Package 'mlr3cmprsk'

Description

Provides a unified interface for right-censored competing risks tasks in 'mlr3'.

Author(s)

Maintainer: John Zobolas [email protected] (ORCID)

Other contributors:

• Andrzej Galecki [email protected] (ORCID) [contributor]

Description

Convert object to a PredictionCompRisks.

Usage

as_prediction_cmprsk(x, ...)

## S3 method for class 'PredictionCompRisks'
as_prediction_cmprsk(x, ...)

## S3 method for class 'data.frame'
as_prediction_cmprsk(x, ...)

Arguments

Value

PredictionCompRisks.

Examples

library(mlr3)
task = tsk("pbc")
learner = lrn("cmprsk.aalen")
learner$train(task)
p = learner$predict(task)

# convert to a data.table
tab = as.data.table(p)

# convert back to a Prediction
as_prediction_cmprsk(tab)

Description

Convert object to a competing risks task (TaskCompRisks).

Usage

as_task_cmprsk(x, ...)

## S3 method for class 'TaskCompRisks'
as_task_cmprsk(x, clone = FALSE, ...)

## S3 method for class 'data.frame'
as_task_cmprsk(
  x,
  time = "time",
  event = "event",
  id = deparse(substitute(x)),
  ...
)

## S3 method for class 'DataBackend'
as_task_cmprsk(
  x,
  time = "time",
  event = "event",
  id = deparse(substitute(x)),
  ...
)

Arguments

Description

This Learner specializes Learner for competing risks problems:

• task_type is set to "cmprsk"

• Creates Predictions of class PredictionCompRisks.

• The only currently available option for predict_types is "cif", which represents the predicted cumulative incidence function for each observation in the test set.

Super class

mlr3::Learner -> LearnerCompRisks

Methods

Public methods

• LearnerCompRisks$new()

• LearnerCompRisks$clone()

Method new()

Creates a new instance of this R6 class.

Usage

LearnerCompRisks$new(
  id,
  param_set = ps(),
  predict_types = "cif",
  feature_types = character(),
  properties = character(),
  packages = character(),
  label = NA_character_,
  man = NA_character_
)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerCompRisks$clone(deep = FALSE)

Arguments

Examples

library(mlr3)
# get all survival learners from mlr_learners:
lrns = mlr_learners$mget(mlr_learners$keys("^cmprsk"))
names(lrns)

# get a specific learner from mlr_learners:
mlr_learners$get("cmprsk.aalen")
lrn("cmprsk.aalen")

Description

This measure specializes Measure for competing risk problems.

• task_type is set to "cmprsk".

• predict_type is set to "cif".

Predefined measures can be found in the dictionary mlr3::mlr_measures.

Super class

mlr3::Measure -> MeasureCompRisks

Methods

Public methods

• MeasureCompRisks$new()

• MeasureCompRisks$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCompRisks$new(
  id,
  param_set = ps(),
  range,
  minimize = NA,
  average = "macro",
  aggregator = NULL,
  properties = character(),
  predict_type = "cif",
  predict_sets = "test",
  task_properties = character(),
  packages = character(),
  label = NA_character_,
  man = NA_character_
)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCompRisks$clone(deep = FALSE)

Arguments

See Also

Default competing risks measure: cmprsk.auc

Description

This learner estimates the Cumulative Incidence Function (CIF) for competing risks using the empirical Aalen-Johansen (AJ) estimator.

Transition probabilities to each competing event are computed from the training data via the survival::survfit.formula() function. Predictions are made at all unique event times (across all causes) observed in the training set.

Dictionary

This Learner can be instantiated via the dictionary mlr_learners or with the associated sugar function lrn():

mlr_learners$get("cmprsk.aalen")
lrn("cmprsk.aalen")

Meta Information

• Task type: “cmprsk”

• Predict Types: “cif”

• Feature Types: “logical”, “integer”, “numeric”, “factor”

• Required Packages: mlr3, mlr3cmprsk, survival

Parameters

Empty ParamSet

Super classes

mlr3::Learner -> mlr3cmprsk::LearnerCompRisks -> LearnerCompRisksAalenJohansen

Active bindings

Methods

Public methods

• LearnerCompRisksAalenJohansen$new()

• LearnerCompRisksAalenJohansen$importance()

• LearnerCompRisksAalenJohansen$selected_features()

• LearnerCompRisksAalenJohansen$clone()

Method new()

Creates a new instance of this R6 class.

