Survival Fully Parametric Learner

Parametric survival model. Calls parametric()] from 'survivalmodels'.

Details

This learner allows you to choose a distribution and a model form to compose a predicted survival probability distribution.

The predict method is implemented in survivalmodels::predict.parametric(). Our implementation is more efficient for composition to distributions than survival::predict.survreg().

Three types of prediction are returned for this learner:

1. lp: a vector of linear predictors (relative risk scores), one per test observation. lp is predicted using the formula \(lp = X\beta\) where \(X\) are the variables in the test data set and \(\beta\) are the fitted coefficients.

2. crank: same as lp.

3. distr: a survival matrix in two dimensions, where observations are represented in rows and time points in columns. The distribution distr is composed using the lp predictions and specifying a model form in the form hyper-parameter. These are as follows, with respective survival functions:

• Accelerated Failure Time (aft) $$S(t) = S_0(\frac{t}{exp(lp)})$$

• Proportional Hazards (ph) $$S(t) = S_0(t)^{exp(lp)}$$

• Proportional Odds (po) $$S(t) = \frac{S_0(t)}{exp(-lp) + (1-exp(-lp)) S_0(t)}$$

• Tobit (tobit) $$S(t) = 1 - \Phi((t - lp)/s)$$

where \(S_0\) is the estimated baseline survival distribution (in this case with a given parametric form), \(lp\) is the predicted linear predictor, \(\Phi\) is the cdf of a N(0, 1) distribution, and \(s\) is the fitted scale parameter.

Whilst any combination of distribution and model form is possible, this does not mean it will necessarily create a sensible or interpretable prediction. The following combinations are 'sensible' (we note that ones mostly used in the literature):

• dist = "gaussian"; form = "tobit";

• dist = "weibull"; form = "ph"; (fairly used)

• dist = "exponential"; form = "ph";

• dist = "weibull"; form = "aft"; (fairly used, default option)

• dist = "exponential"; form = "aft";

• dist = "loglogistic"; form = "aft"; (fairly used)

• dist = "lognormal"; form = "aft";

• dist = "loglogistic"; form = "po";

Custom mlr3 parameters

• discrete determines the class of the returned survival probability distribution. If FALSE (default) continuous probability distributions are returned using distr6::VectorDistribution, otherwise distr6::Matdist (faster to calculate survival measures that require a distr prediction type).

Dictionary

This Learner can be instantiated via lrn():

lrn("surv.parametric")

Meta Information

• Task type: “surv”

• Predict Types: “crank”, “distr”, “lp”

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

• Required Packages: mlr3, mlr3proba, mlr3extralearners, survival, pracma

Parameters

Id	Type	Default	Levels	Range
form	character	aft	aft, ph, po, tobit	-
na.action	untyped	-		-
dist	character	weibull	weibull, exponential, gaussian, lognormal, loglogistic	-
parms	untyped	-		-
init	untyped	-		-
scale	numeric	0		\([0, \infty)\)
maxiter	integer	30		\((-\infty, \infty)\)
rel.tolerance	numeric	1e-09		\((-\infty, \infty)\)
toler.chol	numeric	1e-10		\((-\infty, \infty)\)
debug	integer	0		\([0, 1]\)
outer.max	integer	10		\((-\infty, \infty)\)
robust	logical	FALSE	TRUE, FALSE	-
score	logical	FALSE	TRUE, FALSE	-
cluster	untyped	-		-
discrete	logical	-	TRUE, FALSE	-

Installation

Package 'survivalmodels' is not on CRAN and has to be install from GitHub via remotes::install_github("RaphaelS1/survivalmodels").

References

Kalbfleisch, D J, Prentice, L R (2011). The statistical analysis of failure time data. John Wiley & Sons.

See also

• Dictionary of Learners: mlr3::mlr_learners.

• as.data.table(mlr_learners) for a table of available Learners in the running session (depending on the loaded packages).

• Chapter in the mlr3book: https://mlr3book.mlr-org.com/basics.html#learners

• mlr3learners for a selection of recommended learners.

• mlr3cluster for unsupervised clustering learners.

• mlr3pipelines to combine learners with pre- and postprocessing steps.

• mlr3tuning for tuning of hyperparameters, mlr3tuningspaces for established default tuning spaces.

Author

bblodfon

Super classes

mlr3::Learner -> mlr3proba::LearnerSurv -> LearnerSurvParametric

Methods

Public methods

• LearnerSurvParametric$new()

• LearnerSurvParametric$clone()

Inherited methods

• mlr3::Learner$base_learner()
• mlr3::Learner$format()
• mlr3::Learner$help()
• mlr3::Learner$predict()
• mlr3::Learner$predict_newdata()
• mlr3::Learner$print()
• mlr3::Learner$reset()
• mlr3::Learner$train()

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Method new()

Creates a new instance of this R6 class. returned risk from survivalmodels is hp-style ie higher value => higher risk

Usage

LearnerSurvParametric$new()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerSurvParametric$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Define the Learner
learner = mlr3::lrn("surv.parametric")
print(learner)
#> <LearnerSurvParametric:surv.parametric>: Fully Parametric Learner
#> * Model: -
#> * Parameters: form=aft, dist=weibull, discrete=FALSE
#> * Packages: mlr3, mlr3proba, mlr3extralearners, survival, pracma
#> * Predict Types:  [crank], distr, lp
#> * Feature Types: logical, integer, numeric, factor
#> * Properties: weights

# Define a Task
task = mlr3::tsk("grace")

# Create train and test set
ids = mlr3::partition(task)

# Train the learner on the training ids
learner$train(task, row_ids = ids$train)

print(learner$model)
#> 
#>  Parametric survival model 
#> 
#> Call:
#>   survivalmodels::parametric(data = data.table::setDF(task$data()),      time_variable = task$target_names[1L], status_variable = task$target_names[2L],      dist = "weibull")
#> 
#> Response:
#>   Surv(time, status)
#> Features:
#>   {(Intercept), age, los, revasc, revascdays, stchange, sysbp} 


# Make predictions for the test rows
predictions = learner$predict(task, row_ids = ids$test)

# Score the predictions
predictions$score()
#> surv.cindex 
#>   0.8457149