`Pumas`

Docstrings

`DataFrames.DataFrame`

— Type`DataFrame(events::DosageRegimen, expand::Bool = false)`

Create a DataFrame with the information in the dosage regimen. If expand, create a DataFrame with the information in the event list (expanded form).

`DataFrames.DataFrame`

— Method`DataFrame(bts::Union{SimulatedInference, Bootstraps})`

Returns a data frame of the parameter estimates.

`Distributions.MvNormal`

— Method`MvNormal(pmi::FittedPumasModelInference)`

Returns an `MvNormal`

with a mean equal to the optimal parameter values in the fitted model and a covariance equal to the variance-covariance estimate.

`Distributions.MvNormal`

— Method`MvNormal(model::PumasModel, means::NamedTuple, vcov::NamedTuple)`

Returns an `MvNormal`

with mean equal to the vectorized `means`

argument and a covariance equal to the block diagonal matrix of the covariance matrices in the `vcov`

argument. The `mean`

argument should be a named tuple of values in their natural domain. `vcov`

should be a named tuple of numbers (for real parameters) or matrices for vector and matrix parameters. For parameters that are themselves symmetric matrices, e.g:

```
Ω = [
Ω₁₁ Ω₁₂ Ω₁₃;
Ω₂₁ Ω₂₂ Ω₂₃;
Ω₃₁ Ω₃₂ Ω₃₃;
]
```

the covariance matrix should be the covariance of the vector: `[Ω₁₁, Ω₁₂, Ω₂₂, Ω₁₃, Ω₂₃, Ω₃₃]`

. Note that because the matrix is symmetric, only the upper triangle is used iterating over the columns first in an outer loop then the over the rows of each column in an inner loop.

Example:

```
means = (θ1 = 1.0, θ2 = [1.0, 2.0], θ3 = [1.0 0.1; 0.1 1.0])
vcov = (
θ1 = 0.1,
θ2 = [0.5 -0.2; -0.2 0.6],
θ3 = [0.5 -0.2 0.1; -0.2 0.6 -0.3; 0.1 -0.3 0.45],
)
dist = MvNormal(model, means, vcov)
```

`Pumas.AnalyticalPKPDProblem`

— Type```
AnalyticalPKPDProblem(
f,
u0,
tspan,
events,
time,
p,
bioav)
```

An analytical PK(PD) problem.

Fields:

`f`

: callable that returns the state of the dynamic system`u0`

: initial conditions`tspan`

: time points that define the intervals in which the problem is defined`events`

: events such as dose, reset events, etc`time`

: event times`p`

: a function that returns pre block evaluated at a time point`bioav`

: bioavailability in each compartment

`Pumas.AnalyticalPKProblem`

— TypeAnalyticalPKProblem(pkprob, prob2, sys2)

A problem that is partially an analytical problem that can be evaluated independently of the rest of the system.

Fields:

`pkprob`

: the analytical part of the problem`prob2`

: a problem that represents the rest of the system`sys2`

(optional): the system of`prob2`

- used for latexification.

`Pumas.Censored`

— Type`Censored(distribution::Distribution, lower::Real, upper::Real)::Censored`

Construct a censored distribution based on `distribution`

and the censoring limits `lower`

and `upper`

.

`Pumas.Central1`

— Type`Central1()`

An analytical model for a one compartment model with dosing into `Central`

. Equivalent to

`Central' = -CL/Vc*Central`

where clearance, `CL`

, and volume, `Vc`

, are required to be defined in the `@pre`

block.

`Pumas.Central1Periph1`

— Type`Central1Periph1()`

An analytical model for a two-compartment model with a central compartment, `Central`

and a peripheral compartment, `Peripheral`

. Equivalent to

```
Central' = -(CL+Q)/Vc*Central + Q/Vp*Peripheral
Peripheral' = Q/Vc*Central - Q/Vp*Peripheral
```

where clearance, `CL`

, and volumes, `Vc`

and `Vp`

, and distribution clearance, `Q`

, are required to be defined in the `@pre`

block.

`Pumas.Central1Periph1Meta1`

— Type`Central1Periph1Meta1()`

An analytical model for a two compartment model with a central compartment, `Central`

, with a peripheral compartment, `Peripheral`

, and a metabolite compartment, `Metabolite`

. Equivalent to

```
Central' = -(CL+Q+CLfm)/Vc*Central + Q/Vp*CPeripheral
CPeripheral' = Q/Vc*Central - Q/Vp*CPeripheral
Metabolite' = -CLm/Vm*Metabolite + CLfm/Vc*Central
```

where clearances (`CL`

and `CLm`

) and volumes (`Vc`

, `Vp`

and `Vm`

), distribution clearance (`Q`

), and formation clearance of metabolite `CLfm`

are required to be defined in the `@pre`

block.

`Pumas.Central1Periph1Meta1Periph1`

— Type`Central1Periph1Meta1Periph1()`

An analytical model for a two compartment model with a central compartment, `Central`

, with a peripheral compartment, `Peripheral`

, and a metabolite compartment, `Metabolite`

, with a peripheral compartment, `MPeripheral`

. Equivalent to

```
Central' = -(CL+Q+CLfm)/Vc*Central + Q/Vp*CPeripheral
CPeripheral' = Q/Vc*Central - Q/Vp*CPeripheral
Metabolite' = -(CLm+Qm)/Vm*Metabolite + Qm/Vmp*MPeripheral + CLfm/Vc*Central
MPeripheral' = Qm/Vm*Metabolite - Qm/Vmp*MPeripheral
```

where clearances (`CL`

and `CLm`

) and volumes (`Vc`

, `Vp`

, `Vm`

and `Vmp`

), distribution clearances (`Q`

and `Qm`

) and formation clearance of metabolite `CLfm`

are required to be defined in the `@pre`

block.

`Pumas.Constrained`

— Type`Constrained`

Constrain a `Distribution`

within a `Domain`

. The most common case is an `MvNormal`

constrained within a `VectorDomain`

. The only supported method for `Constrained`

is `logpdf`

. Notice that the result does not represent a probability distribution since the remaining probability mass is not scaled by the mass excluded by the constraints.

**Example**