Usage

LearnerCompRisksAalenJohansen$new()

Method importance()

All features have a score of 0 for this learner. This method exists solely for compatibility with the mlr3 ecosystem, as this learner is used as a fallback for other survival learners that require an importance() method.

Usage

LearnerCompRisksAalenJohansen$importance()

Returns

Named numeric().

Method selected_features()

Selected features are always the empty set for this learner. This method is implemented only for compatibility with the mlr3 API, as this learner does not perform feature selection.

Usage

LearnerCompRisksAalenJohansen$selected_features()

Returns

character(0).

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerCompRisksAalenJohansen$clone(deep = FALSE)

Arguments

References

Aalen, O O, Johansen, Soren (1978). “An empirical transition matrix for non-homogeneous Markov chains based on censored observations.” Scandinavian journal of statistics, 141–150.

See Also

Other competing risk learners: mlr_learners_cmprsk.fg

Examples

# Define the Learner (Aalen-Johansen/AJ estimator)
learner = lrn("cmprsk.aalen")
learner

# Define a Task
task = tsk("pbc")

# Stratification based on event
task$set_col_roles(cols = "status", add_to = "stratum")

# Create train and test set
part = partition(task)

# Train the learner on the training set
learner$train(task, row_ids = part$train)
learner$native_model

# Make predictions for the test set
predictions = learner$predict(task, row_ids = part$test)
predictions

# Score the predictions
# AJ has random discriminative performance
predictions$score(msr("cmprsk.auc", time = 100))

# Prediction error (Brier score) at specific time point
# BS(t) => weighted mean score across causes (default)
predictions$score(msr("cmprsk.brier", time = 100))

Description

Fine-Gray subdistribution hazards model for competing risks using cmprsk::crr().

Details

The fitted model is an S3 object of class "fine_gray" that stores a cause-specific list of crr class models.

At prediction time, each cause-specific model is evaluated with cmprsk::predict.crr() and the resulting CIF matrices are aligned to a common time grid across causes using constant CIF interpolation. The time grid is the unique event times (across all causes) observed in the training set.

Time-interaction terms (via cov2) are not implemented.

Dictionary

This Learner can be instantiated via the dictionary mlr_learners or with the associated sugar function lrn():

mlr_learners$get("cmprsk.fg")
lrn("cmprsk.fg")

Meta Information

• Task type: “cmprsk”

• Predict Types: “cif”

• Feature Types: “logical”, “integer”, “numeric”

• Required Packages: mlr3, mlr3cmprsk, cmprsk

Parameters

Super classes

mlr3::Learner -> mlr3cmprsk::LearnerCompRisks -> LearnerCompRisksFineGray

Methods

Public methods

• LearnerCompRisksFineGray$new()

• LearnerCompRisksFineGray$clone()

Method new()

Creates a new instance of this R6 class.

Usage

LearnerCompRisksFineGray$new()

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerCompRisksFineGray$clone(deep = FALSE)

Arguments

References

Fine, P J, Gray, J R (1999). “A Proportional Hazards Model for the Subdistribution of a Competing Risk.” Journal of the American Statistical Association, 94(446), 496–509. doi:10.1080/01621459.1999.10474144.

See Also

Other competing risk learners: mlr_learners_cmprsk.aalen

Examples

# Define the Learner
learner = lrn("cmprsk.fg")
learner

# Define a Task
task = tsk("pbc")

# Subset task features as Fine-Gray model doesn't accept factors
# Encode factors with `mlr3pipelines::po("encode")` if needed
feats = c("age", "chol", "albumin", "ast", "bili", "protime")
task$select(feats)

# Stratification based on event
task$set_col_roles(cols = "status", add_to = "stratum")

# Create train and test set
part = partition(task)

# Train the learner on the training set
learner$train(task, row_ids = part$train)
learner$native_model

# Make predictions for the test set
predictions = learner$predict(task, row_ids = part$test)
predictions

# Score the predictions
# AUC(t = 100), weighted mean score across causes (default)
predictions$score(msr("cmprsk.auc", cause = "mean", time = 100))

