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targeted: Targeted Inference

Description

Various methods for targeted and semiparametric inference including augmented inverse probability weighted (AIPW) estimators for missing data and causal inference (Bang and Robins (2005)doi:10.1111/j.1541-0420.2005.00377.x), variable importance and conditional average treatment effects (CATE) (van der Laan (2006)doi:10.2202/1557-4679.1008), estimators for risk differences and relative risks (Richardson et al. (2017)doi:10.1080/01621459.2016.1192546), assumption lean inference for generalized linear model parameters (Vansteelandt et al. (2022)doi:10.1111/rssb.12504).

Author(s)

Maintainer: Klaus K. Holstklaus@holst.it

Authors:

• Benedikt Sommerbenediktsommer92@gmail.com

• Andreas Nordlandandreasnordland@gmail.com

Other contributors:

• Christian B. Pippercbpipper@gmail.com [contributor]

Klaus K. Holst (Maintainer)klaus@holst.it

References

Bang & Robins (2005) Doubly Robust Estimation in Missing Data andCausal Inference Models, Biometrics.

Vansteelandt & Dukes (2022) Assumption-lean inference forgeneralised linear model parameters, Journal of the Royal StatisticalSociety: Series B (Statistical Methodology).

Thomas S. Richardson, James M. Robins & Linbo Wang (2017) On Modeling andEstimation for the Relative Risk and Risk Difference, Journal of the AmericanStatistical Association.

Mark J. van der Laan (2006) Statistical Inference for Variable Importance,The International Journal of Biostatistics.

See Also

Useful links:

• https://kkholst.github.io/targeted/

• Report bugs athttps://github.com/kkholst/targeted/issues

Examples

## Not run: example(riskreg)example(cate)example(ate)example(calibration)## End(Not run)

ML model

Description

Wrapper for ml_model

Usage

ML(formula, model = "glm", ...)

Arguments

Responder Average Treatment Effect

Description

Estimation of the Average Treatment Effect among Responders

Usage

RATE(  response,  post.treatment,  treatment,  data,  family = gaussian(),  M = 5,  pr.treatment,  treatment.level,  SL.args.response = list(family = gaussian(), SL.library = c("SL.mean", "SL.glm")),  SL.args.post.treatment = list(family = binomial(), SL.library = c("SL.mean", "SL.glm")),  preprocess = NULL,  efficient = TRUE,  ...)

Arguments

Value

estimate object

Author(s)

Andreas Nordland, Klaus K. Holst

Responder Average Treatment Effect

Description

Estimation of the Average Treatment Effect among Responders for SurvivalOutcomes

Usage

RATE.surv(  response,  post.treatment,  treatment,  censoring,  tau,  data,  M = 5,  pr.treatment,  call.response,  args.response = list(),  SL.args.post.treatment = list(family = binomial(), SL.library = c("SL.mean", "SL.glm")),  call.censoring,  args.censoring = list(),  preprocess = NULL,  ...)

Arguments

Details

Estimation of

\frac{P(T \leq \tau|A=1) - P(T \leq \tau|A=1)}{E[D|A=1]}

under right censoring based on plug-in estimates ofP(T \leq \tau|A=a)andE[D|A=1].

An efficient one-step estimator ofP(T \leq \tau|A=a) is constructedusing the efficient influence function

\frac{I\{A=a\}}{P(A = a)} \Big(\frac{\Delta}{S^c_{0}(\tilde T|X)}I\{\tilde T \leq \tau\} + \int_0^\tau\frac{S_0(u|X)-S_0(\tau|X)}{S_0(u|X)S^c_0(u|X)} d M^c_0(u|X)\Big)

+ \Big(1 - \frac{I\{A=a\}}{P(A = a)}\Big)F_0(\tau|A=a, W)- P(T \leq \tau|A=a).

An efficient one-step estimator ofE[D|A=1] is constructed using theefficient influence function

\frac{A}{P(A = 1)}\left(D-E[D|A=1, W]\right) + E[D|A=1, W] -E[D|A=1].

Value

estimate object

Author(s)

Andreas Nordland, Klaus K. Holst

SuperLearner wrapper for learner

Description

SuperLearner wrapper for learner

Usage

SL(  formula = ~.,  ...,  SL.library = c("SL.mean", "SL.glm"),  binomial = FALSE,  data = NULL,  info = "SuperLearner")

Arguments

Value

learner object

Author(s)

Klaus Kähler Holst

AIPW estimator

Description

AIPW for the mean (and linear projections of the EIF) with missingobservations

Usage

aipw(response_model, propensity_model, formula = ~1, data, ...)

Arguments

Examples

m <- lava::lvm(y ~ x+z, r ~ x) |>     lava::distribution(~ r, value = lava::binomial.lvm()) |>     transform(y0~r+y, value = \(x) { x[x[,1]==0,2] <- NA; x[,2] })d <- lava::sim(m,1e3,seed=1)aipw(y0 ~ x, data=d)

Assumption Lean inference for generalized linear model parameters

Description

Assumption lean inference via cross-fitting (Double ML). See<doi:10.1111/rssb.12504

Usage

alean(  response_model,  exposure_model,  data,  link = "identity",  g_model,  nfolds = 1,  silent = FALSE,  mc.cores,  ...)

Arguments

Details

LetY be the response variable,A the exposure andWcovariates. The target parameter is:

\Psi(P) = \frac{E(Cov[A,g\{E(Y|A,W)\}\mid W])} {E\{Var(A\mid W)\}}

Theresponse_model is the model forE(Y|A,W), andexposure_model is the model forE(A|W).link specifiesg.

Value

alean.targeted object

Author(s)

Klaus Kähler Holst

Examples

sim1 <- function(n, family=gaussian(), ...) {   m <- lava::lvm() |>     lava::distribution(~y, value=lava::binomial.lvm()) |>     lava::regression('a', value=function(l) l) |>     lava::regression('y', value=function(a,l) a + l)     if (family$family=="binomial")        lava::distribution(m, ~a) <- lava::binomial.lvm()   lava::sim(m, n)}library(splines)f <- binomial()d <- sim1(1e4, family=f)e <- alean( response_model=learner_glm(y ~ a + bs(l, df=3), family=binomial), exposure_model=learner_glm(a ~ bs(l, df=3), family=f), data=d, link = "logit", mc.cores=1, nfolds=1)ee <- alean(response_model=learner_glm(y ~ a + l, family=binomial),           exposure_model=learner_glm(a ~ l),           data=d,           link = "logit", mc.cores=1, nfolds=1)e

AIPW (doubly-robust) estimator for Average Treatment Effect

Description

Augmented Inverse Probability Weighting estimator for the Average (Causal)Treatment Effect. All nuisance models are here parametric (glm). For a moregeneral approach see thecate implementation. In this implementationthe standard errors are correct even when the nuisance models aremis-specified (the influence curve is calculated including the term comingfrom the parametric nuisance models). The estimate is consistent if eitherthe propensity model or the outcome model / Q-model is correctly specified.

Usage

ate(  formula,  data = parent.frame(),  weights,  offset,  family = stats::gaussian(identity),  nuisance = NULL,  propensity = nuisance,  all,  labels = NULL,  adjust.nuisance = TRUE,  adjust.propensity = TRUE,  ...)

Arguments

Details

The formula may either be specified as: response ~ treatment |nuisance-formula | propensity-formula

For example:ate(y~a | x+z+a | x*z, data=...)