```
julia> d = Constrained(MvNormal(fill(1.0, 1, 1)), lower=-1, upper=1)
Constrained{ZeroMeanFullNormal{Tuple{Base.OneTo{Int64}}}, VectorDomain{Vector{Int64}, Vector{Int64}, Vector{Float64}}}(ZeroMeanFullNormal(
dim: 1
μ: 1-element Zeros{Float64}
Σ: [1.0]
)
, VectorDomain{Vector{Int64}, Vector{Int64}, Vector{Float64}}([-1], [1], [0.0]))
julia> logpdf(d, [ 0])
-0.9189385332046728
julia> logpdf(d, [-2])
-Inf
```

`Pumas.CorrDomain`

— Type`CorrDomain(template)`

Return a correlation domain.

`template`

provides both the shape and initial values for the resulting correlation parameter.

- if
`template`

is an`Int`

then an identity matrix of size`template`

is returned. - if
`template`

is a square`Matrix`

then the`CorrDomain`

will match its size and will

have initial values according to the `template`

elements.

`Pumas.Depots1Central1`

— Type`Depots1Central1()`

An analytical model for a one compartment model with a central compartment, `Central`

, and a depot, `Depot`

. Equivalent to

```
Depot' = -Ka*Depot
Central' = Ka*Depot - CL/Vc*Central
```

where absoption rate, `Ka`

, clearance, `CL`

, and volume, `Vc`

, are required to be defined in the `@pre`

block.

`Pumas.Depots1Central1Periph1`

— Type`Depots1Central1Periph1()`

An analytical model for a two-compartment model with a central compartment, `Central`

, a peripheral compartment, `Peripheral`

, and a depot `Depot`

. Equivalent to

```
Depot' = -Ka*Depot
Central' = Ka*Depot -(CL+Q)/Vc*Central + Q/Vp*Peripheral
Peripheral' = Q/Vc*Central - Q/Vp*Peripheral
```

where absorption rate, `Ka`

, clearance, `CL`

, and volumes, `Vc`

and `Vp`

, and distribution clearance, `Q`

, are required to be defined in the `@pre`

block.

`Pumas.Depots2Central1`

— Type`Depots2Central1()`

An analytical model for a one compartment model with a central compartment, `Central`

, and two depots, `Depot1`

and `Depot2`

. Equivalent to

```
Depot1' = -Ka1*Depot1
Depot2' = -Ka2*Depot2
Central' = Ka1*Depot1 + Ka2*Depot2 - CL/Vc*Central
```

where absorption rates, `Ka1`

and `Ka2`

, clearance, `CL`

, and volume, `Vc`

, are required to be defined in the `@pre`

block.

When using this model during simulation or estimation, it is preferred to have 2 dosing rows for each subject in the dataset, where the first dose goes into `cmt =1`

(or `cmt = Depot1`

) and the second dose goes into `cmt=2`

(or `cmt=Depot2`

). Central compartment gets `cmt=3`

or (`cmt = Central`

). e.g.

ev = DosageRegimen([100,100],cmt=[1,2]) s1 = Subject(id=1, events=ev)

`Pumas.DosageRegimen`

— Type`DosageRegimen`

Lazy representation of a series of Events.

**Fields**

`data::DataFrame`

: The tabular representation of a series of`Event`

s.Signature

```
evts = 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)
```

- Examples

```
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
```

**From various DosageRegimens**

- Signature

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

`offset`

specifies if `regimen2`

should start after an offset following the end of the last event in `regimen1`

.

- Examples

```
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
```

`Pumas.PDiagDomain`

— Type`@param x ∈ PDiagDomain(n::Int; init=ones(n))`

Specifies a parameter as a positive diagonal matrix, with initial diagonal elements specified by `init`

.

`Pumas.PSDDomain`

— Type`@param x ∈ PSDDomain(n::Int; init=Matrix{Float64}(I, n, n))`

Specifies a parameter as a symmetric `n`

-by-`n`

positive semi-definite matrix. `init`

sets the initial value of the parameter and should be a positive semi-definite `Matrix`

of `Float64`

s.

`Pumas.ParamSet`

— Type`ParamSet(params::NamedTuple)`

Construct a Pumas.jl parameter set.

`params`

should be a `NamedTuple`

that maps a parameter name to a `Domain`

or a `Distribution`

.

**Example**

```
ParamSet((;
tvKa = RealDomain(lower=0.),
tvCL = RealDomain(lower=0.),
tvω = PDiagDomain(2)
))
```

`Pumas.Population`

— TypeA `Population`

is an `AbstractVector`

of `Subject`

s.

`Pumas.PumasModel`

— Type`PumasModel`

A model takes the following arguments (`arg [= default]`

):

`param`

: a`ParamSet`

detailing the parameters and their domain`random`

: a mapping from a named tuple of parameters ->`ParamSet`

`pre`

: a mapping from the (params, randeffs, subject) -> ODE parameters.`dcp`

: a mapping from the (params, randeffs, subject) -> dose-control parameters.`init`

: a mapping (col,t0) -> initial conditions`prob`

: a DEProblem describing the dynamics (either exact or analytical)`derived`

: the derived variables and error distributions (param, randeffs, data, ode vals) -> sampling dist`observed = (_, _, _, _, _, _, samples) -> samples`

: simulated values from the error model and post processing: (param, randeffs, data, ode vals, samples) -> vals`options::PumasModelOptions = PumasModelOptions(; subject_t0=false)`

: pass additional options, see`PumasModelOptions`

.`syms::PumasModelSymbols = PumasModelSymbols()`

: the symbols of all the variables defined inside the model, see`PumasModelSymbols`

.`sys = nothing`

: the ModelingToolkit.jl`System`

used to generate`prob`

- if applicable.`macroexpr::Expr = :()`

: the expression passed to the`@model`

macro - if applicable.`desc::Dict{Symbol, String} = Dict{Symbol, String}()`

: descriptions of the symbols (variables, parameters, etc.) used in the model.`metadata::Dict{Symbol, Any} = Dict{Symbol, Any}()`

: include a`Dict`

of arbitrary metadata.

`Pumas.RealDomain`

— Type`@param x ∈ RealDomain(;lower=-∞,upper=∞,init=0)`

Specifies a parameter as a real value. `lower`

and `upper`

are the respective bounds, `init`

sets the initial value of the parameter and is used for `init_params`

.

`Pumas.Subject`

— Type`Subject`

The data corresponding to a single subject:

Fields:

`id`

: identifier`observations`

: a named tuple of the dependent variables`covariates`

: a named tuple containing the covariates, or`nothing`

.`events`

: a vector of`Event`

s.`time`

: a vector of time stamps for the observations

When there are time varying covariates, each covariate is interpolated with a common covariate time support. The interpolated values are then used to build a multi-valued interpolant for the complete time support.

From the multi-valued interpolant, certain discontinuities are flagged in order to use that information for the differential equation solvers and to correctly apply the analytical solution per region as applicable.

Constructor

