| Title: | Variable Selection for Cox's Model with Interval-Censored Data |
|---|---|
| Description: | Perform variable selection for Cox regression model with interval-censored data. Can deal with both low-dimensional and high-dimensional data. Case-cohort design can be incorporated. Two sets of covariates scenario can also be considered. The references are listed in the URL below. |
| Authors: | Qiwei Wu [aut, cre], Hui Zhao [aut], Jianguo Sun [aut] |
| Maintainer: | Qiwei Wu <[email protected]> |
| License: | Apache License (>= 2) |
| Version: | 1.1.0 |
| Built: | 2024-12-19 06:28:35 UTC |
| Source: | CRAN |
Perform variable selection for Cox regression model with interval-censored data by using the methods proposed in Zhao et al. (2020a), Wu et al. (2020) and Zhao et al. (2020b). Can deal with both low-dimensional and high-dimensional data.
CoxICPen(LR = LR, x = x, lamb = log(nrow(x))/2-2, beta.initial = rep(0,ncol(x)), pen = "BAR", nfold = 5, BernD = 3, subj.wt = rep(1,nrow(x)))CoxICPen(LR = LR, x = x, lamb = log(nrow(x))/2-2, beta.initial = rep(0,ncol(x)), pen = "BAR", nfold = 5, BernD = 3, subj.wt = rep(1,nrow(x)))
LR |
An n by 2 matrix that contains interval-censored failure times (L, R]. Please set time point R to "Inf" if a subject is right-censored. |
x |
An n by p covariate matrix. |
lamb |
The value of the tuning parameter of the penalty term. Can either be a single value or a vector. Cross-validation will be employed to select the optimal lambda if a vector is provided. Default is log(n)/2-2. |
beta.initial |
The initial values for the regression coefficients in the Cox's model. Default is 0. |
pen |
The penalty function. Choices include "RIDGE", "BAR", "LASSO", "ALASSO", "SCAD", "MCP", "SICA", "SELO". Default is "BAR". |
nfold |
Number of folds for cross-validation. Will be ignored if a single lambda value is provided. Default is 5. |
BernD |
The degree of Bernstein polynomials. Default is 3. |
subj.wt |
Weight for each subject in the likelihood function. Can be used to incorporate case-cohort design. Default is 1 for each subject. |
beta: Penalized estimates of the regression coefficients in the Cox's model.
phi: Estimates of the coefficients in Bernstein Polynomials.
logL: Log likelihood function based on current parameter estimates and lambda value.
Lamb0: Estimate of the cumulative baseline hazard function at each observation time point.
cv.out: Cross-validation outcome for each lambda. Will be NULL if cross-validation is not performed.
Zhao, H., Wu, Q., Li, G., Sun, J. (2020a). Simultaneous Estimation and Variable Selection for Interval-Censored Data with Broken Adaptive Ridge Regression. Journal of the American Statistical Association. 115(529):204-216.
Wu, Q., Zhao, H., Zhu, L., Sun, J. (2020). Variable Selection for High-dimensional Partly Linear Additive Cox Model with Application to Alzheimer's disease. Statistics in Medicines.39(23):3120-3134.
Zhao, H., Wu, Q., Gilbert, P. B., Chen, Y. Q., Sun, J. (2020b). A Regularized Estimation Approach for Case-cohort Periodic Follow-up Studies with An Application to HIV Vaccine Trials. Biometrical Journal. 62(5):1176-1191.
