Constructs a LTRC conditional inference forest (LTRCCIF) or
a LTRC relative risk forest (LTRCRRF) for left-truncated and right-censored data,
it also allows for (left-truncated) right-censored survival data with
time-varying covariates (Yao et al. 2022).
The main functions of this package are ltrccif and ltrcrrf.
Continuous-time survival data with time-varying covariates are common in practice.
Methods like the Cox proportional hazards model rely on restrictive assumptions such as
proportional hazards and a log-linear relationship between the hazard function and
covariates. Furthermore, because these methods are often parametric, nonlinear effects
of variables must be modeled by transformations or expanding the design matrix to
include specialized basis functions for more complex data structures in real world
applications. The functions LTRCIT and
LTRCART provide a conditional inference tree method and
a relative risk tree method for
left-truncated right-censored survival data, which also allows for right-censored
survival data with time-varying covariates. Tree estimators are nonparametric and
as such often exhibit
low bias and high variance. Ensemble methods like bagging and random forest can
reduce variance while preserving low bias.
The most popular survival forest methods, including conditional inference forest
(see cforest), relative risk forest, and random survival
forest method (see rfsrc) can only be applied to
right-censored survival data with time-invariant covariates.
This package implements ltrccif and ltrcrrf.
ltrccif extends the conditional inference forest
(see cforest) to LTRC survival data.
It uses LTRC conditional inference survival trees
as base learners.
ltrcrrf extends the relative risk forest
(Ishwaran et al. 2004) to left-truncated right-censored survival data.
It uses LTRC risk relative tree
as base learners.
The main functions ltrccif and ltrcrrf
fit a corresponding LTRC forest for LTRC data, with parameter
mtry tuned by tune.ltrccif or tune.ltrcrrf. This tuning
procedure relies on the evaluation of the out-of-bag errors, which is performed by the
function sbrier_ltrc. print
prints summary output for ltrccif objects and ltrcrrf objects.
predictProb
constructs survival function estimates for ltrccif objects and ltrcrrf objects.
For (left-truncated) right-censored survival data with time-varying covariates, one can first reformat the data structure to one with LTRC observations, where the multiple records of a subject become a list of pseudo-subjects and are treated independently. This procedure is usually referred to as the Andersen-Gill method (Andersen and Gill, 1982). Then LTRC forest methods can be applied on this reformatted dataset.
Overall, the methods in this package can handle all combinations of left truncation,
right censoring, time-invariant covariates, and time-varying covariates.
If one is in the traditional case with right-censored data
and time-invariant covariates, however, then it is recommended to use
the functions cforest and rfsrc
directly to construct conditional inference forests and random survival forests,
respectively.
Yao, W., Frydman, H., Larocque, D. and Simonoff, J. S. (2022). Ensemble methods for survival function estimation with time-varying covariates. Statistical Methods in Medical Research, 31(11):2217-2236.
Andersen, P. and Gill, R. (1982). Cox’s regression model for counting processes, a large sample study. Annals of Statistics, 10:1100-1120.
Ishwaran, H., Blackstone, E. H., Pothier, C., and Lauer, M. S. (2004). Relative risk forests for exercise heart rate recovery as a predictor of mortality. Journal of the American StatisticalAssociation, 99(1):591–600.
Fu, W. and Simonoff, J. S. (2016). Survival trees for left-truncated and right-censored data, with application to time-varying covariate data. Biostatistics, 18(2):352–369.
ltrccif, ltrcrrf,
predictProb, print,
tune.ltrccif, tune.ltrcrrf, sbrier_ltrc.