```
Subject(;id = "1",
observations = nothing,
events = Event[],
time = observations isa AbstractDataFrame ? observations.time : nothing,
event_data = true,
covariates::Union{Nothing, NamedTuple} = nothing,
covariates_time = observations isa AbstractDataFrame ? observations.time : nothing,
covariates_direction = :right)
```

`Subject`

may be constructed from an `<:AbstractDataFrame`

with the appropriate schema or by providing the arguments directly through separate `DataFrames`

/ structures.

Examples:

```
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
```

`Pumas.Subject`

— MethodSubject

Constructor

`Subject(simsubject::SimulatedObservations)`

Roundtrip the result of `simobs`

, i.e. SimulatedObservations to a `Subject`

/`Population`

Example:

`sims = simobs(model, pop, params)`

To convert `sims`

to a `Population`

, broadcast as below

`Subject.(sims)`

`Pumas.TimeToEvent`

— Type`TimeToEvent{T}`

Distribution like struct to store the hazard and the cumulative hazard in a time-to-event model. The dependent variable in a model that uses `TimeToEvent`

should be a censoring variable that is zero if the variable isn't censored and one if the variable is right censored. Currently, no other censoring types are supported.

**Example**

```
...
@pre begin
θeff = θ*DOSE
λ = λ₀*exp(θeff)
end
@dynamics begin
Λ' = λ
end
@derived begin
DV ~ @. TimeToEvent(λ, Λ)
end
...
```

`Pumas.VectorDomain`

— Type`@param x ∈ VectorDomain(n::Int; lower=-∞,upper=∞,init=0)`

Specifies a parameter as a real vector of length `n`

. `lower`

and `upper`

are the respective bounds, `init`

sets the initial value of the parameter and is used for `init_params`

. The keyword arguments can all take either numbers or vectors. If numbers then the same value will be applied to all `n`

vector elements. If a you specify a vector (of length `n`

) then you can adjust the parameters of the `VectorDomain`

elements individually.

`CommonSolve.solve`

— Function```
sol = solve(
model::AbstractPumasModel,
population::Union{Population, Subject},
param::NamedTuple,
randeffs::NamedTuple=sample_randeffs(rng, model, param, population);
ensemblealg=EnsembleSerial(),
diffeq_options=NamedTuple(),
rng=default_rng()
)
```

Solve the `model`

applied to the `Subject`

(s) within `population`

using parameters `param`

and random effects `randeffs`

. By default, the times at which to save the solution are taken to be the observation times for each `Subject`

within `population`

. This can be overriden by supplying a vector or range as `saveat`

to `diffeq_options`

- e.g. `diffeq_options=(; saveat=[0., 0.5, 1.])`

.

**Arguments**

`model`

may either be a`PumasModel`

or a`PumasEMModel`

.`population`

may either be a`Population`

of`Subject`

s or a single`Subject`

.`param`

is parameter set in the form of a`NamedTuple`

, e.g.`(; tvCL=1., tvKa=2., tvV=1.)`

.`randeffs`

is an optional argument that, if used, should specify the random effects for each subject in`population`

. Such random effects are specified by`NamedTuple`

s for`PumasModels`

(e.g.`(; tvCL=1., tvKa=2.)`

) and by`Tuples`

for`PumasEMModel`

s (e.g.`(1., 2.)`

). If`population`

is a single`Subject`

(without being enclosed in a vector) then a single such random effect specifier should be passed. If, however,`population`

is a`Population`

of multiple`Subject`

s then`randeffs`

should be a vector containing one such specifier for each`Subject`

. The functions`init_randeffs`

,`zero_randeffs`

, and`sample_randeffs`

are sometimes convenient for generating`randeffs`

:

```
randeffs = zero_randeffs(model, param, population)
solve(model, population, param, randeffs)
```

If no `randeffs`

is provided, then random ones are generated according to the distribution in the model.

`ensemblealg`

is a keyword argument that allows you to choose between different modes of parallelization. Options include`EnsembleSerial()`

,`EnsembleThreads()`

and`EnsembleDistributed()`

.`diffeq_options`

is a keyword argument that takes a`NamedTuple`

of options to pass on to the differential equation solver.`rng`

is a keyword argument where you can specify which random number generator to use.

`Distributions.logpdf`

— Method`logpdf(d::Pumas.Constrained, x)`

Evaluate the logarithm of the probability density of the constrained distribution, `d`

, at `x`

.

- If
`d`

is a constrained univariate distribution then`x`

should be a scalar. - If
`d`

is a constrained multivariate distribution then`x`

should be a vector.

Evaluations of `x`

outside of `d`

's constraints returns `-Inf`

.

Note that `d`

itself is not a true distribution since its probability mass is not rescaled to 1.

`GlobalSensitivity.gsa`

— FunctionGlobalSensitivity.gsa(model, population, params, method, vars, p*range*low, p*range*high; kwargs...)

Function to perform global sensitivty analysis

The arguments are:

`model`

: a`PumasModel`

, either defined by the`@model`

DSL or the function-based interface.`population`

: a`Population`

.`params`

: a named tuple of parameters.`method`

: one of the`GSAMethod`

s from GlobalSensitivity.jl,`Sobol()`

,`Morris()`

,`eFAST()`

,`RegressionGSA()`

.`vars`

: a list of the derived variables to run GSA on.`p_range_low`

&`p_range_high`

: the lower and upper bounds for the parameters you want to run the GSA on.

For method specific arguments that are passed with the method constructor you can refer to the GlobalSensitivity.jl documentation.

`LinearAlgebra.cond`

— Method`cond(pmi::FittedPumasModelInference)`

Return the condition number of the variance-covariance matrix stored in `pmi`

. Throws an error if `pmi`

is the result of a call to `infer`

with `Pumas.Bootstrap`

or if the

variance-covariance calculation failed.