# Generate an example data require(foreach) n <- 300 # Sample size p <- 20 # Number of covariates bet0 <- c(1, -1, 1, -1, rep(0,p-4)) # True values of regression coefficients set.seed(1) x.example <- matrix(rnorm(n*p,0,1),n,p) # Generate covariates matrix T.example <- c() for (i in 1:n){ T.example[i] <- rexp(1,exp(x.example%*%bet0)[i]) # Generate true failure times } timep <- seq(0,3,,10) LR.example <- c() for (i in 1:n){ obsT <- timep*rbinom(10,1,0.5) if (max(obsT) < T.example[i]) {LR.example <- rbind(LR.example,c(max(obsT), Inf))} else { LR.example <- rbind(LR.example,c(max(obsT[obsT<T.example[i]]), min(obsT[obsT>=T.example[i]]))) } } # Generate interval-censored failure times # Fit Cox's model with penalized estimation model1 <- CoxICPen(LR = LR.example, x = x.example, lamb = 100, pen = "RIDGE") beta.initial <- model1$beta model2 <- CoxICPen(LR = LR.example, x = x.example, beta.initial = beta.initial, pen = "BAR") model2$beta #model3 <- CoxICPen(LR = LR.example, x = x.example, lamb = seq(0.1,1,0.1), # beta.initial = beta.initial, pen = "SELO") #model3$beta# Generate an example data require(foreach) n <- 300 # Sample size p <- 20 # Number of covariates bet0 <- c(1, -1, 1, -1, rep(0,p-4)) # True values of regression coefficients set.seed(1) x.example <- matrix(rnorm(n*p,0,1),n,p) # Generate covariates matrix T.example <- c() for (i in 1:n){ T.example[i] <- rexp(1,exp(x.example%*%bet0)[i]) # Generate true failure times } timep <- seq(0,3,,10) LR.example <- c() for (i in 1:n){ obsT <- timep*rbinom(10,1,0.5) if (max(obsT) < T.example[i]) {LR.example <- rbind(LR.example,c(max(obsT), Inf))} else { LR.example <- rbind(LR.example,c(max(obsT[obsT<T.example[i]]), min(obsT[obsT>=T.example[i]]))) } } # Generate interval-censored failure times # Fit Cox's model with penalized estimation model1 <- CoxICPen(LR = LR.example, x = x.example, lamb = 100, pen = "RIDGE") beta.initial <- model1$beta model2 <- CoxICPen(LR = LR.example, x = x.example, beta.initial = beta.initial, pen = "BAR") model2$beta #model3 <- CoxICPen(LR = LR.example, x = x.example, lamb = seq(0.1,1,0.1), # beta.initial = beta.initial, pen = "SELO") #model3$beta
Perform variable selection for Cox regression model with two sets of covariates by using the method in Wu et al. (2020). Variable selection is performed on the possibly high-dimensional covariates x with linear effects. Covariates z with possibly nonlinear effects are always kept in the model.
CoxICPen.XZ(LR = LR, x = x, z = z, lamb = log(nrow(x))/2-2, beta.initial = rep(0,ncol(x)), pen = "BAR", nfold = 5, BernD = 3, subj.wt = rep(1,nrow(x)))CoxICPen.XZ(LR = LR, x = x, z = z, lamb = log(nrow(x))/2-2, beta.initial = rep(0,ncol(x)), pen = "BAR", nfold = 5, BernD = 3, subj.wt = rep(1,nrow(x)))
LR |
An n by 2 matrix that contains interval-censored failure times (L, R]. Please set time point R to "Inf" if a subject is right-censored. |
x |
An n by p covariate matrix. Variable selection will be performed on x. Linear covariates effects are assumed. Both p>n and p<n are allowed. |
z |
An n by q covariate matrix. Variable selection will NOT be performed on z. Non-linear covariates effects are assumed. Only q<n is allowed. |
lamb |
The value of the tuning parameter of the penalty term. Can either be a single value or a vector. Cross-validation will be employed to select the optimal lambda if a vector is provided. Default is log(n)/2-2. |
beta.initial |
The initial values for the regression coefficients in the Cox's model. Default is 0. |
pen |
The penalty function. Choices include "RIDGE", "BAR", "LASSO", "ALASSO", "SCAD", "MCP", "SICA", "SELO". Default is "BAR". |
nfold |
Number of folds for cross-validation. Will be ignored if a single lambda value is provided. Default is 5. |
BernD |
The degree of Bernstein polynomials for both cumulative baseline hazard and covariate effects of z. Default is 3. |
subj.wt |
Weight for each subject in the likelihood function. Can be used to incorporate case-cohort design. Default is 1 for each subject. |
beta: Penalized estimates of the regression coefficients in the Cox's model.
phi: Estimates of the coefficients in Bernstein Polynomials.
logL: Log likelihood function based on current parameter estimates and lambda value.
