Quantity Package

Medicine is one domain in which symbols representing relative magnitudes are commonly used, without exact values being known. The main purpose is usually to classify patients into groups for which different decisions might be made. Thus, while approximate ranges (technically speaking - "fuzzy intervals") might be stated (such as for a urinalysis), concrete values are not of interest, only categories are. Take for example the characterisation of pain as being "mild", "medium", "severe", or the reflex response to tendon percussion as "-", "+/-", "+", "++", "+++", "++++". There may be no way to scientifically precisely quantify such values because they reflect a subjective experience of the patient or informal judgement by clinician. However, they are understood as being ordered, e.g. "++" is 'greater than' "+".

Similarly, even though the symbolic values for haemolysed blood in a urinalysis have approximate ranges stated for them, as shown below, these 'values' are not usable in the same way as true quantities.

A second requirement for ordinal values is that in many cases there is a need to associate integer values with the symbols, in order to facilitate ordered comparison, and also to enable longitudinal comparison across results of the same kind (e.g. pain, protein). Integer values may be negative, 0 and positive, typically to allow the 0 value to correspond to a neutral value in a range.

An common kind of data value in medicine is the dimensionless countable quantity, e.g. "number of doses: 2", "number of previous pregnancies: 1", "number of tablets: 3". Values of this type are always integral. Countable values need to be convertible to real numbers for statistical purposes, for example for a study of average number of pregnancies per couple.

Some countable entities such as tablets are divisible into major fractions, typically halves and occasionally quarters.

The most common kind of quantity is a measured, dimensioned quantity. Anything which is measurable (rather than countable) involves a number of data aspects, namely:

Examples of dimensioned quantities include:

A common quantitative type in science and medicine is the proportion, or ratio, which is used in situations like the following:

In general ratios have real number values, even if many examples appear to be integer ratios. Proportions with unitary denominator and % (denominator = 100) are common.

A concept superficially similar to proportions and ratios is formulations of materials, such as a solid in a liquid e.g.:

Although a single solute/single solvent formulation appears to have the same form as a ratio, the general form is for any number of substances to be mixed together, usually according to a particular procedure. Formulations are therefore not candidates for direct modelling as fine-grained quantities, but instead are constructed by archetyping a higher-level structure, each leaf element of which contains the required kind of Quantity.

Quantity ranges are ubiquitous in science and medicine, and may be defined for any kind of measured phenomenon. Examples include:

A reference range is a quantity range attached to a measured value, and is common for laboratory result values. The typical form of a reference range found in a pathology result indicates what is considered the 'normal' range for a measured value. Examples of reference ranges:

Ranges can also be quoted for drug administrations, in which case they are usually thought of as the 'therapeutic' range. For example, the anticonvulsant drug Carbamazepine has a therapeutic range of 20 - 40 μMol/L. In some cases, there are multiple ranges associated with a drug, for example, Salicylate has a therapeutic range of 1.0 - 2.5 mmol/L and a toxic range > 3.6 mmol/L

Various examples occur in which multiple ranges may be stated, including the following.

Where there are multiple ranges, the important question is: which range information is relevant to the actual data being recorded for the patient? In theory, only the range corresponding to the particular patient situation should be used, i.e. the range which applies after taking into account sex, age, smoking status, "professional athlete", organ transplanted, etc. In most cases, this is a single "normal" range, or a pair of ranges, typically "therapeutic" and "critical". However, practical factors complicate things. Firstly, data is sometimes supplied from pathology labs along with some or all of the applicable reference ranges, even though only some could possibly apply. This is particularly the case if the laboratory has no other data on the patient, and cannot evaluate which range applies. The requirement for faithfulness of recording might be extended to reference data supplied by laboratories, regardless of how irrelevant or arbitrarily chosen the reference data is, meaning that such data has to be stored in the record anyway. Secondly, there may be circumstances in which physicians want a number of reference ranges, even while knowing that only one range is applicable to the datum. Ranges above and below the relevant one might be useful to a physician wishing to determine how far out of range the datum is.