`Pumas.conditional_nll`

— Method`conditional_nll(m::AbstractPumasModel, subject::Subject, param, randeffs; diffeq_options)`

Compute the conditional negative log-likelihood of model `m`

for `subject`

with parameters `param`

and random effects `randeffs`

. `diffeq_options`

is a `NamedTuple`

of options passed to the ODE solver. Requires that the derived produces distributions.

`Pumas.empirical_bayes`

— Method```
empirical_bayes(fpm::Pumas.FittedPumasModel)
empirical_bayes(fpm::Pumas.FittedPumasEMModel)
empirical_bayes(insp::Pumas.FittedPumasModelInspection)
```

Return sampled random effects or empirical bayes estimates from a fit or model inspection. If the model was estimated with the `Pumas.FO`

likelihood approximation methods the empirical bayes estimates will be obtained using the `Pumas.LaplaceI`

approximation. If either `Pumas.FOCE`

or `Pumas.LaplaceI`

was used the final empirical bayes estimates will be returned. If `Pumas.SAEM`

was used to fit the empirical bayes estimates are obtained using the `Pumas.LaplaceI`

approximation.

`Pumas.eventnum`

— Method`eventnum(t, events) -> # of doses for each time`

Creates an array that matches `t`

in length which denotes the number of events that have occurred prior to the current point in time. If `t`

is a scalar, outputs the number of events before that time point.

`Pumas.expectation`

— Method`expectation(g, ::MonteCarloExpectation, model::PumasModel, subject::Subject, dist::MvNormal; imaxiters = 10000, diffeq_options::NamedTuple = NamedTuple(), rng::AbstractRNG = Pumas.default_rng())`

Computes the expected predictions for `subject`

with respect to the population parameters and the subject-specific random effects using Monte Carlo integration. `dist`

is a multivariate normal distribution used to sample the population parameters e.g. `dist = MvNormal(pmi)`

where `pmi`

is the output of `infer`

. Sampling is done using rejection sampling to ensure the parameter values are in the parameters' domains. `imaxiters`

is the number of Monte Carlo samples used. `diffeq_options`

can be used to customize the options of the differential equation solver used. `rng`

is the random number generator used during the sampling, which defaults to `Pumas.default_rng()`

.

`Pumas.expectation`

— Method`expectation(g, ::MonteCarloExpectation, model::PumasModel, subject::Subject, param_dists::NamedTuple; imaxiters = 10000, diffeq_options::NamedTuple = NamedTuple(), rng::AbstractRNG = Pumas.default_rng())`

Computes the expected predictions for `subject`

with respect to the population parameters and the subject-specific random effects using Monte Carlo integration. `param_dists`

should be a named tuple of distributions for the population parameters. `imaxiters`

is the number of Monte Carlo samples to use. `diffeq_options`

can be used to customize the options of the differential equation solver used. `rng`

is the random number generator used in the sampling, which defaults to `Pumas.default_rng()`

.

`Pumas.expectation`

— Method`expectation(g, quant::QuadratureExpectation, model::PumasModel, subject::Subject, param_dists::NamedTuple; ireltol=1e-3, iabstol=1e-3, imaxiters=10000, diffeq_options::NamedTuple = NamedTuple())`

Computes the expected predictions for `subject`

with respect to the population parameters using quadrature methods. `param_dists`

should be a named tuple of distributions for the population parameters. Currently, random effects are not supported. `ireltol`

and `iabstol`

are the tolerances for the integration. The integration algorithm will terminate if the tolerance or `imaxiters`

is reached, whichever is first. `diffeq_options`

can be used to customize the options of the differential equation solver.

`Pumas.findinfluential`

— Function`findinfluential(fpm::AbstractFittedPumasModel, k::Integer=5)`

Return a vector of the `k`

most influencial observations based on the value of (minus) the log-likelihood function.

`Pumas.icoef`

— Method`icoef(fpm::AbstractFittedPumasModel)::Vector{ConstantInterpolationStructArray}`

Return the individual coefficients from `fpm`

. The individual coefficients are the variables defined in the `@pre`

block in the `@model`

macro. The function return a vector of covariate interpolation objects. Each of which can be evaluated at any time point. Each of the covariate interpolation objects can be converted to a `DataFrame`

by calling the `DataFrame`

constructor. Hence, a complete `DataFrame`

of the individual coefficients can be obtained by calling `reduce(vcat, DataFrame.(icoef(fpm)))`

.

`Pumas.infer`

— Method`infer(fpm::FittedPumasModel; level=0.95, rethrow_error::Bool=false, sandwich_estimator::Bool=true) -> FittedPumasModelInference`

Compute the `vcov`

matrix and return a struct used for inference based on the fitted model `fpm`

. The confidence intervals are calculated as the `(1-level)/2`

and `(1+level)/2`

quantiles of the estimated parameters. `sandwich_estimator`

is a boolean that switches on or off the sandwich estimator. If `rethrow_error`

is `false`

(the default value), no error will be thrown if the variance-covariance matrix estimator fails. If it is `true`

, an error will be thrown if the estimator fails.

`Pumas.infer`

— Methodinfer(fpm::FittedPumasModel, bts::Pumas.Bootstrap; level=0.95)

Perform bootstrapping by resampling the `Subject`

s from the `Population`

stored in `fpm`

. The confidence intervals are calculated as the `(1-level)/2`

and `(1+level)/2`

quantiles of the estimated parameters. The number of `samples`

used in the bootstrapping is `bts.samples`

. `bts.ensemblealg`

specifies the `ensemblealg`

used here. If `ensemblealg`

is `EnsembleSerial()`

, a single thread will be used. If it is `EnsembleThreads()`

(the default value), multiple threads will be used. See the documentation of Bootstrap for more details on constructing an instance of `Bootstrap`

.

`Pumas.infer`

— Method`infer(fpm::FittedPumasModel, sir::SIR; level=0.95, ensemblealg = EnsembleThreads()) -> FittedPumasModelInference`

Perform sampling importance re-sampling for the `Subject`

s from the `Population`

stored in `fpm`

. The confidence intervals are calculated as the `(1-level)/2`

and (1+level)/2`quantiles of the estimated parameters.`

ensemblealg`can be`

EnsembleThreads()`(the default value) to use multi-threading or`

EnsembleSerial()` to use a single thread.

`Pumas.init_params`

— Function`init_params(model::PumasModel)`

Create a parameter set populated with the initial parameters of `PumasModel`

.

`Pumas.init_randeffs`

— Function`init_randeffs(model::AbstractPumasModel, param::NamedTuple, [, pop::Population])`

Create an object with random effects locked to their mean values.

The optional argument `pop`

takes a `Population`

and changes the output to a vector of such random effects with one element for each subject within the population.

`Pumas.inspect`

— Method`inspect(fpm::AbstractFittedPumasModel; wres_approx::LikelihoodApproximation, nsim::Int, rng)`

Output a summary of the model predictions, residuals, Empirical Bayes estimates, and NPDEs (when requested).

Called on a `fit`

output and allows the keyword argument `wres_approx`

for approximation method to be used in residual calculation. The default value is the approximation method used for the marginal likelihood calculation in the `fit`

that produced `fpm`

. The keyword `nsim`

controls the number of times each subject is simulated for `npde`

computation. A `FittedPumasModelInspection`

object with `pred`

, `wres`

, `ebes`

, and `npdes`

is output.

`Pumas.lrtest`

— Method`lrtest(fpm_0::AbstractFittedPumasModel, fpm_A::AbstractFittedPumasModel)::LikelihoodRatioTest`

Compute the likelihood ratio test statistic of the null hypothesis defined by `fpm_0`

against the the alternative hypothesis defined by `fpm_A`

. The `pvalue`

function can be used for extracting the p-value based on the asymptotic `Χ²(k)`

distribution of the test statistic.

`Pumas.probstable`

— Methodprobstable(fpm::FittedPumasModel)

Return a DataFrame with outcome probabilities of all discrete dependent variables.

`Pumas.pvalue`

— Method`pvalue(t::LikelihoodRatioTest)::Real`

Compute the p-value of the likelihood ratio test `t`

based on the asymptotic `Χ²(k)`

distribution of the test statistic.

`Pumas.read_pumas`

— Method```
read_pumas(filepath::String, args...; kwargs...)
read_pumas(
df::AbstractDataFrame;
observations=Symbol[:dv],
covariates=Symbol[],
id::Symbol=:id,
time::Symbol=:time,
evid::Union{Nothing,Symbol}=nothing,
amt::Symbol=:amt,
addl::Symbol=:addl,
ii::Symbol=:ii,
cmt::Symbol=:cmt,
rate::Symbol=:rate,
ss::Symbol=:ss,
route::Symbol=:route,
mdv::Symbol=nothing,
event_data::Bool=true,
covariates_direction::Symbol=:right,
check::Bool=event_data,
adjust_evid34::Bool=true)
```