Alternatively, as a list:ate(list(y~a, ~x+z, ~x*z), data=...)

Or using the nuisance (and propensity argument):ate(y~a, nuisance=~x+z, ...)

Value

An object of class 'ate.targeted' is returned. Seetargeted-class for more details about this class and itsgeneric functions.

Author(s)

Klaus K. Holst

See Also

cate

Examples

m <- lava::lvm(y ~ a+x, a~x) |>     lava::distribution(~y, value = lava::binomial.lvm()) |>     lava::ordinal(K=4, ~a) |>     transform(~a, value = factor)d <- lava::sim(m, 1e3, seed=1)# (a <- ate(y~a|a*x|x, data=d))(a <- ate(y~a, nuisance=~a*x, propensity=~x, data = d))# Comparison with randomized experimentm0 <- lava::cancel(m, a~x)lm(y~a-1, lava::sim(m0,2e4))# Choosing a different contrast for the association measuressummary(a, contrast=c(2,4))

Calibration (training)

Description

Calibration for multiclassication methods

Usage

calibration(  pr,  cl,  weights = NULL,  threshold = 10,  method = "bin",  breaks = nclass.Sturges,  df = 3,  ...)

Arguments

Details

...

Value

An object of class 'calibration' is returned.Seecalibration-classfor more details about this class and its generic functions.

Author(s)

Klaus K. Holst

Examples

sim1 <- function(n, beta=c(-3, rep(.5,10)), rho=.5) { p <- length(beta)-1 xx <- lava::rmvn0(n,sigma=diag(nrow=p)*(1-rho)+rho) y <- rbinom(n, 1, lava::expit(cbind(1,xx)%*%beta)) d <- data.frame(y=y, xx) names(d) <- c("y",paste0("x",1:p)) return(d)}set.seed(1)beta <- c(-2,rep(1,10))d <- sim1(1e4, beta=beta)a1 <- naivebayes(y ~ ., data=d)a2 <- glm(y ~ ., data=d, family=binomial)## a3 <- randomForest(factor(y) ~ ., data=d, family=binomial)d0 <- sim1(1e4, beta=beta)p1 <- predict(a1, newdata=d0)p2 <- predict(a2, newdata=d0, type="response")## p3 <- predict(a3, newdata=d0, type="prob")c2 <- calibration(p2, d0$y, method="isotonic")c1 <- calibration(p1, d0$y, breaks=100)if (interactive()) {  plot(c1)  plot(c2,col="red",add=TRUE)  abline(a=0,b=1)  with(c1$xy[[1]], points(pred,freq,type="b", col="red"))}set.seed(1)beta <- c(-2,rep(1,10))dd <- lava::csplit(sim1(1e4, beta=beta), k=3)mod <- naivebayes(y ~ ., data=dd[[1]])p1 <- predict(mod, newdata=dd[[2]])cal <- calibration(p1, dd[[2]]$y)p2 <- predict(mod, newdata=dd[[3]])pp <- predict(c1, p2)cc <- calibration(pp, dd[[3]]$y)if (interactive()) {#'  plot(cal)  plot(cc, add=TRUE, col="blue")}

calibration class object

Description

The functionscalibration returns an objectof the classcalibration.

An object of class 'calibration' is a list with at least thefollowing components:

stepfun

estimated step-functions(seestepfun) for each class

classes

the unique classes

model

model/method type (string)

xy

list of data.frame's with predictions (pr) and estimatedprobabilities of success (only for 'bin' method)

Value

objects of the S3 class 'calibration'

S3 generics

The following S3 generic functions are available for an objectof classtargeted:

predict

Apply calibration to new data.

plot

Plot the calibration curves (reliability plot).

print

Basic print method.

See Also

calibration,calibrate

Examples

## See example(calibration) for examples

Conditional Average Treatment Effect estimation

Description

Conditional Average Treatment Effect estimation with cross-fitting.

Usage

cate(  response.model,  propensity.model,  cate.model = ~1,  calibration.model = NULL,  data,  contrast,  nfolds = 1,  rep = 1,  silent = FALSE,  stratify = FALSE,  mc.cores = NULL,  rep.type = c("nuisance", "average"),  var.type = "IC",  second.order = TRUE,  response_model = deprecated,  cate_model = deprecated,  propensity_model = deprecated,  treatment = deprecated,  ...)

Arguments

Details

We have observed data(Y,A,W) whereY is the response variable,A the binary treatment, andW covariates. We further letVbe a subset of the covariates. Define the conditional potential mean outcome

\psi_{a}(P)(V) = E_{P}[E_{P}(Y\mid A=a, W)|V]

and letm(V;\beta) denote a parametric working model, then the target parameter is themean-squared error

\beta(P) = \operatorname{argmin}_{\beta}E_{P}[\{\Psi_{1}(P)(V)-\Psi_{0}(P)(V)\} - m(V; \beta)]^{2}

Value

cate.targeted object

Author(s)

Klaus Kähler Holst, Andreas Nordland

References

Mark J. van der Laan (2006) Statistical Inference for VariableImportance, The International Journal of Biostatistics.

Examples

sim1 <- function(n=1000, ...) {  w1 <- rnorm(n)  w2 <- rnorm(n)  a <- rbinom(n, 1, plogis(-1 + w1))  y <- cos(w1) + w2*a + 0.2*w2^2 + a + rnorm(n)  data.frame(y, a, w1, w2)}d <- sim1(5000)## ATEcate(cate.model=~1,     response.model=y~a*(w1+w2),     propensity.model=a~w1+w2,     data=d)## CATEcate(cate.model=~1+w2,     response.model=y~a*(w1+w2),     propensity.model=a~w1+w2,     data=d)## Not run:  ## superlearner examplemod1 <- list(   glm = learner_glm(y~w1+w2),   gam = learner_gam(y~s(w1) + s(w2)))s1 <- learner_sl(mod1, nfolds=5)cate(cate.model=~1,     response.model=s1,     propensity.model=learner_glm(a~w1+w2, family=binomial),     data=d,     stratify=TRUE)## End(Not run)

Conditional Relative Risk estimation

Description

Conditional average treatment effect estimation via Double Machine Learning

Usage

cate_link(  treatment,  link = "identity",  response_model,  propensity_model,  importance_model,  contrast = c(1, 0),  data,  nfolds = 5,  type = "dml1",  ...)

Arguments

Value

cate.targeted object

Author(s)

Klaus Kähler Holst & Andreas Nordland

Examples

# Example 1:sim1 <- function(n=1e4,                 seed=NULL,                 return_model=FALSE, ...){suppressPackageStartupMessages(require("lava"))if (!is.null(seed)) set.seed(seed)m <- lava::lvm()distribution(m, ~x) <- gaussian.lvm()distribution(m, ~v) <- gaussian.lvm(mean = 10)distribution(m, ~a) <- binomial.lvm("logit")regression(m, "a") <- function(v, x){.1*v + x}distribution(m, "y") <- gaussian.lvm()regression(m, "y") <- function(a, v, x){v+x+a*x+a*v*v}if (return_model) return(m)lava::sim(m, n = n)}if (require("SuperLearner",quietly=TRUE)) {  d <- sim1(n = 1e3, seed = 1)  e <- cate_link(data=d,           type = "dml2",           treatment = a ~ v,           response_model = y~ a*(x + v + I(v^2)),           importance_model = SL(D_ ~ v + I(v^2)),           nfolds = 10)  summary(e) # the true parameters are c(1,1)}

Construct a learner

Description

Construct a learner

Arguments

Value

learner object.

cross_validated class object

Description

The functionscv returns an object of the typecross_validated.

