carSurvScore {carSurv}

Estimate Correlation-Adjusted Regression Survival (CARS) Scores

Description

Estimates CARS scores. CARS scores measure the relative importance of each variable with respect to the survival times adjusted by IPC weighting.

Usage

carSurvScore(obsTime, obsEvent, X, maxIPCweight = 10, denom = "1/n")

Arguments

obsTime

Observed time points of a right censored survival process (numeric vector).

obsEvent

Observed event indicator of right censored survival process (numeric vector) 0=no event, 1=event

X

Data of design variables (numeric matrix). Must be already encoded.

maxIPCweight

Specifies the maximum possible weight, to ensure numerical stability.

denom

Specifies the denominator of the weighted sums. Two options are available: The default value "1/n" uses the sample size as denominator. Option "sum_w" uses the sum of all IPC weights in the denominator.

Details

CARS scores are defined as theta=P_X^(-1/2) P_(X, log(T)). The term P_X^(-1/2) is the inverse square root of the correlation matrix between covariates X. P_(X, log(T)) is the correlation vector between covariates and the logarithmic survival time adjusted for censoring by IPC weighting.

Value

Estimated CAR survival score of each variable (numeric vector).

Note

It is recommended to use default setting "denom=1/n" because in this case CARS scores are consistent. Furthermore the simulation results of "1/n" show lower root mean squared error of CARS scores with respect to the true parameter.

Author(s)

Thomas Welchowski

References

Welchowski, T. and Zuber, V. and Schmid, M., (2018), Correlation-Adjusted Regression Survival Scores for High-Dimensional Variable Selection, <arXiv:1802.08178>

Zuber, V. and Strimmer, K., (2011), High-Dimensional Regression and Variable Selection Using CAR Scores, Statistical Applications in Genetics and Molecular Biology

Schaefer, J. and Strimmer, K., (2005), A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics, Statistical Applications in Genetics and Molecular Biology

Van der Laan, M. J. and Robins, J. M., (2003), Unified Methods for Censored Longitudinal Data and Causality, Springer Series in Statistics

See Also

carVarSelect

Examples

##########################################
# Simulate accelerated, failure time model

# Generate multivariate normal distributed covariates
noObs <- 100
noCovar <- 10
library(mvtnorm)
set.seed(190)
X <- rmvnorm(noObs, mean=rep(0, noCovar), sigma=diag(noCovar))

# Generate gamma distributed survival times
# Only the first 5 variables have an influence
eta <- 1 - 2 * X[,1] - X[,2] + X[,3] +
0.5 * X[,4] + 1.5 * X[,5]

# Function to generate survival times
genSurv <- function(x) {
set.seed(x)
rgamma(1, shape=2, scale=exp(eta[x]))
}

# Generate survival times
survT <- sapply(1:length(eta), genSurv)

# Generate exponential distributed censoring times
censT <- rexp(noObs, rate=1)

# Calculate event indicator
eventInd <- ifelse(survT <= censT, 1, 0)

# Calculate observed times
obsTime <- survT
obsTime[survT > censT] <- censT [survT > censT]

# Estimate CAR scores
carScores <- carSurvScore(obsTime=obsTime, obsEvent=eventInd, X=X)
carScores