survivalSL: an R Package for Predicting Survival by a Super Learner

Description

The R package ‘survivalSL’ contains a variety of functions to construct a super learner in the presence of censored times-to-event and to evaluate its prognostic capacities. Several learners are proposed: proportional hazard (PH) regressions, penalized PH semi-parametric models, accelerated failure times (AFT) models, neural networks, random survival forests, etc.). We proposed also a variety of loss functions for the estimation of the weights (concordance index (Pencina and Uno versions), Brier score, area under the time-dependent ROC curve, negative binomial log-likelihood, etc.). S3 methods are included to evaluate the predictive capacities, as well as predicting survival curves from new observations.

Basic Usage

# Simulate a training and validation samples
n.valid <- 500 # sample size for validation
n.learn <- 200 # sample size for training
n <- n.valid + n.learn # overall sample size

max.time <- 50 # maximum follow-up time

mean.x <- 0; sd.x <- 1 # normal distribution of the quantitative predictors
proba.x <- .5 # proportion of the binary predictors

a <- 2; b <- .05 # Weibull baseline distribution of the PH model
beta <- c(log(1.8), log(1.8), log(1.3), 0, 0, 0) # regression coefficients

# simulation of  the training and validation samples
set.seed(123)
x1 <- rnorm(n, mean.x, sd.x)
x2 <- rbinom(n, 1, proba.x)
x3 <- rbinom(n, 1, proba.x)
x4 <- rnorm(n, mean.x, sd.x)
x5 <- rbinom(n, 1, proba.x)
x6 <- rbinom(n, 1, proba.x)
x <- cbind(x1, x2, x3, x4, x5, x6) # matrix of the potential predictors

times <- 1/b*((-exp(-1*(x %*% beta))*(log(1-runif(n, 0, 1))))**(1/a)) # time to event
censoring <- runif(n, min=0, max=max.time)

status <- ifelse(times <= censoring, 1, 0) # event status
obs.times <- ifelse(times <= censoring, times, censoring) # follow-up times

data <- cbind(obs.times, status, as.data.frame(x))

data.simul <- list(data[1:n.valid,], data[(n.valid+1):n,])

# model estimation with default parameters and three learners

formula<-Surv(obs.times,status) ~ x1+x2+x3+x4+x5+x6
slres <- survivalSL(formula=formula,
                    methods=c("LIB_COXen", "LIB_AFTgamma", "LIB_PHexponential"),
                    metric="auc",  data=data.simul[[1]], seed=123, optim.method="SANN")


# prognostic capacities from training sample
summary(slres, digits=3) 
#>     p_ci uno_ci   auc   bs   ibs  ribs   bll  ibll ribll        ll
#>   0.677  0.677 0.719 0.21 0.095 0.107 0.609 0.314 0.354 -1310.989

# prognostic capacities from validation sample
summary(slres, newdata=data.simul[[2]], digits=3) 
#>  p_ci uno_ci   auc    bs   ibs  ribs   bll  ibll ribll       ll
#>  0.722  0.726 0.784 0.192 0.093 0.098 0.57 0.312 0.333 -475.514

Installation

To install the latest release from CRAN:

install.packages("survivalSL")

To install the development version from GitHub:

remotes::install_github("foucher-y/survivalSL")

Reporting bugs

You can report any issues at this link.