An object of class 'cross_validated' is a list with at least thefollowing components:

cv

An array with the model score(s) evaluated for each fold,repetition, and model estimates(seeestimate.default)

names

Names (character vector) of the models

rep

number of repetitions of the CV

folds

Number of folds of the CV

Value

objects of the S3 class 'cross_validated'

S3 generics

The following S3 generic functions are available for an object ofclasscross_validated:

coef

Extract average model scores from thecross-validation procedure.

print

Basic print method.

summary

Summary of the cross-validation procedure.

'

See Also

cv

Examples

# See example(cv) for examples

Conditional Relative Risk estimation

Description

Conditional Relative Risk estimation via Double Machine Learning

Usage

crr(  treatment,  response_model,  propensity_model,  importance_model,  contrast = c(1, 0),  data,  nfolds = 5,  type = "dml1",  ...)

Arguments

Value

cate.targeted object

Author(s)

Klaus Kähler Holst & Andreas Nordland

Examples

sim1 <- function(n=1e4,                 seed=NULL,                 return_model=FALSE, ...){suppressPackageStartupMessages(require("lava"))if (!is.null(seed)) set.seed(seed)m <- lava::lvm()distribution(m, ~x) <- gaussian.lvm()distribution(m, ~v) <- gaussian.lvm(mean = 10)distribution(m, ~a) <- binomial.lvm("logit")regression(m, "a") <- function(v, x){.1*v + x}distribution(m, "y") <- gaussian.lvm()regression(m, "y") <- function(a, v, x){v+x+a*x+a*v*v}if (return_model) return(m)lava::sim(m, n = n)}d <- sim1(n = 2e3, seed = 1)if (require("SuperLearner",quietly=TRUE)) {  e <- crr(data=d,   type = "dml2",   treatment = a ~ v,   response_model = learner_glm(y~ a*(x + v + I(v^2))),   importance_model = learner_glm(D_ ~ v + I(v^2)),   propensity_model = learner_glm(a ~ x + v + I(v^2), family=binomial),           nfolds = 2)  summary(e) # the true parameters are c(1,1)}

Predict the cumulative hazard/survival function for a survival model

Description

Predict the cumulative hazard/survival function for a survival model

Usage

cumhaz(  object,  newdata,  times = NULL,  individual.time = FALSE,  extend = FALSE,  ...)

Arguments

Value

List with elements:

• time: numeric vector

• chf:cumulative hazard function. If individual.time = FALSE, matrix withdimension (nrow(newdata), length(times)). If individual.time = TRUE, vectorof length length(times).

• surv: survival function, exp(-chf).

• dchf: t(diff(rbind(0, t(chf))))

Author(s)

Klaus K. Holst, Andreas Nordland

Cross-validation

Description

Generic cross-validation function

Usage

## Default S3 method:cv(  object,  data,  response = NULL,  nfolds = 5,  rep = 1,  weights = NULL,  model.score = scoring,  seed = NULL,  shared = NULL,  args.pred = NULL,  args.future = list(),  mc.cores,  silent = FALSE,  ...)

Arguments

Details

object should be list of objects of classlearner.Alternatively, each element of models should be a list with a fittingfunction and a prediction function.

Theresponse argument can optionally be a named list where the name isthen used as the name of the response argument in models. Similarly, if datais a named list with a single data.frame/matrix then this name will be usedas the name of the data/design matrix argument in models.

Value

An object of class 'cross_validated' is returned. Seecross_validated-class for more details about this class andits generic functions.

Author(s)

Klaus K. Holst

See Also

cv.learner_sl

Examples

m <- list(learner_glm(Sepal.Length~1),          learner_glm(Sepal.Length~Species),          learner_glm(Sepal.Length~Species + Petal.Length))x <- cv(m, rep=10, data=iris)x

Cross-validation forlearner_sl

Description

Cross-validation estimation of the generalization error of thesuper learner and each of the separate models in the ensemble. Both thechosen model scoring metrics as well as the model weights of the stackedensemble.

Usage

## S3 method for class 'learner_sl'cv(object, data, nfolds = 5, rep = 1, model.score = scoring, ...)

Arguments

Examples

sim1 <- function(n = 5e2) {   x1 <- rnorm(n, sd = 2)   x2 <- rnorm(n)   y <- x1 + cos(x1) + rnorm(n, sd = 0.5**.5)   data.frame(y, x1, x2)}sl <- learner_sl(list(                   "mean" = learner_glm(y ~ 1),                   "glm" = learner_glm(y ~ x1),                   "glm2" = learner_glm(y ~ x1 + x2)                  ))cv(sl, data = sim1(), rep = 2)

Cast warning for deprecated function argument names

Description

Cast warning for deprecated function argument names

Usage

deprecate_arg_warn(old, new, fun, vers)

Arguments

Deprecated argument names

Description

Deprecated argument names

Arguments

Extract design matrix

Description

Extract design matrix from data.frame and formula

Usage

design(  formula,  data,  ...,  intercept = FALSE,  response = TRUE,  rm_envir = FALSE,  specials = NULL,  specials.call = NULL,  levels = NULL,  design.matrix = TRUE)

Arguments

Value

An object of class 'design'

Author(s)

Klaus Kähler Holst

Estimation of mean clinical outcome truncated by event process

Description

LetY denote the clinical outcome,A the binary treatmentvariable,X baseline covariates,T the failure time,andepsilon=1,2 the cause of failure.The following are our two target parameters

E(Y|T>t, A=1)- E(Y|T>t, A=0)

P(T<t,\epsilon=1|A=1)- P(T<t,\epsilon=1|A=0)

Usage

estimate_truncatedscore(  data,  mod.y,  mod.r,  mod.a,  mod.event,  time,  cause = NULL,  cens.code = 0,  naive = FALSE,  control = list(),  ...)

Arguments

Value

lava::estimate.default object

Author(s)

Klaus Kähler Holst

Examples

data(truncatedscore)mod1 <- learner_glm(y ~ a * (x1 + x2))mod2 <- learner_glm(r ~ a * (x1 + x2), family = binomial)a <- estimate_truncatedscore(  data = truncatedscore,  mod.y = mod1,  mod.r = mod2,  mod.a = a ~ 1,  mod.event = mets::Event(time, status) ~ x1+x2,  time = 2)s <- summary(a, noninf.t = -0.1)print(s)parameter(s)# the above is equivalent to# a <- estimate_truncatedscore(#   data = truncatedscore,#   mod.y = y ~ a * (x1 + x2),#   mod.r = r ~ a * (x1 + x2),#   mod.a = a ~ 1,#   mod.event = mets::Event(time, status) ~ x1+x2,#   time = 2# )

Create a list from all combination of input variables

Description

Similar toexpand.grid function, this function creates all combinationsof the input arguments but returns the result as a list.

Usage

expand.list(..., INPUT = NULL, envir = NULL)

Arguments

Value

list

Author(s)

Klaus Kähler Holst

Examples

expand.list(x = 2:4, z = c("a", "b"))

Integral approximation of a time dependent function.Computes an approximation of\int_start^stop S(t) dt, whereS(t) is a survival function, for a selection of start and stop timepoints.

