# Theory and Design of asclepias

asclepias is organized around three abstractions: events, features and cohorts.

## Event Data Theory

asclepias provides the types and functions for defining models of event data. The types and terminology are intended to be consistent with the event-data-model project.

### Definitions

#### Event

An Event is a Context with an associated time interval.

Concretely, an Event is a wrapper around the interval-algebra package’s PairedInterval type:

newtype Event t m a= MkEvent ( PairedInterval (Context t m) a )

#### Context

A Context contains up to three types of information:

1. A TagSet (required)

2. Fact s about the event (required)

3. Metadata on the source of the event (optional)

An example of a context is below.

data Context t m = MkContext
{ -- | the 'TagSet' of a @Context@
getTagSet :: TagSet t (1)
-- | the facts of a @Context@.
, getFacts  :: m (2)
-- | the 'Source' of @Context@
, getSource :: Maybe Source (3)
}
 1 a TagSet; 2 Fact s about the event whose shape and possible values are determined by the Model type m; 3 optionally, information on the source of the event data.

#### Tags

A TagSet is a collection labels ("tags") that summarize the information in the data Model, as given by the Fact s of that model attached to a particular event. Each Event has an associated TagSet, which can contain multiple unique tags.

A Fact is a collection of metadata about an Event, which serves to classify for the purpose of building study cohorts and analyses. A Model for a given study defines which particular Fact s are allowed to bee used in that study.

Fact s can contain a lot of information. For example a Fact to denote a medical insurance claim could contain procedure codes, cost information and provider information.

The tags in a TagSet synthesize the Fact s associated with an Event to provide a kind of short-hand, useful when programming for or reasoning about the groups of Event s relevant a study.

For example, "diabetes_treatment" and "in_hospital" are possible tags that could be used to summarize a Fact with medical claim information. A tag might synthesize information across multiple Fact s in a single Model by, say, combining claims information with an ICD9 code to label an Event as "diabetes_diagnosis".

At present, tags are created by manually specifying how the Fact s of a Model should be summarized, typically using the helper functions in the notionate package in a project-specific concepts.dhall file.

#### Facts and Model

See the event-data-model documentation for a definition of Facts and Model. Note that Fact and Model defined there are types defined in the Dhall programming language. The programmer using asclepias must manually define in Haskell code a type m within the Context c m that corresponds to the Model for a given project.

#### Source

The Source type stores information on the origins of the data. This allows for increased traceability of the data from source to final analysis.

A Source type has the following definition:

---
data Source = MkSource
{ column   :: Maybe T.Text
, file     :: Maybe T.Text
, row      :: Maybe Integer
, table    :: T.Text
, database :: T.Text
}
deriving (Eq, Show, Generic)
---

column is the column name of the source data. file is the path of the source data. row is the row number of the source data. table is the name of the source data table. database refers to the name of the data source. For example "Optum" or "Medicaid"

#### Example

Here is an example of an Event:

data SillySchema =
A Int
| B Text
| C
| D
deriving (Show, Eq, Generic, Data)

instance FromJSON SillySchema where
parseJSON = genericParseJSON
(defaultOptions
{ sumEncoding = TaggedObject { tagFieldName      = "domain"
, contentsFieldName = "facts"
}
}
)

type SillyEvent1 a = Event Text SillySchema a

The SillyEvent type is a project-specific synonym for an Event where the TagSet is Text.

SillySchema is the Model, a Haskell sum type, with a different Fact given by each of its possible value types

and the Interval type is any valid type a, such as Int.

This structure provides a high degree of flexibility in defining new structures for study-specific cohort definitions and analysis.

See the event-data-model documentation for details.

## Design of the Features module

A Feature is a type parametrized by two types, name and d:

newtype (KnownSymbol name) => Feature name d =
MkFeature  ( FeatureData d )

The type d here stands for "data", which then parametrizes the FeatureData type. The FeatureData type is wrapper around an Either:

newtype FeatureData d = MkFeatureData {
getFeatureData :: Either MissingReason d  -- ^ Unwrap FeatureData.
}

Type of d can be almost anything and need not be a scalar. All the following are valid types for d:

• Int

• Text

• (Int, Maybe Text)

• [Double]

The name type is a bit special: it does not appear on the right-hand side of the =. In type-theory parlance, name is a phantom type. So, a Feature type constructor takes two arguments (name and d), but its value constructor (MkFeature) takes a single value of type FeatureData d.

Values of the FeatureData type contain the data we’re ultimately interested in analyzing or passing along to downstream applications. However, a FeatureData value does not simply contain data of type d. The type allows for the possibility of missingness, failures, or errors via the Either type. A content of a FeatureData d, then, is either a Left MissingReason or a Right d.

The use of Either has important implications when defining features, as we will see. Now that we know the internals of a Feature, how do we create them? There are two ways to create features:

1. a pure lifting of data into a Feature or

2. writing a Definition: a function that defines a Feature based on other Feature s.

