trafotree {trtf}

Transformation Trees

Description

Partitioned transformation models

Usage

trafotree(object, parm = 1:length(coef(object)), reparm = NULL,
          intercept = c("none", "shift", "scale", "shift-scale"),
          min_update = length(coef(object)) * 2,
          mltargs = list(), ...)
## S3 method for class 'trafotree'
predict(object, newdata, K = 20, q = NULL,
    type = c("node", "coef", "trafo", "distribution", "survivor", "density",
             "logdensity", "hazard", "loghazard", "cumhazard", "quantile"),
    perm = NULL, ...)
## S3 method for class 'trafotree'
logLik(object, newdata, weights = NULL, perm = NULL, ...)

Arguments

object

an object of class ctm or mlt specifying the abstract model to be partitioned. For predict and logLik, object is an object of class trafotree.

parm

parameters of object those corresponding score is used for finding partitions.

reparm

optional matrix of contrasts for reparameterisation of the scores. teststat = "quadratic" is invariant to this operation but teststat = "max" might be more powerful for example when formulating an implicit into an explicit intercept term.

intercept

add optional intercept parameters (constraint to zero) to the model. It may make sense to restrict attention to scores corresponding to those intercept parameters, the additional argument parm = NULL is needed in this case.

min_update

number of observations necessary to refit the model in a node. If less observations are available, the parameters from the parent node will be reused.

mltargs

arguments to mlt for fitting the transformation models.

newdata

an optional data frame of observations.

K

number of grid points to generate (in the absence of q).

q

quantiles at which to evaluate the model.

type

type of prediction or plot to generate.

weights

an optional vector of weights.

perm

a vector of integers specifying the variables to be permuted prior before splitting (i.e., for computing permutation variable importances). The default NULL doesn't alter the data, see fitted_node.

...

arguments to ctree, at least formula and data.

Details

Conditional inference trees are used for partitioning likelihood-based transformation models as described in Hothorn and Zeileis (2017). The method can be seen in action in Hothorn (2018) and the corresponding code is available as demo("BMI"). demo("applications") performs transformation tree analyses for some standard benchmarking problems.

Value

An object of class trafotree with corresponding plot, logLik and predict methods.

References

Torsten Hothorn and Achim Zeileis (2021). Predictive Distribution Modelling Using Transformation Forests. Journal of Computational and Graphical Statistics, doi:10.1080/10618600.2021.1872581.

Torsten Hothorn (2018). Top-Down Transformation Choice. Statistical Modelling, 3-4, 274-298. doi:10.1177/1471082X17748081

Natalia Korepanova, Heidi Seibold, Verena Steffen and Torsten Hothorn (2019). Survival Forests under Test: Impact of the Proportional Hazards Assumption on Prognostic and Predictive Forests for ALS Survival. doi:10.1177/0962280219862586.

Examples

### Example: Stratified Medicine Using Partitioned Cox-Models
### A combination of <DOI:10.1515/ijb-2015-0032> and <arXiv:1701.02110>
### based on infrastructure in the mlt R add-on package described in
### https://cran.r-project.org/web/packages/mlt.docreg/vignettes/mlt.pdf

library("trtf")
library("survival")
### German Breast Cancer Study Group 2 data set
data("GBSG2", package = "TH.data")
GBSG2$y <- with(GBSG2, Surv(time, cens))

### set-up Cox model with overall treatment effect in hormonal therapy
cmod <- Coxph(y ~ horTh, data = GBSG2, support = c(100, 2000), order = 5)

### overall log-hazard ratio
coef(cmod)
### roughly the same as 
coef(coxph(y ~ horTh, data = GBSG2))

### partition the model, ie both the baseline hazard function AND the
### treatment effect
(part_cmod <- trafotree(cmod, formula = y ~ horTh | age + menostat + tsize + 
    tgrade + pnodes + progrec + estrec, data = GBSG2))

### compare the log-likelihoods
logLik(cmod)
logLik(part_cmod)

### stronger effects in nodes 2 and 4 and no effect in node 5
coef(part_cmod)[, "horThyes"]

### plot the conditional survivor functions; blue is untreated
### and green is hormonal therapy
nd <- data.frame(horTh = sort(unique(GBSG2$horTh)))
plot(part_cmod, newdata = nd, 
     tp_args = list(type = "survivor", col = c("cadetblue3", "chartreuse4")))

### same model, but with explicit intercept term and max-type statistic
### for _variable_ selection
(part_cmod_max <- trafotree(cmod, formula = y ~ horTh | age + menostat + tsize + 
    tgrade + pnodes + progrec + estrec, data = GBSG2, intercept = "shift",
    control = ctree_control(teststat = "max")))
logLik(part_cmod_max)
coef(part_cmod_max)[, "horThyes"]

### the trees (and log-likelihoods are the same) but the
### p-values are sometimes much smaller in the latter tree
cbind(format.pval(info_node(node_party(part_cmod))$criterion["p.value",]),
      format.pval(info_node(node_party(part_cmod_max))$criterion["p.value",]))