# AUC(t = 100), with user-specified weights
predictions$score(msr("cmprsk.auc", cause = "mean", cause_weights = c(0.2, 0.8),
  time = 100))

# AUC(t = 100), 1st cause
predictions$score(msr("cmprsk.auc", cause = 1, time = 100))

# AUC(t = 100), 2nd cause
predictions$score(msr("cmprsk.auc", cause = 2, time = 100))

# Prediction error (Brier score) at specific time point
# BS(t = 100) => weighted mean score across causes (default)
predictions$score(msr("cmprsk.brier", time = 100))

# BS(t = 100), 1st cause
predictions$score(msr("cmprsk.brier", cause = 1, time = 100))

# BS(t = 100), 2nd cause
predictions$score(msr("cmprsk.brier", cause = 2, time = 100))

Description

Calculates the time-dependent ROC-AUC at a specific time point, as described in Blanche et al. (2013).

Details

By default, this measure returns a cause-independent AUC(t) score, calculated as a weighted average of the cause-specific AUCs. The weights correspond to the relative event frequencies of each cause, following Equation (7) in Heyard et al. (2020). User-supplied weights are also supported. Alternatively, users can obtain the cause-specific AUC(t) for any individual cause by specifying the cause parameter.

Calls riskRegression::Score() with:

• metric = "auc"

• cens.method = "ipcw"

• cens.model = "km"

Notes on the riskRegression implementation:

1. IPCW weights are estimated using the test data only, so smaller test sets may lead to less stable estimates.

2. No extrapolation is supported: if time exceeds the maximum observed time on the test data, an error is thrown.

3. The choice of time is critical: if, at that time, no events of a given cause have occurred and all predicted CIFs are zero, riskRegression will return NaN for that cause-specific AUC (and subsequently for the summary AUC).

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("cmprsk.auc")
msr("cmprsk.auc")

Meta Information

• Task type: “cmprsk”

• Range: $[0, 1]$

• Minimize: FALSE

• Average: macro

• Required Prediction: “cif”

• Required Packages: mlr3, mlr3cmprsk, riskRegression

Parameters

Parameter details

• cause (numeric(1)|"mean")
  Integer number indicating which cause to use. Default value is "mean" which returns an event-frequency weighted mean of the cause-specific AUCs.

• cause_weights (numeric() | NULL)
  Optional custom weights for cause = "mean". If NULL, observed cause frequencies in the test data are used. The weights must be non-negative, sum to 1 and match the number of causes 1-1, i.e. first weight for first cause, second weight for second cause, etc.

• time (numeric(1))
  Single time point at which to return the score. If NULL, the median observed time point from the test set is used.

Super classes

mlr3::Measure -> mlr3cmprsk::MeasureCompRisks -> MeasureCompRisksAUC

Methods

Public methods

• MeasureCompRisksAUC$new()

• MeasureCompRisksAUC$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCompRisksAUC$new()

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCompRisksAUC$clone(deep = FALSE)

Arguments

References

Blanche, Paul, Dartigues, Francois J, Jacqmin-Gadda, Helene (2013). “Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks.” Statistics in Medicine, 32(30), 5381–5397. ISSN 1097-0258, doi:10.1002/SIM.5958, https://onlinelibrary.wiley.com/doi/10.1002/sim.5958.

Spitoni, Claudia, Lammens, Valerie, Putter, Hein (2018). “Prediction errors for state occupation and transition probabilities in multi-state models.” Biometrical Journal, 60(1), 34–48. ISSN 0323-3847, doi:10.1002/BIMJ.201600191, https://doi.org/10.1002/BIMJ.201600191.

Heyard, Rachel, Timsit, Jean-Francois, Held, Leonhard (2020). “Validation of discrete time-to-event prediction models in the presence of competing risks.” Biometrical Journal, 62(3), 643–657. https://doi.org/10.1002/BIMJ.201800293.