Description

Integral approximation of a time dependent function.Computes an approximation of\int_start^stop S(t) dt, whereS(t) is a survival function, for a selection of start and stop timepoints.

Usage

int_surv(times, surv, start = 0, stop = max(times), extend = FALSE)

Arguments

Value

Numeric vector, value of the integral.

Author(s)

Andreas Nordland

R6 class for prediction models

Description

Interface for statistical and machine learning models to be usedfor nuisance model estimation in targeted learning.

The following list provides an overview of constructors for many commonlyused models.

Regression and classification:learner_glm,learner_gam,learner_grf,learner_hal,learner_glmnet_cv,learner_svm,learner_xgboost,learner_mars
Regression:learner_isoreg
Classification:learner_naivebayes
Ensemble (super learner):learner_sl

Public fields

Active bindings

Methods

Public methods

• learner$new()

• learner$estimate()

• learner$predict()

• learner$update()

• learner$print()

• learner$summary()

• learner$response()

• learner$design()

• learner$opt()

• learner$clone()

Methodnew()

Create a new prediction model object

Usage

learner$new(  formula = NULL,  estimate,  predict = stats::predict,  predict.args = NULL,  estimate.args = NULL,  info = NULL,  specials = c(),  formula.keep.specials = FALSE,  intercept = FALSE)

Arguments

Methodestimate()

Estimation method

Usage

learner$estimate(data, ..., store = TRUE)

Arguments

Methodpredict()

Prediction method

Usage

learner$predict(newdata, ..., object = NULL)

Arguments

Methodupdate()

Update formula

Usage

learner$update(formula)

Arguments

Methodprint()

Print method

Usage

learner$print()

Methodsummary()

Summary method to provide more extensive information thanlearner$print().

Usage

learner$summary()

Returns

summarized_learner object, which is a list with the followingelements:

info

description of the learner

formula

formula specifying outcome and design matrix

estimate

function for fitting the model

estimate.args

arguments to estimate function

predict

function for making predictions from fitted model

predict.args

arguments to predict function

specials

provided special terms

intercept

include intercept in design matrix

Examples

lr <- learner_glm(y ~ x, family = "nb")lr$summary()lr_sum <- lr$summary() # store returned summary in new objectnames(lr_sum)print(lr_sum)

Methodresponse()

Extract response from data

Usage

learner$response(data, eval = TRUE, ...)

Arguments

Methoddesign()

Generatedesign object (design matrix and response) from data

Usage

learner$design(data, ...)

Arguments

Methodopt()

Get options

Usage

learner$opt(arg)

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

learner$clone(deep = FALSE)

Arguments

Author(s)

Klaus Kähler Holst, Benedikt Sommer

Examples

data(iris)rf <- function(formula, ...) {  learner$new(formula,    info = "grf::probability_forest",    estimate = function(x, y, ...) {      grf::probability_forest(X = x, Y = y, ...)    },    predict = function(object, newdata) {      predict(object, newdata)$predictions    },    estimate.args = list(...)  )}args <- expand.list(  num.trees = c(100, 200), mtry = 1:3,  formula = c(Species ~ ., Species ~ Sepal.Length + Sepal.Width))models <- lapply(args, function(par) do.call(rf, par))x <- models[[1]]$clone()x$estimate(iris)predict(x, newdata = head(iris))# Reduce Ex. timinga <- targeted::cv(models, data = iris)cbind(coef(a), attr(args, "table"))# defining learner via function with arguments y (response)# and x (design matrix)f1 <- learner$new(  estimate = function(y, x) lm.fit(x = x, y = y),  predict = function(object, newdata) newdata %*% object$coefficients)# defining the learner via arguments formula and dataf2 <- learner$new(  estimate = function(formula, data, ...) glm(formula, data, ...))# generic learner defined from function (predict method derived per default# from stats::predictf3 <- learner$new(  estimate = function(dt, ...) {    lm(y ~ x, data = dt)  })## ------------------------------------------------## Method `learner$summary`## ------------------------------------------------lr <- learner_glm(y ~ x, family = "nb")lr$summary()lr_sum <- lr$summary() # store returned summary in new objectnames(lr_sum)print(lr_sum)

Construct learners from a grid of parameters

Description

Construct learners from a grid of parameters

Usage

learner_expand_grid(fun, args, names = TRUE, params = FALSE)

Arguments

Value

list

Examples

lrs <- learner_expand_grid(  learner_xgboost,  list(formula = Sepal.Length ~ ., eta = c(0.2, 0.5, 0.3)))lrs # use info of constructed learner as nameslrs <- learner_expand_grid(  learner_xgboost,  list(formula = Sepal.Length ~ ., eta = c(0.2, 0.5, 0.3)),  names = "xgboost")names(lrs) # use xgboost instead of info field for nameslrs <- learner_expand_grid(  learner_xgboost,  list(formula = Sepal.Length ~ ., eta = c(0.2, 0.5, 0.3)),  names = "xgboost",  params = TRUE)names(lrs) # also add parameters to nameslrs <- learner_expand_grid(  learner_xgboost,  list(formula = Sepal.Length ~ ., eta = c(0.2, 0.5, 0.3)),  names = FALSE)names(lrs) # unnamed list since names = FALSE

Construct a learner

Description

Constructslearner class object for fitting generalizedadditive models withmgcv::gam.

Usage

learner_gam(  formula,  info = "mgcv::gam",  family = gaussian(),  select = FALSE,  gamma = 1,  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)y <- x1 + cos(x1) + rnorm(n, sd = 0.5**.5)d0 <- data.frame(y, x1, x2)lr <- learner_gam(y ~ s(x1) + x2)lr$estimate(d0)if (interactive()) {  plot(lr$fit)}

Construct a learner

Description

Constructs alearner class object for fitting generalizedlinear models withstats::glm andMASS::glm.nb. Negative binomialregression is supported withfamily = "nb" (or alternativelyfamily = "negbin").

Usage

learner_glm(  formula,  info = "glm",  family = gaussian(),  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n <- 5e2x <- rnorm(n)w <- 50 + rexp(n, rate = 1 / 5)y <- rpois(n, exp(2 + 0.5 * x + log(w)) * rgamma(n, 1 / 2, 1 / 2))d0 <- data.frame(y, x, w)lr <- learner_glm(y ~ x) # linear Gaussian modellr$estimate(d0)coef(lr$fit)# negative binomial regression model with offset (using MASS::glm.nb)lr <- learner_glm(y ~ x + offset(log(w)), family = "nb")lr$estimate(d0)coef(lr$fit)lr$predict(data.frame(x = 1, w = c(1, 5))) # response scalelr$predict(data.frame(x = 1, w = c(1, 5)), type = "link") # link scale

Construct a learner

Description

Constructs alearner class object for fitting entire lasso orelastic-net regularization paths for various linear and non-linear regressionmodels withglmnet::cv.glmnet. Predictions are returned for the value oflambda that gives minimumcvm. That is,glmnet::predict.cv.glmnet iscalled withs = "lambda.min".

