# Estimate Correlation-Adjusted Regression Survival (CARS) Scores Estimates CARS scores. CARS scores measure the relative importance of each variable with respect to the survival times adjusted by IPC weighting. ```r 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. ## Returns Estimated CAR survival score of each variable (numeric vector). ## 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. ## 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. ## Examples ```r ########################################## # 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 ``` ## References Welchowski, T. and Zuber, V. and Schmid, M., (2018), Correlation-Adjusted Regression Survival Scores for High-Dimensional Variable Selection, 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` ## Author(s) Thomas Welchowski

carSurvScore function