Parametric survival model. Calls survival::survreg() from survival.

## Details

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

The internal predict method is implemented in this package as our implementation is more efficient for composition to distributions than survival::predict.survreg().

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.

The distribution distr is composed using the lp and specifying a model form in the type 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) $$S(t) = 1 - F((t - lp)/s)$$

where $$S_0$$ is the estimated baseline survival distribution (in this case with a given parametric form), $$lp$$ is the predicted linear predictor, $$F$$ 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':

• dist = "gaussian"; type = "tobit";

• dist = "weibull"; type = "ph";

• dist = "exponential"; type = "ph";

• dist = "weibull"; type = "aft";

• dist = "exponential"; type = "aft";

• dist = "loglogistic"; type = "aft";

• dist = "lognormal"; type = "aft";

• dist = "loglogistic"; type = "po";

## Dictionary

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

mlr_learners\$get("surv.parametric")
lrn("surv.parametric")

## Parameters

 Id Type Default Levels Range type 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 - -

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