It is quite common for laboratories to include a normal range with each measured value, and/or a normal 'status', which indicates where the value lies with respect to the normal range. The latter will commonly take the form of markers like "HHH" (critically high), HH (abnormally high), H (borderline high), L, LL, LLL in HL7v2 messaging, although other schemes are undoubtedly used.

In order to make sense of the requirements in a systematic way, a proper typology for quantities is needed. The most basic characteristic of all values typically called 'quantities' is that they are ordered, meaning that the operator "<" (less-than) is defined between any two values in the domain. An ancestor class for all quantities called DV_ORDERED is accordingly defined. This type is subtyped into ordinals and true quantities, represented by the classes DV_ORDINAL and DV_QUANTIFIED respectively. DV_ORDINAL represents data values whose exact numeric values are not known, and which use symbolic renderings instead, such as "+", "++", "+++", or "mild", "medium", "severe". Each symbol can be assigned any integer value, providing a basis for computable comparison. In contrast, instances of DV_QUANTIFIED and all its subtypes have precise numeric magnitudes.

DV_QUANTIFIED itself introduces the concepts of magnitude and magnitude_status. The magnitude attribute is guaranteed to be available on any DV_QUANTIFIED, carrying the effective value, regardless of the particular subtype. The optional magnitude_status attribute can be used to provide a nonquantified indication of accuracy, and takes the following values:

If not present, meaning is "=".

Logically, an accuracy attribute should also be included in DV_QUANTIFIED, but as its modelling is different in the subtypes in a way that does not easily lend itself to a common ancestor, it is only included in the subtypes.

The DV_QUANTIFIED class has two subtypes: DV_AMOUNT and DV_ABSOLUTE_QUANTITY. The former corresponds to relative 'amounts' of something, either a physical property(such as mass) or items (e.g. cigarettes). Mathematically, the '+' and '-' operators (as well as '*' and '/') are defined in the same way as for the real numbers (or any other mathematical 'field'), with the semantics that adding two relative quantities measuring the same thing (i.e. with the same units) produces another relative quantity of the same kind; while the semantics of subtraction are that one relative quantity subtracted from another generates a third.

The second subtype of DV_QUANTIFIED, DV_ABSOLUTE_QUANTITY, models quantities whose values are absolute along a line having a defined origin. The main example of absolute quantities are the temporal concepts date, time and date/time. These are distinguished from relative quantities in that the normal addition and subtraction operations don’t apply. Instead, the semantics of such operators are based on the idea of the difference between absolute values being a relative amount. For example, two dates can be subtracted, but the result is a duration, not another date. For this reason, the operations add, subtract and diff are defined rather than '+' or '-'. Date/time types, as well as the relative concept duration, are defined in [Date Time Package].

Subtypes of DV_AMOUNT are DV_PROPORTION, DV_QUANTITY, DV_COUNT, and DV_DURATION (see date_time package). The type DV_COUNT has an integer magnitude and is used to record naturally countable things such as number of previous pregnancies, number of steps taken by a recovering stroke victim and so on. There are no units or precision in a DV_COUNT. Countable quantities can be used to create instances of DV_QUANTITY, such as during a statistical study which average tobacco consumption over a time period. Such a computation might cause the creation of DV_QUANTITY objects representing values like {magnitude = 5.85, units = '/ week'}

DV_QUANTITY is used to represent amounts of measurable things, and has a real number magnitude, precision, units and accuracy. The units attribute contains the scientific unit in a parsable form defined by the Unified Code for Units of Measure (UCUM). A valid units string always implies a measured property, such as "force" or "pressure". The property of a Quantity can conveniently constrained in archetypes, e.g. to "pressure", which would allow any pressure unit. Unit strings can be compared to determine if they measure the same property (e.g. "bar" and "kPa" are both units corresponding to the property "pressure"), which enables the is_strictly_comparable_to function defined on DV_ORDERED to be properly specified on DV_QUANTITY.