Usage

learner_glmnet_cv(  formula,  info = "glmnet::cv.glmnet",  family = gaussian(),  lambda = NULL,  alpha = 1,  nfolds = 10,  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

# continuous outcomen <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)lp <- x1 + x2*x1 + cos(x1)y <- rnorm(n, lp, sd = 2)d0 <- data.frame(y, x1, x2)lr <- learner_glmnet_cv(y ~ x1 + x2)lr$estimate(d0, nfolds = 3)lr$predict(data.frame(x1 = c(0, 1), x2 = 1))# count outcome with different exposure timew <- 50 + rexp(n, rate = 1 / 5)y <- rpois(n, exp(0.5 * x1 - 1 * x2 + log(w)) * rgamma(n, 1 / 2, 1 / 2))d0 <- data.frame(y, x1, x2, w)lr <- learner_glmnet_cv(y ~ x1 + x2 + offset(log(w)), family = "poisson")lr$estimate(d0, nfolds = 3)lr$predict(data.frame(x1 = 1, x2 = 1, w = c(1, 5)))

Construct a learner

Description

Constructs alearner class object for fitting generalizedrandom forest models withgrf::regression_forest orgrf::probability_forest. As shown in the examples, the constructed learnerreturns predicted class probabilities of class 2 in case of binaryclassification. A⁠n times p⁠ matrix, withn being the number ofobservations andp the number of classes, is returned for multi-classclassification.

Usage

learner_grf(  formula,  num.trees = 2000,  min.node.size = 5,  alpha = 0.05,  sample.fraction = 0.5,  num.threads = 1,  model = "grf::regression_forest",  info = model,  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)lp <- x2*x1 + cos(x1)yb <- rbinom(n, 1, lava::expit(lp))y <-  lp + rnorm(n, sd = 0.5**.5)d <- data.frame(y, yb, x1, x2)# regressionlr <- learner_grf(y ~ x1 + x2)lr$estimate(d)lr$predict(head(d))# binary classificationlr <- learner_grf(as.factor(yb) ~ x1 + x2, model = "probability_forest")lr$estimate(d)lr$predict(head(d)) # predict class probabilities of class 2# multi-class classificationlr <- learner_grf(Species ~ ., model = "probability_forest")lr$estimate(iris)lr$predict(head(iris))

Construct a learner

Description

Constructs alearner class object for fitting a highlyadaptive lasso model withhal9001::fit_hal.

Usage

learner_hal(  formula,  info = "hal9001::fit_hal",  smoothness_orders = 0,  reduce_basis = NULL,  family = "gaussian",  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

## Not run: n <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)y <- x1 + cos(x1) + rnorm(n, sd = 0.5**.5)d <- data.frame(y, x1, x2)lr <- learner_hal(y ~ x1 + x2, smoothness_orders = 0.5, reduce_basis = 1)lr$estimate(d)lr$predict(data.frame(x1 = 0, x2 = c(-1, 1)))## End(Not run)

Construct a learner

Description

Constructs alearner class object for isotonic regression withisoregw.

Usage

learner_isoreg(formula, info = "targeted::isoregw", learner.args = NULL, ...)

Arguments

Value

learner object.

Examples

x <- runif(5e3, -5, 5)pr <- lava::expit(-1 + x)y <- rbinom(length(pr), 1, pr)d <- data.frame(y, x)lr <- learner_isoreg(y ~ x)lr$estimate(d)pr_iso <- lr$predict(d)if (interactive()) {  plot(pr ~ x, cex=0.3)  lines(sort(x), pr_iso[order(x)], col="red", type="s")}

Construct a learner

Description

Constructs alearner class object for fitting multivariateadaptive regression splines withearth::earth.

Usage

learner_mars(  formula,  info = "earth::earth",  degree = 1,  nprune = NULL,  glm = NULL,  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

# poisson regressionn <- 5e2x <- rnorm(n)w <- 50 + rexp(n, rate = 1 / 5)y <- rpois(n, exp(2 + 0.5 * x + log(w)) * rgamma(n, 1 / 2, 1 / 2))d0 <- data.frame(y, x, w)lr <- learner_mars(y ~ x + offset(log(w)), degree = 2,  glm = list(family = poisson()))lr$estimate(d0)lr$predict(data.frame(x = 0, w = c(1, 2)))

Construct a learner

Description

Constructs alearner class object for fitting a naive bayesclassifier withnaivebayes. As shown in the examples, the constructedlearner returns predicted class probabilities of class 2 in case of binaryclassification. A⁠n times p⁠ matrix, withn being the number ofobservations andp the number of classes, is returned for multi-classclassification.

Usage

learner_naivebayes(  formula,  info = "Naive Bayes",  laplace.smooth = 0,  kernel = FALSE,  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)y <- rbinom(n, 1, lava::expit(x2*x1 + cos(x1)))d <- data.frame(y, x1, x2)# binary classificationlr <- learner_naivebayes(y ~ x1 + x2)lr$estimate(d)lr$predict(head(d))# multi-class classificationlr <- learner_naivebayes(Species ~ .)lr$estimate(iris)lr$predict(head(iris))

Construct a learner

Description

Constructs alearner class object for fitting asuperlearner.

Usage

learner_sl(  learners,  info = NULL,  nfolds = 5L,  meta.learner = metalearner_nnls,  model.score = mse,  learner.args = NULL,  ...)

Arguments

Value

learner object.

See Also

cv.learner_sl

Examples

sim1 <- function(n = 5e2) {   x1 <- rnorm(n, sd = 2)   x2 <- rnorm(n)   y <- x1 + cos(x1) + rnorm(n, sd = 0.5**.5)   data.frame(y, x1, x2)}d <- sim1()m <- list(  "mean" = learner_glm(y ~ 1),  "glm" = learner_glm(y ~ x1 + x2),  "iso" = learner_isoreg(y ~ x1))s <- learner_sl(m, nfolds = 10)s$estimate(d)pr <- s$predict(d)if (interactive()) {    plot(y ~ x1, data = d)    points(d$x1, pr, col = 2, cex = 0.5)    lines(cos(x1) + x1 ~ x1, data = d[order(d$x1), ],          lwd = 4, col = lava::Col("darkblue", 0.3))}print(s)# weights(s$fit)# score(s$fit)cvres <- cv(s, data = d, nfolds = 3, rep = 2)cvres# coef(cvres)# score(cvres)

Construct stratified learner

Description

This function creates a stratified learner from an existinglearner wrapper function such aslearner_glm orlearner_xgboost. Thestratification variable can be specified either using thestratifyargument (which can be given as a string "a" or a formula , for example ~I(a==0)), or it can be defined as a special term directly in the formula, y~ ... + stratify(a). The formula will subsequently be passed to thelearner_ wrapper without the stratify special term.

Usage

learner_stratify(  formula,  learner,  stratify = NULL,  info = NULL,  learner.args = list(),  ...)

Arguments

Value

learner object

Examples

simdata <- function(n=1000) {  a <- rbinom(n, 1, 0.5)  x <- rnorm(n)  y <- rbinom(n, 1, plogis(-1 + a + a * x))  data.frame(y, a, x)}d <- simdata()lr <- learner_stratify(  y ~ x + stratify(a),  learner_glm,  family=binomial())lr$estimate(d)lr$predict(head(d))

Construct a learner

Description

Constructs alearner class object for fitting support vectormachines withe1071::svm. As shown in the examples, the constructed learnerreturns predicted class probabilities of class 2 in case of binaryclassification. A⁠n times p⁠ matrix, withn being the number ofobservations andp the number of classes, is returned for multi-classclassification.