Examples

# Define the Learner
learner = lrn("cmprsk.fg")
learner

# Define a Task
task = tsk("pbc")

# Subset task features as Fine-Gray model doesn't accept factors
# Encode factors with `mlr3pipelines::po("encode")` if needed
feats = c("age", "chol", "albumin", "ast", "bili", "protime")
task$select(feats)

# Stratification based on event
task$set_col_roles(cols = "status", add_to = "stratum")

# Create train and test set
part = partition(task)

# Train the learner on the training set
learner$train(task, row_ids = part$train)
learner$native_model

# Make predictions for the test set
predictions = learner$predict(task, row_ids = part$test)
predictions

# Score the predictions
# AUC(t = 100), weighted mean score across causes (default)
predictions$score(msr("cmprsk.auc", cause = "mean", time = 100))

# AUC(t = 100), with user-specified weights
predictions$score(msr("cmprsk.auc", cause = "mean", cause_weights = c(0.2, 0.8),
  time = 100))

# AUC(t = 100), 1st cause
predictions$score(msr("cmprsk.auc", cause = 1, time = 100))

# AUC(t = 100), 2nd cause
predictions$score(msr("cmprsk.auc", cause = 2, time = 100))

# Prediction error (Brier score) at specific time point
# BS(t = 100) => weighted mean score across causes (default)
predictions$score(msr("cmprsk.brier", time = 100))

# BS(t = 100), 1st cause
predictions$score(msr("cmprsk.brier", cause = 1, time = 100))

# BS(t = 100), 2nd cause
predictions$score(msr("cmprsk.brier", cause = 2, time = 100))

Description

Calculates the competing risks prediction error (Brier score, BS) at a specific time point, using IPCW as described in Schopp et al. (2011).

Details

By default, this measure returns a cause-independent BS(t) score, calculated as a weighted average of the cause-specific Brier scores. The weights correspond to the relative event frequencies of each cause, following Equation (8) in Spitoni et al. (2018). User-supplied weights are also supported. Alternatively, users can obtain the cause-specific Brier score for any individual cause by specifying the cause parameter.

Calls riskRegression::Score() with:

• metric = "brier"

• cens.method = "ipcw"

• cens.model = "km"

Notes on the riskRegression implementation:

1. IPCW weights are estimated using the test data only, so smaller test sets may lead to less stable estimates.

2. No extrapolation is supported: if time exceeds the maximum observed time on the test data, an error is thrown.

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("cmprsk.brier")
msr("cmprsk.brier")

Meta Information

• Task type: “cmprsk”

• Range: $[0, \infty)$

• Minimize: TRUE

• Average: macro

• Required Prediction: “cif”

• Required Packages: mlr3, mlr3cmprsk, riskRegression

Parameters

Parameter details

• cause (numeric(1)|"mean")
  Integer number indicating which cause to use. Default value is "mean" which returns an event-frequency weighted mean of the cause-specific Brier scores.

• cause_weights (numeric() | NULL)
  Optional custom weights for cause = "mean". If NULL, observed cause frequencies in the test data are used. The weights must be non-negative, sum to 1 and match the number of causes 1-1, i.e. first weight for first cause, second weight for second cause, etc. See Spitoni et al. (2018), Equation (8) for a similar weighting scheme.

• time (numeric(1))
  Single time point at which to return the score. If NULL, the median observed time point from the test set is used.

Super classes

mlr3::Measure -> mlr3cmprsk::MeasureCompRisks -> MeasureCompRisksBrierScore

Methods

Public methods

• MeasureCompRisksBrierScore$new()

• MeasureCompRisksBrierScore$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCompRisksBrierScore$new()

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCompRisksBrierScore$clone(deep = FALSE)

Arguments

References

Schoop, Roland, Beyersmann, Jan, Schumacher, Martin, Binder, Harald (2011). “Quantifying the predictive accuracy of time-to-event models in the presence of competing risks.” Biometrical Journal, 53(1), 88–112. https://doi.org/10.1002/BIMJ.201000073.

Spitoni, Claudia, Lammens, Valerie, Putter, Hein (2018). “Prediction errors for state occupation and transition probabilities in multi-state models.” Biometrical Journal, 60(1), 34–48. ISSN 0323-3847, doi:10.1002/BIMJ.201600191, https://doi.org/10.1002/BIMJ.201600191.