Import NMTRAN-formatted data.

`df`

:`DataFrame`

contaning the data to be converted to a`Vector{<:Subject}`

`observations`

: dependent variables specified by a vector of column names`covariates`

: covariates specified by a vector of column names`id`

: specifies the ID column of the dataframe`time`

: specifies the time column of the dataframe`evid`

: specifies the event ID column of the dataframe. See`?Pumas.Event`

for more details.`amt`

: specifies the dose amount column of the dataframe. See`?Pumas.Event`

for more details.`addl`

: specifies the column of the dataframe that indicated the number of repeated dose events. If not specified then the value is zero.`ii`

: specifies the dose interval column of the dataframe. See`?Pumas.Event`

for more details.`cmt`

: specifies the compartment column of the dataframe. See`?Pumas.Event`

for more details.`rate`

: specifies the infusion rate column of the dataframe. See`?Pumas.Event`

for more details.`ss`

: specifies the steady state column of the dataframe. See`?Pumas.Event`

for more details.`route`

: specifies the route of administration column of the dataframe. See`?Pumas.Event`

for more details.`mdv`

: specifies the the column of the dataframe indicating if observations are missing.`event_data`

: toggles assertions applicable to event data`covariates_direction`

: specifies direction of covariate interpolation. Either`:left`

or`:right`

(default)`check`

: toggles NMTRAN compliance check of the input data`adjust_evid34`

: toggles adjustment of time vector for reset events (`evid=3`

and`evid=4`

). If true (the default) then the time of the previous event is added to the time on record to ensure that the time vector is monotonically increasing.

`Pumas.sample_randeffs`

— Function`sample_randeffs([rng::AbstractRNG=Random.default_rng(),] model::AbstractPumasModel, param::NamedTuple [, pop::Population])`

Generate a random set of random effects for model `model`

, using parameters `param`

. Optionally, a random number generator object `rng`

can be passed as the first argument.

The optional argument `pop`

takes a `Population`

and changes the output to a vector of such random effects with one element for each subject within the population.

`Pumas.simobs`

— Function`simobs(fpm::FittedPumasModel, [population::Population,] vcov::AbstractMatrix, randeffs::Union{Nothing, AbstractVector{<:NamedTuple}} = nothing; samples::Int, rng = default_rng(), kwargs...)`

Simulates observations from the fitted model using a truncated multi-variate normal distribution for the parameter values. The optimal parameter values are used for the mean and the user supplied variance-covariance (`vcov`

) is used as the covariance matrix. Rejection sampling is used to avoid parameter values outside the parameter domains. Each sample uses a different parameter value. `samples`

is the number of samples to sample. `population`

is the population of subjects which defaults to the population associated the fitted model so it's optional to pass. `randeffs`

can be set to a vector of named tuples, one for each sample. If `randeffs`

is not specified (the default behaviour), it will be sampled from its distribution.