Usage

learner_svm(  formula,  info = "e1071::svm",  cost = 1,  epsilon = 0.1,  kernel = "radial",  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n <- 5e2x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)lp <- x2*x1 + cos(x1)yb <- rbinom(n, 1, lava::expit(lp))y <-  lp + rnorm(n, sd = 0.5**.5)d <- data.frame(y, yb, x1, x2)# regressionlr <- learner_svm(y ~ x1 + x2)lr$estimate(d)lr$predict(head(d))# binary classificationlr <- learner_svm(as.factor(yb) ~ x1 + x2)# alternative to transforming response variable to factor# lr <- learner_svm(yb ~ x1 + x2, type = "C-classification")lr$estimate(d)lr$predict(head(d)) # predict class probabilities of class 2lr$predict(head(d), probability = FALSE) # predict labels# multi-class classificationlr <- learner_svm(Species ~ .)lr$estimate(iris)lr$predict(head(iris))

Construct a learner

Description

Constructs alearner class object forxgboost::xgboost.

Usage

learner_xgboost(  formula,  max_depth = 2L,  learning_rate = 1,  nrounds = 2L,  subsample = 1,  reg_lambda = 1,  objective = "reg:squarederror",  info = paste("xgboost", objective),  learner.args = NULL,  ...)

Arguments

Value

learner object.

Examples

n  <- 1e3x1 <- rnorm(n, sd = 2)x2 <- rnorm(n)lp <- x2*x1 + cos(x1)yb <- rbinom(n, 1, lava::expit(lp))y <-  lp + rnorm(n, sd = 0.5**.5)d0 <- data.frame(y, yb, x1, x2)# regressionlr <- learner_xgboost(y ~ x1 + x2, nrounds = 5)lr$estimate(d0)lr$predict(head(d0))# binary classificationlr <- learner_xgboost(yb ~ x1 + x2, nrounds = 5, objective = "binary:logistic")lr$estimate(d0)lr$predict(head(d0))# multi-class classificationd0 <- irisd0$y <- as.numeric(d0$Species)- 1lr <- learner_xgboost(y ~ ., objective = "multi:softprob", num_class = 3)lr$estimate(d0)lr$predict(head(d0))

R6 class for prediction models

Description

Replaced bylearner

Super class

targeted::learner ->ml_model

Methods

Public methods

• ml_model$new()

• ml_model$clone()

Methodnew()

Create a new prediction model object

Usage

ml_model$new(...)

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

ml_model$clone(deep = FALSE)

Arguments

Naive Bayes classifier

Description

Naive Bayes Classifier

Usage

naivebayes(  formula,  data,  weights = NULL,  kernel = FALSE,  laplace.smooth = 0,  prior = NULL,  ...)

Arguments

Value

An object of class 'naivebayes' is returned. Seenaivebayes-class for more details about this class andits generic functions.

Author(s)

Klaus K. Holst

Examples

library(data.table)data(iris)m <- naivebayes(Species ~ Sepal.Width + Petal.Length, data = iris)pr <- predict(m, newdata = iris)# using weights to reduce the size of the datasetn <- 5e2x <- rnorm(n, sd = 2) > 0y <- rbinom(n, 1, lava::expit(x))# full data setd1 <- data.frame(y, x = as.factor(x > 0))m1 <- naivebayes(y ~ x, data = d1)# reduced data setd2 <- data.table(d1)[, .(.N), by = .(y, x)]m2 <- naivebayes(y ~ x, data = d2, weights = d2$N)all(predict(m1, d1) == predict(m2, d1))

naivebayes class object

Description

The functionsnaivebayes returns an object of the typenaivebayes.

An object of class 'naivebayes' is a list with at leastthe following components:

prior

Matrix with prior probabilities,i.e. marginal class probabilities Pr(class)

pcond

list of matrices with conditional probabilitiesof the features given the classes (one list element per class), Pr(x|class)

classes

Names (character vector) of the classes

xvar

Names of predictors

xmodel

Conditional model for each predictor

design

Model design object

call

The function call which instantiated the object

Value

objects of the S3 class 'naivebayes'

S3 generics

The following S3 generic functions are available for an objectof classnaivebayes:

predict

Predict class probabilities for new features data.

print

Basic print method.

See Also

naivebayes()

Examples

## See example(naivebayes) for examples

Find non-dominated points of a set

Description

Find the non-dominated point of a set (minima of a point set).

Usage

nondom(x, ...)

Arguments

Details

A point x dominates y if it is never worse and at leastin one case strictly better.Formally, let f_i denote the ith coordinate of thecondition (objective) function,then for all i: f_i(x)<=f_i(y) and there exists j: f_j(x)<f_j(y).

Based on the algorithm of Kung et al. 1975.

Value

matrix

Author(s)

Klaus Kähler Holst

Examples

rbind(  c(1.0, 0.5),  c(0.0, 1.0),  c(1.0, 0.0),  c(0.5, 1.0),  c(1.0, 1.0),  c(0.8, 0.8)) |> nondom()

Pooled Adjacent Violators Algorithm

Description

Pooled Adjacent Violators Algorithm

Usage

pava(y, x = numeric(0), weights = numeric(0))

Arguments

Value

List with index (idx) of jump points and values (value)at each jump point.

Author(s)

Klaus K. Holst

Examples

x <- runif(5e3, -5, 5)pr <- lava::expit(-1 + x)y <- rbinom(length(pr), 1, pr)pv <- pava(y, x)plot(pr ~ x, cex=0.3)with(pv, lines(sort(x)[index], value, col="red", type="s"))

Prediction for kernel density estimates

Description

Kernel density estimator predictions

Usage

## S3 method for class 'density'predict(object, xnew, ...)

Arguments

Author(s)

Klaus K. Holst

Predictions for Naive Bayes Classifier

Description

Naive Bayes Classifier predictions

Usage

## S3 method for class 'naivebayes'predict(object, newdata, expectation = NULL, threshold = c(0.001, 0.001), ...)

Arguments

Author(s)

Klaus K. Holst

Predict Method for superlearner Fits

Description

Obtains predictions for ensemble model or individual learners.

Usage

## S3 method for class 'superlearner'predict(object, newdata, all.learners = FALSE, ...)

Arguments

Value

numeric (all.learners = FALSE) or matrix (all.learners = TRUE)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the linksbelow to see their documentation.

lava

estimate,IC,parameter,score,sim

survival

strata,Surv

Risk regression

Description

Risk regression with binary exposure and nuisance model for theodds-product.

LetA be the binary exposure,V the set of covariates, andY the binary response variable, and definep_a(v) = P(Y=1 \midA=a, V=v), a\in\{0,1\}.

Thetarget parameter is either therelative risk

\mathrm{RR}(v) = \frac{p_1(v)}{p_0(v)}

or therisk difference

\mathrm{RD}(v) = p_1(v)-p_0(v)

We assume a target parameter model given by either

\log\{RR(v)\} =\alpha^t v

or

\mathrm{arctanh}\{RD(v)\} = \alpha^tv

and similarly a working linearnuisancemodel for theodds-product

\phi(v) =\log\left(\frac{p_{0}(v)p_{1}(v)}{(1-p_{0}(v))(1-p_{1}(v))}\right) = \beta^tv

.

Apropensity model forE(A=1|V) is also fitted using a logisticregression working model

\mathrm{logit}\{E(A=1\mid V=v)\} = \gamma^tv.

If both the odds-product model and the propensity model are correct theestimator is efficient. Further, the estimator is consistent in the unionmodel, i.e., the estimator is double-robust in the sense that only one ofthe two models needs to be correctly specified to get a consistent estimate.

