Dosage Regimens, Subjects, and Populations

In Pumas, subjects are represented by the Subject type and collections of subjects are represented as Vectors of Subjects and aliased as a Population. Subjects are defined by their identifier, observations, covariates, and events. In this section we will specify the methods used for defining Subjects programmatically or using the read_pumas function that reads in data that follows the Pumas NLME Data Format (PumasNDF) data format. Before we look at Subjects, we will take a look at how to define events as represented by the DosageRegimen type.

Dosage Regimen Terminology

When subjects are subjected to treatment it is represented by an event in Pumas. Administration of a drug is represented by a DosageRegimen that describes the amount, type, frequency and route. DosageRegimens can either be constructed programmatically using the DosageRegimen constructor or from a data source in the PumasNDF format using read_pumas. The names of the inputs are the same independent of how the DosageRegimen is constructed. The definition of the values are as follows:

• amt: the amount of the dose. This is the only required value.
• time: the time at which the dose is given. Defaults to 0.
• evid: the event id. 1 specifies a normal event. 3 means it's a reset event, meaning that the value of the dynamical variable is reset to the amt at the dosing event. If 4, then the dynamical value and time are reset, and then a final dose is given. Defaults to 1.
• ii: the inter-dose interval. For steady state events, this is the length of time between successive doses. When addl is specified, this is the length of time between dose events. Defaults to 0.
• addl: the number of additional events of the same type, spaced by ii. Defaults to 0.
• rate: the rate of administration. If 0, then the dose is instantaneous. Otherwise the dose is administrated at a constant rate for a duration equal to amt/rate.
• ss: an indicator for whether the dose is a steady state dose. A steady state dose is defined as the result of having applied the dose with the interval ii infinitely many successive times. 0 indicates that the dose is not a steady state dose. 1 indicates that the dose is a steady state dose. 2 indicates that it is a steady state dose that is added to the previous amount. The default is 0.
• route: route of administration to be used in NCA analysis if it is carried out with the integrated interface inside @model. Defaults to NullRoute which is basically no route specified.

This specification leads to the following default constructor for the DosageRegimen type:

DosageRegimen(
  amt::Numeric;
  time::Numeric = 0,
  cmt::Union{Numeric,Symbol} = 1,
  evid::Numeric = 1,
  ii::Numeric = zero.(time),
  addl::Numeric = 0,
  rate::Numeric = zero.(amt)./oneunit.(time),
  duration::Numeric = zero(amt)./oneunit.(time),
  ss::Numeric = 0,
  route::NCA.Route = NCA.NullRoute,
)

julia> DosageRegimen(100; ii = 24, addl = 6)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    100.0     1     24.0      6      0.0       0.0     0  NullRoute

julia> DosageRegimen(50; ii = 12, addl = 13)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1     50.0     1     12.0     13      0.0       0.0     0  NullRoute

julia> DosageRegimen(200; ii = 24, addl = 2)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    200.0     1     24.0      2      0.0       0.0     0  NullRoute

julia> DosageRegimen(200; ii = 24, addl = 2, route = NCA.IVBolus)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    200.0     1     24.0      2      0.0       0.0     0  IVBolus

evs = DosageRegimen(
  regimen1::DosageRegimen,
  regimen2::DosageRegimen;
  offset = nothing
)

julia> e1 = DosageRegimen(100; ii = 24, addl = 6)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    100.0     1     24.0      6      0.0       0.0     0  NullRoute

julia> e2 = DosageRegimen(50; ii = 12, addl = 13)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1     50.0     1     12.0     13      0.0       0.0     0  NullRoute

julia> evs = DosageRegimen(e1, e2)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    100.0     1     24.0      6      0.0       0.0     0  NullRoute
   2 │     0.0      1     50.0     1     12.0     13      0.0       0.0     0  NullRoute

julia> DosageRegimen(e1, e2; offset = 10)
DosageRegimen
 Row │ time     cmt    amt      evid  ii       addl   rate     duration  ss    route
     │ Float64  Int64  Float64  Int8  Float64  Int64  Float64  Float64   Int8  NCA.Route
─────┼───────────────────────────────────────────────────────────────────────────────────
   1 │     0.0      1    100.0     1     24.0      6      0.0       0.0     0  NullRoute
   2 │   178.0      1     50.0     1     12.0     13      0.0       0.0     0  NullRoute

Steady State Dosing

In addition to applying the specified dose, steady state dosing resets the compartments to a steady state (if ss = 1) or adds the the steady state values to the current compartment values (if ss = 2).