Theoretically it might be argued that 'accuracy' should not be included in a model for quantified values, because it is an artifact of a measuring process and/or device, not of a quantity itself. For example, a weight of "82 kg ±5%" can be represented in two parts. The "82 kg" is represented as a DV_QUANTITY, while the "±5%" could be included in the protocol description of the weighing instrument, since this is where the error comes from. For practical purposes however, (in)accuracy in a measured quantity corresponds to a range of possible values. In realistic computing in health, it is quite likely that the accuracy will be required in computations on quantities, especially for statistical population queries in which measurement error must be disambiguated from true correlation.

Accuracy is therefore introduced as the abstract feature accuracy of the DV_QUANTIFIED class. It is defined concretely in the two descendants, DV_AMOUNT, where it is of type Real, and DV_ABSOLUTE_QUANTITY, where it is of a differential type defined by subtypes. A value of 0 in either case indicates 100% accuracy, i.e. no error in measurement. Where accuracy is not recorded in a quantity, it is represented by a special value. In DV_AMOUNT, a value of -1 for the accuracy attribute is used for this purpose, and the constant unknown_accuracy_value = -1 is provided within the class to give a symbolic name for the special value. In the DV_ABSOLUTE_QUANTITY class, accuracy_unknown is represented by a Void (i.e. null) value for the accuracy attribute. An abstract Boolean feature accuracy_unknown is defined in the parent class DV_QUANTIFIED to provide a logical test of accuracy being absent, and is implemented in the respective descendants by concrete functions that check for the special values.

In addition, the class DV_AMOUNT, provides a feature accuracy_is_percent: Boolean to indicate if accuracy value is to be understood as a percentage, or an absolute value.

When two compatible quantities are added or subtracted using the + or - operators (DV_AMOUNT descendants) or add and substract (DV_ABSOLUTE_QUANTITY class), accuracy behaves in the following way:

The related notion of 'uncertainty' is understood as a subjective judgement made by the clinician, indicating that he/she is not certain of a particular statement. It is not the same as accuracy: uncertainty may apply to non-quantified values, such as subjective statements, and it is not an aspect of objective measurement processes, but of human confidence. Where the uncertainty is due to subjective memory e.g. "I think my grandfather was 56 when he died", the uncertainty is simply recorded as another value, along with the main data item being recorded. Uncertainty is therefore not directly modelled in the openEHR data types, but appears instead in particular archetypes.

Ranges are modelled by the generic type DV_INTERVAL<T:DV_ORDERED> which enables a range of any of the other quantity types (except ratio) to be constructed. This allows any subtype of DV_ORDERED to occur as a range as well.

The DV_PROPORTION type is provided for representing true ratios, i.e. relative values, and consists of numerator and denominator Real values, and a magnitude function which is computed as the result of the numerator/denominator division. The type attribute is used to indicate the logical type of the proportion. Supported types include:

Lastly, the is_integral function indicates that the numerator and denominator are both integer values; this is used for fractions (the fraction and integer_fraction types above) and other commonly occurring ratios where both parts are always integer values.

Normal range for any of the quantity types (i.e. any instance of a subtype of DV_ORDERED) can be included via the attribute DV_ORDERED.normal_range, of type REFERENCE_RANGE. Other reference ranges (e.g. sub-critical, critical etc) can be included via the attribute DV_ORDERED.other_reference_ranges. The separation of normal and other reference range attributes is used because the former constitute the vast majority of ranges quoted for quantitative data.

Normal status can be included via the attribute DV_ORDERED.normal_status, which takes the form of a DV_ORDINAL, whose symbol attribute is coded according to the openEHR terminology group "normal status", and takes values "HHH" (critically high), "HH" (abnormally high), "H" (borderline high)", "N" (normal), "L" …​ "LLL".

Time can be recorded in two ways. Absolute times in the social time domain, such as dates and time of day are recorded using the types in the date_time package. Fine-grained 'time', which is a duration rather than a time, is recorded using a DV_QUANTITY with units = 's' or another temporal unit ('h', 'ms', 'ns' etc).