Usage

riskreg(  formula,  nuisance = ~1,  propensity = ~1,  target = ~1,  data,  weights,  type = "rr",  optimal = TRUE,  std.err = TRUE,  start = NULL,  mle = FALSE,  ...)

Arguments

Details

The 'formula' argument should be given asresponse ~ exposure | target-formula | nuisance-formula orresponse ~ exposure | target | nuisance | propensity

E.g.,riskreg(y ~ a | 1 | x+z | x+z, data=...)

Alternatively, the model can specifed using the target, nuisance andpropensity arguments:riskreg(y ~ a, target=~1, nuisance=~x+z, ...)

Theriskreg_fit function can be used with matrix inputs rather thanformulas.

Value

An object of class 'riskreg.targeted' is returned. Seetargeted-class for more details about this class and itsgeneric functions.

Author(s)

Klaus K. Holst

References

Richardson, T. S., Robins, J. M., & Wang, L. (2017). On modelingand estimation for the relative risk and risk difference. Journal of theAmerican Statistical Association, 112(519), 1121–1130.http://dx.doi.org/10.1080/01621459.2016.1192546

Examples

m <- lava::lvm(a[-2] ~ x,         z ~ 1,         lp.target[1] ~ 1,         lp.nuisance[-1] ~ 2*x) |>     lava::distribution(~a, value=lava::binomial.lvm("logit")) |>     lava::binomial.rr("y","a","lp.target","lp.nuisance")d <- sim(m,5e2,seed=1)I <- model.matrix(~1, d)X <- model.matrix(~1+x, d)with(d, riskreg_mle(y, a, I, X, type="rr"))with(d, riskreg_fit(y, a, nuisance=X, propensity=I, type="rr"))riskreg(y ~ a | 1, nuisance=~x ,  data=d, type="rr")## Model with same design matrix for nuisance and propensity model:with(d, riskreg_fit(y, a, nuisance=X, type="rr"))## a <- riskreg(y ~ a, target=~z, nuisance=~x,## propensity=~x, data=d, type="rr")a <- riskreg(y ~ a | z, nuisance=~x,  propensity=~x, data=d, type="rr")apredict(a, d[1:5,])riskreg(y ~ a, nuisance=~x,  data=d, type="rr", mle=TRUE)

Binary regression models with right censored outcomes

Description

Binary regression models with right censored outcomes

Usage

riskreg_cens(  response,  censoring,  treatment = NULL,  prediction = NULL,  data,  newdata,  tau,  type = "risk",  M = 1,  call.response = "phreg",  args.response = list(),  call.censoring = "phreg",  args.censoring = list(),  preprocess = NULL,  efficient = TRUE,  control = list(),  ...)

Arguments

Details

The one-step estimator depends on the calculation of an integralwrt. the martingale process corresponding to the counting process N(t) =I(C>min(T,tau)). This can be decomposed into an integral wrt the countingprocess,dN_c(t) and the compensatord\Lambda_c(t) where thelatter term can be computational intensive to calculate. Rather thancalculating this integral in all observed time points, we can make acoarser evaluation which can be controlled by settingcontrol=(sample=N). WithN=0 the (computational intensive)standard evaluation is used.

Value

estimate object

Author(s)

Klaus K. Holst, Andreas Nordland

Extract average cross-validated score of individual learners

Description

Extract average cross-validated score of individual learners

Usage

## S3 method for class 'superlearner'score(x, ...)

Arguments

Predictive model scoring

Description

Predictive model scoring

Usage

scoring(  response,  ...,  type = "quantitative",  levels = NULL,  metrics = NULL,  weights = NULL,  names = NULL,  object = NULL,  newdata = NULL,  messages = 1)

Arguments

Value

Numeric matrix of dimension m x p, where m is the number ofdifferent models and p is the number of model metrics

Examples

data(iris)set.seed(1)dat <- lava::csplit(iris,2)g1 <- naivebayes(Species ~ Sepal.Width + Petal.Length, data=dat[[1]])g2 <- naivebayes(Species ~ Sepal.Width, data=dat[[1]])pr1 <- predict(g1, newdata=dat[[2]], wide=TRUE)pr2 <- predict(g2, newdata=dat[[2]], wide=TRUE)table(colnames(pr1)[apply(pr1,1,which.max)], dat[[2]]$Species)table(colnames(pr2)[apply(pr2,1,which.max)], dat[[2]]$Species)scoring(dat[[2]]$Species, pr1=pr1, pr2=pr2)## quantitative response:scoring(response=1:10, prediction=rnorm(1:10))

Softmax transformation

Description

Softmax transformation

Usage

softmax(x, log = FALSE, ref = TRUE, ...)

Arguments

Value

Numeric matrix of dimension n x p, wheren= nrow(x) andp = ncol(x) + (ref==TRUE)

Solve ODE

Description

Solve ODE with Runge-Kutta method (RK4)

Usage

solve_ode(ode_ptr, input, init, par = 0)

Arguments

Details

The external point should be created with the functiontargeted::specify_ode.

Value

Matrix with solution

Author(s)

Klaus Kähler Holst

See Also

specify_ode

Examples

example(specify_ode)

Specify Ordinary Differential Equation (ODE)

Description

Define compiled code for ordinary differential equation.

Usage

specify_ode(code, fname = NULL, pname = c("dy", "x", "y", "p"))

Arguments

Details

The model (code) should be specified as the body of of C++ function.The following variables are defined bye default(see the argumentpname)

dy

Vector with derivatives, i.e. the rhs of the ODE (the result).

x

Vector with the first element being the time, and the followingelements additional exogenous input variables,

y

Vector with the dependent variable

p

Parameter vector

y'(t) = f_{p}(x(t), y(t))All variables are treated as Armadillo (http://arma.sourceforge.net/)vectors/matrices.

As an example consider theLorenz Equations\frac{dx_{t}}{dt} = \sigma(y_{t}-x_{t})\frac{dy_{t}}{dt} = x_{t}(\rho-z_{t})-y_{t}\frac{dz_{t}}{dt} = x_{t}y_{t}-\beta z_{t}

We can specify this model asode <- 'dy(0) = p(0)*(y(1)-y(0)); dy(1) = y(0)*(p(1)-y(2)); dy(2) = y(0)*y(1)-p(2)*y(2);'dy <- specify_ode(ode)

As an example of model with exogenous inputs consider the following ODE:y'(t) = \beta_{0} + \beta_{1}y(t) +\beta_{2}y(t)x(t) + \beta_{3}x(t)\cdot tThis could be specified asmod <- 'double t = x(0); dy = p(0) + p(1)*y + p(2)*x(1)*y + p(3)*x(1)*t;'dy <- specify_ode(mod)

Value

pointer (externalptr) to C++ function

Author(s)

Klaus Kähler Holst

See Also

solve_ode

Examples

ode <- paste0(  "dy(0) = p(0)*(y(1)-y(0));",  "dy(1) = y(0)*(p(1)-y(2));",  "dy(2) = y(0)*y(1)-p(2)*y(2);", collapse="\n") # Reduce test timedy <- specify_ode(ode)tt <- seq(0, 100, length.out=2e4)yy <- solve_ode(dy, input=tt, init=c(1, 1, 1), par=c(10, 28, 8/3))

Identify Stratification Variables

Description

This is a special function that identifies stratificationvariables when they appear on the right hand side of a formula.

Usage

stratify(..., na.group = FALSE, shortlabel, sep = ", ")

Arguments

Details

When used outside of acoxph formula the result of the functionis essentially identical to theinteraction function, though the labels fromstrata are often more verbose.