There are three classes of steady state doses:

The steady state of the system can be viewed as the result of having applied the steady state dose from the infinite past, depending on the type of the dose as a constant infusion or as a sequence of doses. These so-called implied past doses do not affect the values of the system prior to the time point (time) of the dose record.

Constant Infusion

The time point (time) of a steady state dose record with constant infusion denotes the time point at which the infusion from the infinite past ends. Therefore, absorption lag (lags) does not apply to constant infusions and the dose event cannot be applied multiple times (ii and addl must be zero). Since the dose amount (amt) is zero, also other dose control parameters (bioav, rate, and duration) do not apply to steady state events with constant infusion.

Multiple Doses

For steady state events with multiple infusions or bolus doses, the time point (time) of the dose record denotes the time point at which the infusion is started or the bolus is injected. Dose control parameters (lags, bioav, rate, and duration) at the time point (time) of the dose record apply to all doses, including the implied doses prior to the dose event.

The Subject Constructor

The dosage regimen is only a subset of what we need to fully specify a subject. As mentioned above, we use the Subject type to represent individuals in Pumas. They can be constructed using the Subject constructor programmatically:

Subject

Subject(;id = "1",
         observations = NamedTuple(),
         events = nothing,
         time = observations isa AbstractDataFrame ? observations.time : nothing,
         covariates::Union{Nothing, NamedTuple} = nothing,
         covariates_time = observations isa AbstractDataFrame ? observations.time : nothing,
         covariates_direction = :left)

julia> Subject()
Subject
  ID: 1

julia> Subject(
         id = 20,
         events = DosageRegimen(200, ii = 24, addl = 2),
         covariates = (WT = 14.2, HT = 5.2),
       )
Subject
  ID: 20
  Events: 3
  Covariates: WT, HT

julia> Subject(covariates = (WT = [14.2, 14.7], HT = fill(5.2, 2)), covariates_time = [0, 3])
Subject
  ID: 1
  Covariates: WT, HT

or using read_pumas from tabular data:

read_pumas(filepath::AbstractString; missingstring = ["", ".", "NA"], kwargs...)
read_pumas(df::AbstractDataFrame; kwargs...)

You can also create Subjects from an existing Subject:

Subject(subject::Subject; id::AbstractString, events)

julia> s1 = Subject(; id = "AKJ491", events = DosageRegimen(1.0; time = 1.0))
Subject
  ID: AKJ491
  Events: 1

julia> Subject(s1; id = "AKJ492")
Subject
  ID: AKJ492
  Events: 1

The simulated output of a PumasModel as a result of simobs is Pumas.SimulatedObservations. Passing this simobs output into a vectorized Subject will result in a Population (an alias for a vector of Subjects) that is equivalent to the output of read_pumas. This is a convenient feature that allows one to simulate data and turn it back into a Population that can then be passed into a fit function:

Subject(simsubject::SimulatedObservations)

sims = simobs(model, pop, params)

Subject.(sims)

PumasNDF

The PumasNDF is a specification for building a Population (an alias for a vector of Subjects) from tabular data. Generally this tabular data is given by a database like a CSV. The CSV has columns described as follows:

• id: the ID of the individual. Each individual should have a unique integer, or string.
• time: the time corresponding to the row. Should be unique per id, i.e. no duplicate time values for a given subject.
• evid: the event id. 1 specifies a normal dose event. 3 means it's a reset event, meaning that the value of the dynamical variable is reset to the amt at the dosing event. If 4, then the dynamical value and time are reset, and then a final dose is given. Defaults to 0 if amt is 0 or missing, and 1 otherwise.
• amt: the amount of the dose. If the evid column exists and is non-zero, this value should be non-zero. Defaults to 0.
• ii: the inter-dose interval. When addl is specified, this is the length of time to the next dose. For steady state events, this is the length of time between successive doses. Defaults to 0, and is required to be non-zero on rows where a steady-state event is specified.
• addl: the number of additional doses of the same amt to give. Defaults to 0.
• rate: the rate of administration. If 0, then the dose is instantaneous. Otherwise, the dose is administered at a constant rate for a duration equal to amt/rate. A rate=-2 allows the rate to be determined by Dose Control Parameters (DCP). Defaults to 0.
• ss: an indicator for whether the dose is a steady state dose. A steady state dose is defined as the result of having applied the dose with the interval ii infinitely many successive times. 0 indicates that the dose is not a steady state dose. 1 indicates that the dose is a steady state dose. 2 indicates that it is a steady state dose that is added to the previous amount. The default is 0.
• cmt: the compartment being dosed. Defaults to 1.
• duration: the duration of administration. If 0, then the dose is instantaneous. Otherwise, the dose is administered at a constant rate equal to amt/duration. Defaults to 0.
• Observation and covariate columns should be given as a time series of values of matching type. Constant covariates should be constant through the full column. Time points without a measurement should be denoted by a dot (.).

If a column does not exist, its values are imputed to be the defaults. Special notes:

• If rate and duration exist, then it is enforced that amt=rate*duration.
• All values and header names are interpreted as lower case.

using CSV
data = CSV.read(
    joinpath("pathtomyfile", "mydata.csv"),
    DataFrame;
    missingstring = ["", ".", "NA", "BQL"],
)

For more information check out the CSV documentation.

PumasNDF Checks

The read_pumas function performs some general checks on the provided data and informs the user about inconsistency in the data. It throws an error in case of invalid data, reporting the row number and column name causing the problem such that the user can resolve the issue.

Following is the list of checks applied by the read_pumas function.

Necessary columns in case of event and non-event data

In case of event_data=true (the default), the dataset must contain id, time, amt, and observations columns.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

[ Info: The input has keys: [:id, :time, :cmt, :dv, :age, :sex, :evid]
ERROR: PumasDataError: The input must have: `id, time, amt, and observations` when `event_data` is `true`
[...]

In case of event_data=false, only the id column is required.

df = DataFrame(
    time = [0, 1],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex], event_data = false)

# output

ERROR: ArgumentError: column name "id" not found in the data frame; existing most similar names are: "dv" and "evid"
[...]

Event data without evid column

In case of event_data=true (the default), a warning is displayed if the provided dataset doesn't have an evid column.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

┌ Warning: Your dataset has dose event but it hasn't an evid column. We are adding 1 for dosing rows and 0 for others in evid column. If this is not the case, please add your evid column.
│
└ @ Pumas
Population
  Subjects: 1
  Covariates: age, sex
  Observations: dv

Non-numeric/string entries in an observation column

If there are non-numeric or string entries in an observation column, read_pumas throws an error and reports row(s) and column(s) having this issue.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    cmt = [1, 2],
    dv = [missing, "k@"],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: [1], row = [2], col = dv]  We expect the dv column to be of numeric type.
These are the unique non-numeric values present in the column dv: ("k@",)
[...]

Non-numeric/string entries in the amt column

Similarly, if there are non-numeric or string entries in an observation column, read_pumas throws an error and reports row(s) and column(s) having this issue.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = ["k8", 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: [1], row = [1], col = amt]  We expect the amt column to be of numeric type.
These are the unique non-numeric values present in the column amt: ("k8",)
[...]

cmt must be a positive integer or valid string/symbol for non-zero evid data record

The cmt column should contain positive numbers or string/symbol identifiers of the compartment being dosed.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    cmt = [-1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = cmt] column had invalid value: -1. Pumas does not currently support negative compartment values to turn off compartments.
[...]

amt can only be missing or zero when evid is zero

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 5],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 2, col = evid] amt can only be missing or 0 when evid is 0
[...]

amt can only be positive or zero when evid is 1

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [-10, 0],
    cmt = [1, 2],
    evid = [1, 0],
    dv = [10, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = evid] amt can only be positive or zero when evid is 1
[...]