`Pumas.simobs`

— Function```
simobs(
model::AbstractPumasModel,
population::Union{Subject, Population}
param,
randeffs=sample_randeffs(model, param, population);
obstimes=nothing,
ensemblealg=EnsembleSerial(),
diffeq_options=NamedTuple(),
rng=Random.default_rng(),
)
```

Simulate random observations from `model`

for `population`

with parameters `param`

at `obstimes`

(by default, use the times of the existing observations for each subject). If no `randeffs`

is provided, then random ones are generated according to the distribution in the model.

**Arguments**

`model`

may either be a`PumasModel`

or a`PumasEMModel`

.`population`

may either be a`Population`

of`Subject`

s or a single`Subject`

.`param`

should be either a single parameter set, in the form of a`NamedTuple`

, or a vector of such parameter sets. If a vector then each of the parameter sets in that vector will be applied in turn. Example:`(; tvCL=1., tvKa=2., tvV=1.)`

`randeffs`

is an optional argument that, if used, should specify the random effects for each subject in`population`

. Such random effects are specified by`NamedTuple`

s for`PumasModels`

(e.g.`(; tvCL=1., tvKa=2.)`

) and by`Tuples`

for`PumasEMModel`

s (e.g.`(1., 2.)`

). If`population`

is a single`Subject`

(without being enclosed in a vector) then a single such random effect specifier should be passed. If, however,`population`

is a`Population`

of multiple`Subject`

s then`randeffs`

should be a vector containing one such specifier for each`Subject`

. The functions`init_randeffs`

,`zero_randeffs`

, and`sample_randeffs`

are sometimes convenient for generating`randeffs`

:

```
randeffs = zero_randeffs(model, param, population)
solve(model, population, param, randeffs)
```

If no `randeffs`

is provided, then random ones are generated according to the distribution in the model.

`obstimes`

is a keyword argument where you can pass a vector of times at which to simulate observations. The default,`nothing`

, ensures the use of the existing observation times for each`Subject`

.`ensemblealg`

is a keyword argument that allows you to choose between different modes of parallelization. Options include`EnsembleSerial()`

,`EnsembleThreads()`

and`EnsembleDistributed()`

.`diffeq_options`

is a keyword argument that takes a`NamedTuple`

of options to pass on to the differential equation solver.`rng`

is a keyword argument where you can specify which random number generator to use.

`Pumas.simobs`

— Function`simobs(pmi::FittedPumasModelInference, population::Population = pmi.fpm.data, randeffs::Union{Nothing, AbstractVector{<:NamedTuple}} = nothing; samples::Int, rng = default_rng(), kwargs...,)`

Simulates observations from the fitted model using a truncated multi-variate normal distribution for the parameter values. The optimal parameter values are used the mean and the variance-covariance estimate is used as the covariance matrix. Rejection sampling is used to avoid parameter values outside the parameter domains. Each sample uses a different parameter value. `samples`

is the number of samples to sample. `population`

is the population of subjects which defaults to the population associated the fitted model. `randeffs`

can be set to a vector of named tuples, one for each sample. If `randeffs`

is not specified (the default behaviour), it will be sampled from its distribution.

`Pumas.simobstte`

— Function```
simobstte(
model::PumasModel,
subject::Union{Subject,Population},
param::NamedTuple,
randeffs::Union{Vector{<:NamedTuple}, NamedTuple, Nothing}=nothing;
minT=0.0,
maxT=nothing,
nT=10,
repeated=false,
rng = default_rng())
```

Simulate observations from a time-to-event model, i.e. one with a `TimeToEvent`

dependent variable and return either a new `Subject`

or `Population`

with random event time stamps in the `time`

vector.

The function first computes `nT`

values of survival probability from `t=minT`

to `maxT`

and then interpolate with a cubic spline to get a smooth survival funtion. Given a survival funtion, it is possible to simulate from the distribution by using inverse cdf sampling. Instead of sampling a uniform variate to use with the survival probability, we sample an exponential and compare to the cumulative hazard which is equivalent. The Roots package is then used for computing the root. If `repeated=true`

then new event times are drawn until `maxT`

has been reached.

`Pumas.tad`

— Method`tad(t, events) -> time after most recent dose`

Converts absolute time `t`

(scalar or array) to relative time after the most recent dose. If `t`

is earlier than all dose times, then the (negative) difference between `t`

and the first dose time is returned instead. If no dose events exist, `t`

is returned unmodified.