Value

a new factor, whose levels are all possible combinations of the factors supplied as arguments.

See Also

survival::strata,learner_stratify,interaction

Examples

a <- factor(rep(1:3, 4), labels=c("low", "medium", "high"))b <- factor(rep(1:4, 3))levels(stratify(b))levels(stratify(a, b, shortlabel=TRUE))

Superlearner (stacked/ensemble learner)

Description

This function creates a predictor object (classlearner) froma list of existinglearner objects. When estimating this model a stackedprediction will be created by weighting together the predictions of each ofthe initial learners The weights are learned using cross-validation.

Usage

superlearner(  learners,  data,  nfolds = 10,  meta.learner = metalearner_nnls,  model.score = mse,  mc.cores = NULL,  future.seed = TRUE,  silent = TRUE,  name.prefix = NULL,  ...)

Arguments

References

Luedtke & van der Laan (2016) Super-Learning of an OptimalDynamic Treatment Rule, The International Journal of Biostatistics.

See Also

predict.superlearnerweights.superlearnerscore.superlearner

Examples

sim1 <- function(n = 5e2) {   x1 <- rnorm(n, sd = 2)   x2 <- rnorm(n)   y <- x1 + cos(x1) + rnorm(n, sd = 0.5**.5)   data.frame(y, x1, x2)}m <- list(  "mean" = learner_glm(y ~ 1),  "glm" = learner_glm(y ~ x1 + x2))sl <- superlearner(m, data = sim1(), nfolds = 2)predict(sl, newdata = sim1(n = 5))predict(sl, newdata = sim1(n = 5), all.learners = TRUE)

targeted class object

Description

The functionsriskreg andatereturns an object of the typetargeted.

An object of class 'targeted' is a list with at least thefollowing components:

estimate

Anestimate object with the target parameterestimates (seeestimate.default)

opt

Object returned from the applied optimization routine

npar

number of parameters of the model (target and nuisance)

type

String describing the model

Value

objects of the S3 class 'targeted'

S3 generics

The following S3 generic functions are available for an object ofclasstargeted:

coef

Extract target coefficients of the estimated model.

vcov

Extract the variance-covariance matrix ofthe target parameters.

IC

Extract the estimated influence function.

print

Print estimates of the target parameters.

summary

Extract information on both target parameeters andestimated nuisance model.

'

See Also

riskreg,ate

Examples

## See example(riskreg) for examples

Extract model component fromdesign object

Description

Extract model component fromdesign object

Usage

## S3 method for class 'design'terms(x, specials, ...)

Arguments

Signed Wald intersection test

Description

Calculating test statistics and p-values for the signed Waldintersection test given by

SW = \inf_{\theta \in \cap_{i=1}^n H_i} \{(\widehat{\theta}-\theta)^\top W\widehat{\Sigma}W (\widehat{\theta}-\theta)\}

with individual hypotheses for eachcoordinate of\theta given byH_i: \theta_j < \delta_j for somenon-inferiority margin\delta_j,j=1,\ldots,n. #

Usage

test_intersection_sw(  par,  vcov,  noninf = 0,  weights = 1,  nsim.null = 10000,  index = NULL,  control = list(),  par.name = "theta")

Arguments

Details

The constrained least squares problem is solved using Dykstra'salgorithm. The following parameters for the optimization can be controlledvia thecontrol list argument:dykstra_niter sets the maximum number ofiterations (default 500),dykstra_tol convergence tolerance of thealternating projection algorithm (default 1e-7),pinv_tol tolerance forcalculating the pseudo-inverse matrix (defaultlength(par).Machine$double.epsmax(eigenvalue)).

Value

htest object

Author(s)

Klaus Kähler Holst, Christian Bressen Pipper

References

Christian Bressen Pipper, Andreas Nordland & Klaus Kähler Holst(2025) A general approach to construct powerful tests for intersections ofone-sided null-hypotheses based on influence functions. arXiv:https://arxiv.org/abs/2511.07096.

See Also

test_zmax_onesidedlava::test_waldlava::closed_testing

Examples

S <- matrix(c(1, 0.5, 0.5, 2), 2, 2)thetahat <- c(0.5, -0.2)test_intersection_sw(thetahat, S, nsim.null = 1e5)test_intersection_sw(thetahat, S, weights = NULL)## Not run: # only on 'lava' >= 1.8.2e <- estimate(coef = thetahat, vcov = S, labels = c("p1", "p2"))lava::closed_testing(e, test_intersection_sw, noninf = c(-0.1, -0.1)) |>  summary()## End(Not run)

One-sided Zmax test

Description

Calculating test statistics and p-values for theonesided Zmax / minP test.z

Given parameter estimates(\widehat{\theta}_1, \ldots, \widehat{\theta}_p)^\top with approximate assymptotic covariance matrix\widehat{S}, let Z_i = \frac{\widehat{\theta}_i - \delta_i}{\operatorname{SE}(\widehat{\theta}_i)} , where\operatorname{SE}(\widehat{\theta}_i) = \widehat{S}_{ii}. The Zmaxtest statistic is thenZ_{max} = \max \{Z_1,\ldots,Z_p\}, and thenull-hypothesis isH_0: \theta_i \leq \delta_i, i=1,\ldots,p withnon-inferiority margin\delta_i, i=1,\ldots,p, for which the p-valueis calculated as 1 - \Phi_R(Z_{max}) where\phi_R is the CDFof the multivariate normal distribution with mean zero and correlationmatrixR = \operatorname{diag}(S_{11}^{-0.5}, \ldots, S_{pp}^{-0.5})S\operatorname{diag}(S_{11}^{-0.5}, \ldots, S_{pp}^{-0.5}).

Usage

test_zmax_onesided(par, vcov, noninf = 0, index = NULL, par.name = "theta")

Arguments

Value

htest object

Author(s)

Christian Bressen Pipper, Klaus Kähler Holst

See Also

test_intersection_sw()lava::test_wald()lava::closed_testing()

Scores truncated by death

Description

Simulated data inspired by the FLOW study (Perkovic 2024)...elt()The following variables are considered in this simulated dataset

• time: time of first event in years (first major irreversible kidneyevent or non-related death)

• status: event type at first major irreversible kidney event (=1),non-related death (=2), or right censoring (=0)

• y: clinical outcome measurement (eGFR) at landmark time (:=2)

• r: missing indicator fory (1 if observed, 0 if either t<2 or if theoutcome was not measured for other reasons)

• a: binary treatment (1 := active, 0 := placebo)

• x1: covariate, clinical outcome at baseline (eGFR)

• x2: covariate, binary treatment usage indicator (1: SGLT2 treatment,0: none).

The actual failure times and censoring times are also included(failure.time,cens.time), and the full-data outcome (y0) given t>2.

Source

Simulated data

References

Perkovic, V., Tuttle, K. R., Rossing, P.,Mahaffey, K. W., Mann, J. F., Bakris, G., Baeres, F. M., Idorn, T.,Bosch-Traberg, H., Lausvig, N. L., and Pratley, R. (2024). Effects ofsemaglutide on chronic kidney disease in patients with type 2 diabetes. NewEngland Journal of Medicine, 391(2):109–121.

Examples

data(truncatedscore)

Extract ensemble weights

Description

Extract ensemble weights

Usage

## S3 method for class 'superlearner'weights(object, ...)

Arguments