Observations at the time of dose

Observations should be missing at the time of dose (or when amt > 0).

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    cmt = [1, 2],
    evid = [1, 0],
    dv = [10, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = dv] an observation is present at the time of dose in column dv. A blank record (`missing`) is required at time of dosing, i.e. when `amt` is positive.
[...]

Steady-state dosing requires ii column

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    ss = [1, 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: your dataset does not have ii which is a required column for steady state dosing.
[...]

Steady-state dosing with multiple infusions or bolus doses requires positive ii

In case of a steady-state event with multiple infusions or bolus doses (ss = 1 or ss = 2 and amt > 0), the value of the dose interval column ii must be non-zero.

If the rate column is not provided it is assumed to be zero.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    ss = [1, 0],
    ii = [0, 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = ii] for steady-state dosing the value of the interval column ii must be non-zero but was 0
[...]

Steady-state dosing with constant infusion requires zero ii

In case of a steady-state event with constant infusion (ss = 1 or ss = 2, amt = 0 and rate > 0), the value of the dose interval column ii must be zero.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [0, 0],
    ss = [1, 0],
    rate = [2, 0],
    ii = [1, 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = ii] for steady-state infusion the value of the interval column ii must be zero but was 1
[...]

Steady-state dosing with constant infusion requires zero addl

In case of a steady-state event with constant infusion (ss = 1 or ss = 2, amt = 0 and rate > 0), the value of the additional dose column addl must be zero.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [0, 0],
    ss = [1, 0],
    rate = [2, 0],
    ii = [0, 0],
    addl = [5, 0],
    cmt = [1, 2],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
    evid = [1, 0],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = addl] for steady-state infusion the value of the additional dose column addl must be zero but was 5
[...]

Non-zero addl requires ii column

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [5, 0],
    cmt = [1, 2],
    evid = [1, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: The dataset has an `addl` column specified with non-zero entries but does not have an `ii` column specified. It is not possible to specify the additional doses without providing the interval of time between them. Please specify which column the `ii` information is present in in your `read_pumas` call.
[...]

Non-zero addl requires positive ii

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [5, 0],
    ii = [0, 0],
    cmt = ["Depot", "Central"],
    evid = [1, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = ii]  ii must be positive for addl > 0
[...]

Positive ii requires non-zero addl

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [0, 0],
    ii = [12, 0],
    cmt = ["Depot", "Central"],
    evid = [1, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = addl]  addl must be positive for ii > 0
[...]

ii can only be missing or zero when evid is zero

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [5, 2],
    ii = [12, 4],
    cmt = ["Depot", "Central"],
    evid = [1, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 2, col = evid]  ii can only be missing or zero when evid is 0
[...]

addl can only be positive or zero when evid is 1

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [-10, 0],
    ii = [12, 0],
    cmt = ["Depot", "Central"],
    evid = [1, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = evid]  addl can only be positive or zero when evid is 1
[...]

evid must be nonzero when amt is positive or addl and ii are positive

When amt is positive, evid must be non-zero as evid=0 indicates an observation record.

df = DataFrame(
    id = [1, 1],
    time = [0, 1],
    amt = [10, 0],
    addl = [5, 0],
    ii = [12, 0],
    cmt = ["Depot", "Central"],
    evid = [0, 0],
    dv = [missing, 8],
    age = [45, 45],
    sex = ["M", "M"],
)
read_pumas(df; observations = [:dv], covariates = [:age, :sex])

# output

ERROR: PumasDataError: [Subject id: 1, row = 1, col = evid] amt can only be missing or 0 when evid is 0
[...]