Examples

# Define the Learner
learner = lrn("cmprsk.fg")
learner

# Define a Task
task = tsk("pbc")

# Subset task features as Fine-Gray model doesn't accept factors
# Encode factors with `mlr3pipelines::po("encode")` if needed
feats = c("age", "chol", "albumin", "ast", "bili", "protime")
task$select(feats)

# Stratification based on event
task$set_col_roles(cols = "status", add_to = "stratum")

# Create train and test set
part = partition(task)

# Train the learner on the training set
learner$train(task, row_ids = part$train)
learner$native_model

# Make predictions for the test set
predictions = learner$predict(task, row_ids = part$test)
predictions

# Score the predictions
# AUC(t = 100), weighted mean score across causes (default)
predictions$score(msr("cmprsk.auc", cause = "mean", time = 100))

# AUC(t = 100), with user-specified weights
predictions$score(msr("cmprsk.auc", cause = "mean", cause_weights = c(0.2, 0.8),
  time = 100))

# AUC(t = 100), 1st cause
predictions$score(msr("cmprsk.auc", cause = 1, time = 100))

# AUC(t = 100), 2nd cause
predictions$score(msr("cmprsk.auc", cause = 2, time = 100))

# Prediction error (Brier score) at specific time point
# BS(t = 100) => weighted mean score across causes (default)
predictions$score(msr("cmprsk.brier", time = 100))

# BS(t = 100), 1st cause
predictions$score(msr("cmprsk.brier", cause = 1, time = 100))

# BS(t = 100), 2nd cause
predictions$score(msr("cmprsk.brier", cause = 2, time = 100))

Description

A competing risks task for the pbc data set.

Format

R6::R6Class inheriting from TaskCompRisks.

Dictionary

This Task can be instantiated via the dictionary mlr_tasks or with the associated sugar function tsk():

mlr_tasks$get("pbc")
tsk("pbc")

Meta Information

• Task type: “cmprsk”

• Dimensions: 276x19

• Properties: -

• Has Missings: FALSE

• Target: “time”, “status”

• Features: “age”, “albumin”, “alk.phos”, “ascites”, “ast”, “bili”, “chol”, “copper”, “edema”, “hepato”, “platelet”, “protime”, “sex”, “spiders”, “stage”, “trig”, “trt”

Pre-processing

• Removed column id.

• Kept only complete cases (no missing values).

• Column age has been converted to integer.

• Columns trt, stage, hepato, edema and ascites have been converted to factors.

• Column trt has levels Dpenicillmain and placebo instead of 1 and 2.

• Column status has 0 for censored, 1 for transplant and 2 for death.

• Column time as been converted from days to months.

See Also

• Chapter in the mlr3book: https://mlr3book.mlr-org.com/chapters/chapter2/data_and_basic_modeling.html

• Dictionary of Tasks: mlr3::mlr_tasks

• as.data.table(mlr_tasks) for a table of available Tasks in the running session

Other Task: TaskCompRisks

Description

This object stores the predictions returned by a learner of class LearnerCompRisks.

The task_type is set to "cmprsk".

For accessing survival and hazard functions, as well as other complex methods from a LearnerCompRisks object is not possible atm.

Super class

mlr3::Prediction -> PredictionCompRisks

Active bindings

Methods

Public methods

• PredictionCompRisks$new()

• PredictionCompRisks$clone()

Method new()

Creates a new instance of this R6 class.

Usage

PredictionCompRisks$new(
  task = NULL,
  row_ids = task$row_ids,
  truth = task$truth(),
  cif = NULL,
  check = TRUE
)

Arguments

Details

The cif input currently is a list of CIF matrices.

Method clone()

The objects of this class are cloneable with this method.

Usage

PredictionCompRisks$clone(deep = FALSE)

Arguments

Examples

library(mlr3)
task = tsk("pbc")
learner = lrn("cmprsk.aalen")
part = partition(task)
p = learner$train(task, part$train)$predict(task, part$test)
p

# CIF list: 1 matrix (obs x times) per competing event
names(p$cif) # competing events
# CIF matrix for competing event 1 (first 5 test observations and 20 time points)
p$cif[["1"]][1:5, 1:20]
# CIF matrix for competing event 2 (first 5 test observations and 20 time points)
p$cif[["2"]][1:5, 1:20]

# data.table conversion
tab = as.data.table(p)
tab$CIF[[1]] # for first test observation, list of CIF vectors

Description

This task extends mlr3::Task and mlr3::TaskSupervised to handle survival problems with competing risks. The target variable consists of survival times and an event indicator, which must be a non-negative integer in the set $(0,1,2,...,K)$. $0$ represents censored observations, while other integers correspond to distinct competing events. Every row corresponds to one subject/observation.