`Pumas.vpc`

— Method```
vpc(fpm::AbstractFittedPumasModel;
samples::Integer = 499
qreg_method = IP(),
observations::Array{Symbol} = [keys(fpm.data[1].observations)[1]],
stratify_by::Array{Symbol} = Symbol[],
quantiles::NTuple{3,Float64}=(0.1, 0.5, 0.9),
level::Real=0.95,
ensemblealg=EnsembleSerial(),
bandwidth=2,
maxnumstrats=[6 for i in 1:length(stratify_by)],
covariates::Array{Symbol} = [:time],
smooth::Bool = true,
rng::AbstractRNG=default_rng(),
obstimes::AbstractVector = [])
```

Computes the quantiles for VPC for a `FittedPumasModel`

or `FittedPumasEMModel`

with simulated confidence intervals around the empirical quantiles based on `samples`

simulated populations.

The following keyword arguments are supported:

`samples`

: The number of simulated populations to generate, defaults to`499`

`quantiles::NTuple{3,Float64}`

: A three-tuple of the quantiles for which the quantiles will be computed. The default is`(0.1, 0.5, 0.9)`

which computes the 10th, 50th and 90th percentile.`level::Real`

: Probability level to use for the simulated confidence intervals. The default is`0.95`

.`observations::Array{Symbol}`

: The name of the dependent variable to use for the VPCs. The default is the first dependent variable in the`Population`

.`stratify_by`

: The covariates to be used for stratification. Takes an array of the`Symbol`

s of the stratification covariates.`ensemblealg`

: This is passed to the`simobs`

call for the`samples`

simulations. For more description check the docs for`simobs`

.`bandwidth`

: The kernel bandwidth in the quantile regression. If you are seeing`NaN`

s or an error, increasing the bandwidth should help in most cases. With higher values of the`bandwidth`

you will get more smoothened plots of the quantiles so it's a good idea to check with your data the right`bandwidth`

.`maxnumstrats`

: The maximum number of strata for each covariate. Takes an array with the number of strata for the corresponding covariate, passed in`stratify_by`

. It defaults to`6`

for each of the covariates.`covariates`

: The independent variable for VPC, defaults to`[:time]`

.`smooth`

: In case of discrete VPC used to determine whether to interpolate the dependent variable if independent variable is continuous, defaults to`true`

.`rng`

: A random number generator, uses the`default_rng`

from`Random`

as default.`obstimes`

: The times for simulation in case of continuous VPC, same as`obstimes`

in`simobs`

. Defaults to union of all subject's unique times in the data where observation is not missing.`qreg_method`

: Defaults to`IP()`

. For most users the method used in quantile regression is not going to be of concern, but if you see large run times switching`qreg_method`

to`IP(true)`

should help in improving the performance with a tradeoff in the accuracy of the fitting.

`Pumas.wresiduals`

— Function`wresiduals(fpm::AbstractFittedPumasModel, approx::LikelihoodApproximation; nsim=nothing)`

Calculate the individual and population weighted residual.

Takes a `fit`

result, an approximation method for the marginal likelihood calculation which defaults to the method used in the `fit`

and the number of simulations with the keyword argument `nsim`

. If `nsim`

is specified only the Expected Simulation based Individual Weighted Residuals (EIWRES) is included in the output as individual residual and population residual is not computed. Using the `FO`

approximation method corresponds to the WRES and while `FOCE(I)`

corresponds to CWRES. The output is a `SubjectResidual`

object that stores the population (`wres`

) and individual (`iwres`

) residuals along with the `subject`

and approximation method (`approx`

).

`Pumas.zero_randeffs`

— Function`zero_randeffs(model::AbstractPumasModel, param::NamedTuple [, pop::Population])`

Create an object to signify that the random effects should be zero.

The optional argument `pop`

takes a `Population`

and changes the output to a vector of such random effects with one element for each subject within the population.

`Pumas.ηshrinkage`

— Method`ηshrinkage(fpm::AbstractFittedPumasModel)`

Calculate the η-shrinkage.

Takes the result of a `fit`

as the only input argument. A named tuple of the random effects and corresponding η-shrinkage values is output.

`Pumas.ϵshrinkage`

— Method`ϵshrinkage(fpm::AbstractFittedPumasModel)`

Calculate the ϵ-shrinkage.

Takes the result of a `fit`

as the only input argument. A named tuple of derived variables and corresponding ϵ-shrinkage values is output.

`StatsBase.aic`

— Method`aic(fpm::AbstractFittedPumasModel)`

Calculate the Akaike information criterion (AIC) of the fitted Pumas model `fpm`

.

`StatsBase.bic`

— Method`bic(fpm::AbstractFittedPumasModel)`

Calculate the Bayesian information criterion (BIC) of the fitted Pumas model `fpm`

.

`StatsBase.coeftable`

— Method`coeftable(pmi::FittedPumasModelInference) -> DataFrame`

Construct a DataFrame of parameter names, estimates, standard error, and confidence interval from a `pmi`

.

`StatsBase.coeftable`

— Method`coeftable(fpm::FittedPumasModel) -> DataFrame`

Construct a DataFrame of parameter names and estimates from `fpm`

.

`StatsBase.coeftable`

— Method`coeftable(cfpm::Vector{<:FittedPumasModel}) -> DataFrame`

Construct a DataFrame of parameter names and estimates and their standard deviation from vector of fitted single-subject models `vfpm`

.

`StatsBase.fit`

— Method```
fit(
model::PumasEMModel,
population::Population,
param::NamedTuple,
approx::Union{SAEM,LaplaceI};
ensemblealg = EnsembleThreads(),
rng = default_rng()
)
```

Fit the `PumasEMModel`

to the dataset `population`

using the initial values specified in `param`

. The supported methods for the `approx`

argument are currently `SAEM`

and `LaplaceI`

. See the online documentation for more details about these two methods.

When fitting with `SAEM`

the variance terms of the random effects (`Ω`

) and the dispersion parameters for the error model (`σ`

) are initialized to the identity matrix or `1`

as appropriate. They may also be specified. With SAEM, it is reccomended to choose an init larger than the true values to facilitate exploration of the parameter space and avoid getting trapped in local optima early. Currently `LaplaceI`

fits with a `PumasEMModel`

require `Ω`

to be diagonal.

Options for `ensemblealg`

are `EnsembleSerial()`

and `EnsembleThreads()`

(the default). The fit will be parallel if `ensemblealg == EnsembleThreads()`

. SAEM imposes the additional requirement for threaded fits that either the `rng`

used supports `Future.randjump`

or that `rng`

be a vector of rngs, one per thread. The `default_rng()`

supports `randjump()`

.

`StatsBase.fit`

— Method```
fit(
model::PumasModel,
population::Population,
param::NamedTuple,
approx::Union{LikelihoodApproximation, MAP};
optimize_fn = DefaultOptimizeFN(),
constantcoef::NamedTuple = NamedTuple(),
omegas::Tuple = tuple(),
ensemblealg::DiffEqBase.EnsembleAlgorithm = EnsembleSerial(),
checkidentification=true,
diffeq_options))
```

Fit the Pumas model `model`

to the dataset `population`

with starting values `param`

using the estimation method `approx`

. Currently supported values for the `approx`

argument are `FO`

, `FOCE`

, `LaplaceI`

, `NaivePooled`

, and `BayesMCMC`

. See the online documentation for more details about the different methods.

The argument `optimize_fn`

is used for optimizing the objective function for all `approx`

methods except `BayesMCMC`

. The default optimization function uses the quasi-Newton routine `BFGS`

method from the `Optim`

package. Optimization specific arguments can be passed to `DefaultOptimizeFN`

, e.g. the optimization trace can be disabled and the algorithm can be changed to L-BFGS by passing `optimize_fn=DefaultOptimizeFN(Optim.LBFGS(); show_trace=false)`

to `fit`

. The positional argument is a zero or first or method from `Optim`

and the keywords are used to the available options in `Optim`

. See `Optim`

for more defails.

It is possible to fix one or more parameters of the fit by passing a `NamedTuple`

as the `constantcoef`

argument with keys and values corresponding to the names and values of the fixed parameters, e.g. `constantcoef=(σ=0.1,)`

.

When models include an `@random`

block and fitting with `NaivePooled`

is requested, it is required that the user supplies the names of the parameters of the random effects as the `omegas`

argument such that these can be ignored in the optimization, e.g. `omegas=(Ω,)`

.

Parallelization of the optimization is supported for most estimation methods via the ensemble interface of DifferentialEquations.jl. The default is `EnsembleSerial()`

. Currently, the only supported parallelization for model fitting is `EnsembleThreads()`

.

The `fit`

function will check if any gradients and throw an exception if any of the elements are exactly zero unless `checkidentification`

is set to `false`

.

Further keyword arguments can be passed via the `diffeq_options`

argument. This allows for passing arguments to the differential equations solver such as `alg`

, `abstol`

, and `reltol`

. The default values for these are `AutoVern7(Rodas5(autodiff=true))`

, `1e-12`

, and `1e-8`

respectively. See the DifferentialEquations.jl documentation for more details.

`StatsBase.loglikelihood`

— Method`loglikelihood(fpm::AbstractFittedPumasModel)`

Compute the loglikelihood of a fitted Pumas model.

`StatsBase.predict`

— Method```
predict(
fpm::AbstractFittedPumasModel,
[population::Union{Subject,Population};
[obstimes::AbstractVector]
)::Union{SubjectPrediction,Vector{SubjectPrediction}}
```