The first method is a way to get data directly into a Feature. The following function takes a list of Events and makes a Feature of them:

allEvents :: [Event Day] -> Feature "allEvents" [Event Day]
allEvents = pure

The pure lifting is generally used to lift a subject’s input data into a Feature, so that other features can be defined from a subject’s data. Features are derived from other Feature by the Definition type Specifically, Definition is a type containing a function that maps Feature inputs to a Feature output. define (or defineA) constructs the Definition. For example:

myDef :: Definition (Feature "a" Int -> Feature "b" Bool)
myDef = define (\x -> if x > 0 then True else False)

x is type Int not Feature "a" Int and the return type is Bool not Feature "b" Bool. The define function and Definition type do the magic of lifting these types to the Feature level. To see this more clearly, see myDef2 below:

intToBool :: Int -> Bool
intToBool x = if x > 0 then True else False)

myDef2 :: Definition (Feature "a" Int -> Feature "b" Bool)
myDef2 = define intToBoo

myDef2 is equivalent to myDef.

The define function, then, let’s us focus on the logic of our Feature without needing to worry about handling the error cases. If we were to write a function with signature Feature "a" Int → Feature "b" Bool directly, it would look something like:

myFeat :: Feature "a" Int -> Feature "b" Bool
myFeat (MkFeature (MkFeatureData (Left r))) = MkFeature (MkFeatureData (Left r))
myFeat (MkFeature (MkFeatureData (Right x))) = MkFeature (MkFeatureData (Right $intToBool x)) One would need to pattern match all the possible types of inputs, which gets more complicated as the number of inputs increases. As an aside, since Feature are Functors, one could instead write: myFeat :: Feature "a" Int -> Feature "b" Bool myFeat = fmap intToBool This would require understanding how Functors and similar structures are used. The define and defineA functions provide a common interface to these structures without needing to understand the details. ### Evaluating Definitions To evaluate a Definition, we use the eval function. Consider the following example. The input data is a list of Ints. If the list is empty (null), this is considered an error in feat1. If the list has more than 3 elements, then in feat2, the sum is computed; otherwise 0 is returned. featInts :: [Int] -> Feature "someInts" [Int] featInts = pure feat1 :: Definition (Feature "someInts" [Int] -> Feature "hasMoreThan3" Bool) feat1 = defineA (\ints -> if null ints then makeFeature (missingBecause$ Other "no data")
else makeFeature \$ featureDataR (length ints > 3))

feat2 :: Definition (
Feature "hasMoreThan3" Bool
-> Feature "someInts" [Int]
-> Feature "sum" Int)
feat2 = define (\b ints -> if b then sum ints else 0)

ex0 = featInts []
ex0a = eval feat1 ex0 -- MkFeature (MkFeatureData (Left (Other "no data")))
ex0b = eval feat2 (ex0a, ex0) -- MkFeature (MkFeatureData (Left (Other "no data")))

ex1 = featInts [3, 8]
ex1a = eval feat1 ex1 -- MkFeature (MkFeatureData (Right False))
ex1b = eval feat2 (ex1a, ex1) -- MkFeature (MkFeatureData (Right 0))

ex2 = featInts [1..4]
ex2a = eval feat1 ex2 -- MkFeature (MkFeatureData (Right True))
ex2b = eval feat2 (ex2a, ex2) -- MkFeature (MkFeatureData (Right 10))

Note the value of ex0b. It is a Left because the value of ex0a is a Left; in other words, errors propogate along Feature. If a given Feature dependency is a Left then that Feature will also be Left. This propogation of Left s often increases performance. In a sequence of computations, after the first Left occurs, no subsequent computations are needed.

### Type Safety of Features

In describing the Feature type, the utility of having the name as a type may not have been clear. To clarify, consider the following example:

x :: Feature "someInt" Natural
x = pure 39

y :: Feature "age" Natural
y = pure 43

f :: Definition (Feature "age" Natural -> Feature "isOld" Bool)
f = define (>= 39)

fail = eval f x
pass = eval f y

In the example, fail does not compile because "someInt" is not "age", even though both the data types are Natural.

If the fail line is uncommented, you will see a compiler error like this:

    * Couldn't match type "someInt"' with "age"'
Expected type: Feature "age" Natural
Actual type: Feature "someInt" Natural
* In the second argument of eval', namely x'
In the expression: eval f x
In an equation for fail': fail = eval f x

Commenting out fail will produce a pass value that looks like this when printed,

"isOld": MkFeatureData {getFeatureData = Right True}

Make note of what the compiler error is telling you: The string "age" in the type signature of f is actually part of the type of the input. The compiler says Feature "age" Natural is not the same type as Feature "someInt" Natural and therefore does not compile the program.

In other words, if you correctly declare that the input type of f must be a Feature "age" Natural then you can only give f some input that has that type, including the name "age".

Therefore, the name field of a Feature can serve as a tool to declare your intention about which inputs should be paired with which functions via their names.

You can easily abuse this aspect of Feature.

For example, this safety mechanism breaks down when you allow the compiler to choose any name it wants by setting the name to be a type variable rather than an explicit string.

The following version compiles just fine, with x, y as above.

f :: Definition (Feature n Natural -> Feature "isOld" Bool)
f = define (>= 39)

gotcha = eval f x

The only difference is that Feature n Natural has a type variable n where "age" used to be. gotcha when printed produces

"isOld": MkFeatureData {getFeatureData = Right True}

If you do not wish to be intentional about using names as a means to specify named inputs and outputs via the type system, it is likely not worth using Feature` at all.