Correlation-Adjusted Regression Survival Scores

Description

Contains functions to estimate the Correlation-Adjusted Regression Survival (CARS) Scores. The main function is carSurvScore, which estimates CARS scores of each variable. The higher the absolute values of CARS scores, the higher the variable importance. Additionally there is the function carVarSelect to select cut-off thresholds to separate variables associated with survival from noise variables. There are two possible cut-off threshold options: False non-discovery rate q-values and empirical quantiles of the raw scores.

Details

Package: carSurv

Type: Package

Version: 1.0.0

Date: 2018-02-24

License: GPL-3

Author(s)

Thomas Welchowski (Maintainer) welchow@imbie.meb.uni-bonn.de

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 Strimmer, K., (2008), A unified approach to false discovery rate estimation, BMC Bioinformatics

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

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

Variable selection with Correlation-Adjusted Regression Survival (CARS) Scores

Description

Computes the CARS scores and selects significant variables. If the false non discovery rate (fndr) approach is used, significant and null variables are distinguished by an a priori defined q-value.

Usage

carVarSelect(carSurvScores, method = "fndr", plotDiag = FALSE,
  threshold = 0.05)

Arguments

Value

Index giving the significant variables of the original data (integer vector).

Note

The quality of estimated, significant variables depends on the sample size and on the number of variables.

Author(s)

Thomas Welchowski

References

Strimmer, K., (2008), A unified approach to false discovery rate estimation, BMC Bioinformatics

See Also

carSurvScore

Examples

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

# Generate multivariate normal distributed covariates
noObs <- 100
noCovar <- 250
library(mvtnorm)
set.seed(7903)
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]

# Conduct variable selection using fndr
carScores <- carSurvScore(obsTime=obsTime, obsEvent=eventInd, X=X)
selectedVar <- carVarSelect(carSurvScores=carScores)
selectedVar

# Check true positive and true negative rate
TPR <- mean(c(1:5) %in% selectedVar)
TNR <- mean(c(6:250) %in% setdiff(6:250, selectedVar))
perf <- TPR + TNR -1
perf

Estimate weighted covariance

Description

Efficient C implementation of the sample covariance estimator. The denominator is defined as the sum of all weights.

Usage

weightedCovarRcpp(x, y, w)

Arguments

Value

Weighted variance (numeric scalar).

Note

If all weights are set to 1, the denominator is identical to n. There are no safety checks of input arguments.

Author(s)

Thomas Welchowski

Examples

# Simulate two random vectors
set.seed(3975)
x <- rnorm(100)
set.seed(-3975)
y <- rnorm(100)
# Calculate variance with standard R function
# Rescaling ensures that both calculations use same denominator "n"
covarEst <- cov(x, y) * (100-1) / 100
# Calculate weighted variance with equal weights
equalW <- rep(1, 100)
weightCovarEst <- weightedCovarRcpp(x=x, y=y, w=equalW)
# Output comparison
all.equal(covarEst, weightCovarEst)
# Runtime comparison
library(microbenchmark)
microbenchmark(Default=cov(x, y), New=weightedCovarRcpp(x=x, y=y, w=equalW), times=25)
# -> New method is multiple times faster

Estimate weighted covariance

Description

Efficient C implementation of the sample covariance estimator. The denominator is defined as the sample size.

Usage

weightedCovarRcppN(x, y, w)

Arguments

Value

Weighted variance (numeric scalar).

Note

There are no safety checks of input arguments.

Author(s)

Thomas Welchowski

Examples

# Simulate two random vectors
set.seed(3975)
x <- rnorm(100)
set.seed(-3975)
y <- rnorm(100)
# Calculate variance with standard R function
# Rescaling ensures that both calculations use same denominator "n"
covarEst <- cov(x, y) * (100-1) / 100
# Calculate weighted variance with equal weights
equalW <- rep(1, 100)
weightCovarEst <- weightedCovarRcppN(x=x, y=y, w=equalW)
# Output comparison
all.equal(covarEst, weightCovarEst)
# Runtime comparison
library(microbenchmark)
microbenchmark(Default=cov(x, y), New=weightedCovarRcpp(x=x, y=y, w=equalW), times=25)
# -> New method is multiple times faster

Estimate weighted variance

Description

Efficient C implementation of the sample variance estimator. The denominator is defined as sum of all weights.

Usage

weightedVarRcpp(y, w)

Arguments

Value

Weighted variance (numeric scalar).

Note

If all weights are set to 1, the denominator is identical to n. There are no safety checks of input arguments.

Author(s)

Thomas Welchowski

Examples

# Simulate a random vector
set.seed(3975)
x <- rnorm(100)
# Calculate variance with standard implementation
# Rescaling ensures that both calculations use same denominator "n"
varEst <- var(x) * (100-1) / 100
# Calculate weighted variance with equal weights
equalW <- rep(1/100, 100)
weightVarEst <- weightedVarRcpp(y=x, w=equalW)
# Output comparison
all.equal(varEst, weightVarEst)
# Runtime comparison
library(microbenchmark)
microbenchmark(Default=var(x), New=weightedVarRcppN(y=x, w=equalW), times=25)
# -> New method is multiple times faster

Estimate weighted variance

Description

Efficient C implementation of the sample variance estimator. The denominator is defined as the sample size.

Usage

weightedVarRcppN(y, w)

Arguments

Value

Weighted variance (numeric scalar).

Note

There are no safety checks of input arguments.

Author(s)

Thomas Welchowski

Examples

# Simulate a random vector
set.seed(3975)
x <- rnorm(100)
# Calculate variance with standard implementation
varEst <- var(x) * (100-1) / 100
# Calculate weighted variance with equal weights
equalW <- rep(1, 100)
weightVarEst <- weightedVarRcppN(y=x, w=equalW)
# Output comparison
all.equal(varEst, weightVarEst)
# Runtime comparison
library(microbenchmark)
microbenchmark(Default=var(x), New=weightedVarRcppN(y=x, w=equalW), times=25)
# -> New method is multiple times faster