Compute population and individual predictions for the fitted model `fpm`

. By default, the predictions are computed for the estimation data but the predictions can also be computed for user supplied data by passing either a single subject or a vector of subjects (`Population`

) as the `population`

argument.

If the optional `obstimes`

argument is passed then the time points in `obstimes`

are used for the predictions. Otherwise, the time points of the observations for each subject in the `population`

are used for the predictions.

Any optional keyword arguments used when fitting `fpm`

are reused when computing the predictions.

`StatsBase.predict`

— Method```
predict(
model::AbstractPumasModel,
population::Union{Subject,Population},
param::NamedTuple;
[obstimes::AbstractVector,
diffeq_options::NamedTuple]
)::Union{SubjectPrediction,Vector{SubjectPrediction}}
```

Compute population and individual predictions for either the single subject or vector of subjects (`Population`

) `population`

based on `model`

and the population parameters `param`

.

If the optional `obstimes`

argument is passed then the time points in `obstimes`

are used for the predictions. Otherwise, the time points of the observations for each subject in the `population`

are used for the predictions.

The function allows for extra keyword arguments to be passed on to the differential equations solver through the `diffeq_options`

keyword. See the online documentation for more details.

`StatsBase.predict`

— Method```
predict(
model::AbstractPumasModel,
subject::Subject,
param::NamedTuple,
[randeffs,];
[obstimes::AbstractVector,
diffeq_options::NamedTuple]
)::Union{SubjectPrediction,Vector{SubjectPrediction}}
```

Compute population and individual predictions for the single `subject`

based on `model`

and the population parameters `param`

. A `NamedTuple`

of random effects, `randeffs`

, can be omitted or provided by the user. If they are omitted, they will be estimated from the data in the `subject`

.

If the optional `obstimes`

argument is passed then the time points in `obstimes`

are used for the predictions. Otherwise, the time points of the observations of the `subject`

are used for the predictions.

The function allows for extra keyword arguments to be passed on to the differential equations solver through the `diffeq_options`

keyword. See the online documentation for more details.

`StatsBase.stderror`

— Method`stderror(f::AbstractFittedPumasModel) -> NamedTuple`

Compute the standard errors of the population parameters and return the result as a `NamedTuple`

matching the `NamedTuple`

of population parameters.

`StatsBase.vcov`

— Method`vcov(f::AbstractFittedPumasModel) -> Matrix`

Compute the covariance matrix of the population parameters

`Pumas.@emmodel`

— Macro`@emmodel`

Define a `PumasEMModel`

. It may have the following blocks:

`@param`

and`@random`

: Defines fixed and random effects, e.g.

```
@random begin
CL ~ 1 + wt | LogNormal
θbioav ~ 1 | LogitNormal
end
```

Distributions specify the parameter's support. Only `Normal`

(-∞,∞) `LogNormal`

(0,∞), and `LogitNormal`

(0,1) are currently supported.

These define 1 unconstrained parameter per term in the formula, for example `CL = exp(μ + wt * β + η)`

where `μ, β ∈ (-∞,∞)`

and `wt`

is a covariate constant with respect to time. `η`

is a random effect. The `@param`

block is equivalent, with the exception that there is no random effect `η`

. These variables are accessible in `@pre`

, `@dosecontrol`

, `@dynamics`

, `@post`

, and `@error`

blocks.

`@covariates`

: Covariates available in the`@pre`

,`@dosecontrol`

,`@dynamics`

, and`@post`

blocks.`@pre`

: Block evaluated before the`@dynamics`

.`@dosecontrol`

: Block specifying dose control parameters. Function of`@param`

and`@random`

variables only.`@init`

: return initial conditions for dynamical variables.`@dynamics`

: Dynamics, equivalent to the functionality in the`@model`

macro.`@post`

: Block evalauted after the`@dynamics`

and before the`@error`

.`@error`

: Block describing the error model. Dispersion parameters are implicit.`Y ~ ProportionalNormal(μ)`

indicates that`Y`

has a`Normal`

distribution with mean`μ`

.`Y`

must be observed subject data, while`μ`

can can be defined in the`@param`

,`@random`

,`@pre`

,`@dynamics`

, or`@post`

blocks.

`Pumas.@model`

— Macro`@model`

Defines a Pumas model, with the following possible blocks:

`@param`

: defines the model's fixed effects and corresponding domains, e.g.`tvcl ∈ RealDomain(lower = 0)`

.`@random`

: defines the model's random effects and corresponding distribution, e.g.`η ~ MvNormal(Ω)`

.`@covariates`

: Names of covariates used in the model.`@pre`

: pre-processes variables for the dynamic system and statistical specification.`@dosecontrol`

: defines dose control parameters as a function of fixed and random effects.`@vars`

: define variables usable in other blocks. It is recomended to define them in`@pre`

instead if not a function of dynamic variables.`@init`

: defines initial conditions of the dynamic system.`@dynamics`

: defines the dynamic system.`@derived`

: defines the statistical model of the dependent variables.`@observed`

: lists model information to be stored in the solution.`@options`

specifies model options, including`checklinear`

,`inplace`

, and`subject_t0`

.

`Pumas.@nca`

— Macro` @nca`

Defines a macro that can be used in the `observed`

block to compute NCA metrics of the computed model solutions.

**Example**

```
...
@derived begin
cp := Central/Vc
DV ~ @. Normal(cp, σ*cp)
end
@observed begin
nca = @nca cp
auc = NCA.auc(nca, interval = (0,4))
cmax = NCA.cmax(nca)
end
...
```