prevOfKi67 iao:is quality specification of :Ki-67+ cell ratio specification pato:quality :tumor cells tumor _:tumor bfo:inheres in :has_denominator :has_numerator My current modeling approach of dimensionless ratios Possible logical definitions ‘tumor cell’ := cell and inheres_in SOME tumor ‘Ki-67 positive tumor cell’ := ‘tumor cell’ AND has_quality SOME ‘Ki-67+’ :Ki-67 positive tumor cells Problem: Often the ratio is not calculated from two measurements. E.g. a pathology report might specify only (an estimation of) the percentage of Ki-67+ tumor cells without specifying the count of Ki-67+ cells and the total number of tumor cells. Similarly, a description of a concentration might be given in g/ml without the measurements of the mass and the volume. obi:has value specification uo:percent uo:ratio obi:scalar value specification _:svs “10”^^xsd:float obi:has specified value iao:has measurement unit label stato:dimensionless ratio stato:ratio

15. Example: Mass concentration Alan’s proposal for “zinc in a solute” The problem occurs when we represent an instance of the solute when there is in fact none - the case of true concentration being 0. The solution is to use a universal restriction on the relation to the solute rather than an existential, and have the relation not be filled (i.e. absent) in the case where there is not. Notice that in the case that there is no zinc there is no instance of zinc (properly "portion of zinc"). The zero, when there is one, is part of an information entity about the quality. The quality, while it generally refers to some zinc, might not. What it represents when there is no zinc is admittedly odd, but presumably it is something to do only with the solute. Perhaps "Solute lacking Zinc". There is no implication that a zero magnitude datum implies that there is in fact no zinc - this saves us from the "limit of detectibility" problem - that we might measure nothing because the instrument can't detect that little. While in the general case, magnitude zero doesn't distinguish between some and no zinc, that can be tightened up for other classes - if the quality were a count of large objects, then the constraint could be tightened to >0, and then zero magnitude would imply no object.

16. Example: Mass concentration Using STATO A ‘mass concentration’ defined by numerator and denominator is automatically classified as a ratio:

17. Discussion

18. 1.Distinction of dimensionless and dimensional ratios? 2.Which ratio related concepts should be defined direcly in OBI? 3.Definition of properties: has_numerator and has_denominator to explicitly define the respective qualities 4.Use uo:percentage as unit label for dimensionless ratios? 5.Relation to assays/calculation process analogue to measurements using is_specified_output_of SOME ‘planned process’ ? Proposals for Discussion