Predefined tasks are stored in mlr3::mlr_tasks.

The task_type is set to "cmprsk".

Note: Currently only right-censoring is supported.

Super classes

mlr3::Task -> mlr3::TaskSupervised -> TaskCompRisks

Active bindings

Methods

Public methods

• TaskCompRisks$new()

• TaskCompRisks$truth()

• TaskCompRisks$formula()

• TaskCompRisks$times()

• TaskCompRisks$event()

• TaskCompRisks$unique_events()

• TaskCompRisks$unique_times()

• TaskCompRisks$unique_event_times()

• TaskCompRisks$aalen_johansen()

• TaskCompRisks$cens_prop()

• TaskCompRisks$filter()

• TaskCompRisks$clone()

Method new()

Creates a new instance of this R6 class.

Usage

TaskCompRisks$new(
  id,
  backend,
  time = "time",
  event = "event",
  label = NA_character_
)

Arguments

Details

Only right-censoring competing risk tasks are currently supported.

Method truth()

True response for specified row_ids. This is the multi-state format using Surv with the event target column as a factor: Surv(time, as.factor(event))

Defaults to all rows with role "use".

Usage

TaskCompRisks$truth(rows = NULL)

Arguments

Returns

survival::Surv().

Method formula()

Creates a formula for competing risk models with survival::Surv() on the LHS (left hand side).

Usage

TaskCompRisks$formula(rhs = NULL)

Arguments

Returns

stats::formula().

Method times()

Returns the (unsorted) outcome times.

Usage

TaskCompRisks$times(rows = NULL)

Arguments

Returns

numeric()

Method event()

Returns the event indicator.

Usage

TaskCompRisks$event(rows = NULL)

Arguments

Returns

integer()

Method unique_events()

Returns the unique events (excluding censoring).

Usage

TaskCompRisks$unique_events(rows = NULL)

Arguments

Returns

integer()

Method unique_times()

Returns the sorted unique outcome times.

Usage

TaskCompRisks$unique_times(rows = NULL)

Arguments

Returns

numeric()

Method unique_event_times()

Returns the sorted unique event outcome times (by any cause).

Usage

TaskCompRisks$unique_event_times(rows = NULL)

Arguments

Returns

numeric()

Method aalen_johansen()

Calls survival::survfit() to calculate the Aalen–Johansen estimator.

Usage

TaskCompRisks$aalen_johansen(strata = NULL, rows = NULL, ...)

Arguments

Returns

survival::survfit.object.

Method cens_prop()

Returns the proportion of censoring for this competing risks task. By default, this is returned for all observations, otherwise only the specified ones (rows).

Usage

TaskCompRisks$cens_prop(rows = NULL)

Arguments

Returns

numeric()

Method filter()

Subsets the task, keeping only the rows specified via row ids rows. This operation mutates the task in-place.

Usage

TaskCompRisks$filter(rows = NULL)

Arguments

Returns

Returns the object itself, but modified by reference.

Method clone()

The objects of this class are cloneable with this method.

Usage

TaskCompRisks$clone(deep = FALSE)

Arguments

See Also

Other Task: mlr_tasks_pbc

Examples

library(mlr3)
task = tsk("pbc")

# meta data
task$target_names # target is always (time, status) for right-censoring tasks
task$feature_names
task$formula()

# survival data
task$truth() # survival::Surv() object
task$times() # (unsorted) times
task$event() # event indicators (0 = censored, >0 = different causes)
task$unique_times() # sorted unique times
task$unique_event_times() # sorted unique event times (from any cause)
task$aalen_johansen(strata = "sex") # Aalen-Johansen estimator

# proportion of censored observations across all dataset
task$cens_prop()