Lamb0: Estimate of the cumulative baseline hazard function at each observation time point.
cv.out: Cross-validation outcome for each lambda. Will be NULL if cross-validation is not performed.
f.est.all: A matrix that contains the values of covariates z and the corresponding estimated effects.
Wu, Q., Zhao, H., Zhu, L., Sun, J. (2020). Variable Selection for High-dimensional Partly Linear Additive Cox Model with Application to Alzheimer's disease. Statistics in Medicines.39(23):3120-3134.
# Generate an example data require(foreach) n <- 300 # Sample size p <- 20 # Number of covariates bet0 <- c(1, -1, 1, -1, rep(0,p-4)) # True values of regression coefficients f1 <- function(z) sin(2*pi*z) # True effects of z1 f2 <- function(z) cos(2*pi*z) # True effects of z2 set.seed(1) x.example <- matrix(rnorm(n*p,0,1),n,p) # Generate x covariates matrix z.example <- cbind(runif(n,0,1),runif(n,0,1)) # Generate z covariates matrix T.example <- c() for (i in 1:n){ T.example[i] <- rexp(1,exp(x.example%*%bet0+ f1(z.example[,1])+f2(z.example[,2]))[i]) # Generate true failure times } timep <- seq(0,3,,10) LR.example <- c() for (i in 1:n){ obsT <- timep*rbinom(10,1,0.5) if (max(obsT) < T.example[i]) {LR.example <- rbind(LR.example,c(max(obsT), Inf))} else { LR.example <- rbind(LR.example,c(max(obsT[obsT<T.example[i]]), min(obsT[obsT>=T.example[i]]))) } } # Generate interval-censored failure times # Fit Cox's model with penalized estimation model1 <- CoxICPen.XZ(LR = LR.example, x = x.example, z = z.example, lamb = 100, pen = "RIDGE") beta.initial <- model1$beta model2 <- CoxICPen.XZ(LR = LR.example, x = x.example, z = z.example, beta.initial = beta.initial, pen = "BAR") model2$beta # Plots of covariate effects of z par(mfrow=c(1,2)) plot(model2$f.est.all$z1, model2$f.est.all$f1, type="l", ylim=c(-1,2), xlab="z1", ylab="f1") lines(model2$f.est.all$z1, f1(model2$f.est.all$z1), col="blue") legend("topright", col=c("black","blue"), lty=rep(1,2), c("Estimate", "True")) plot(model2$f.est.all$z2, model2$f.est.all$f2, type="l", ylim=c(-1,2), xlab="z2", ylab="f2") lines(model2$f.est.all$z2, f2(model2$f.est.all$z2), col="blue") legend("topright", col=c("black","blue"), lty=rep(1,2), c("Estimate", "True"))# Generate an example data require(foreach) n <- 300 # Sample size p <- 20 # Number of covariates bet0 <- c(1, -1, 1, -1, rep(0,p-4)) # True values of regression coefficients f1 <- function(z) sin(2*pi*z) # True effects of z1 f2 <- function(z) cos(2*pi*z) # True effects of z2 set.seed(1) x.example <- matrix(rnorm(n*p,0,1),n,p) # Generate x covariates matrix z.example <- cbind(runif(n,0,1),runif(n,0,1)) # Generate z covariates matrix T.example <- c() for (i in 1:n){ T.example[i] <- rexp(1,exp(x.example%*%bet0+ f1(z.example[,1])+f2(z.example[,2]))[i]) # Generate true failure times } timep <- seq(0,3,,10) LR.example <- c() for (i in 1:n){ obsT <- timep*rbinom(10,1,0.5) if (max(obsT) < T.example[i]) {LR.example <- rbind(LR.example,c(max(obsT), Inf))} else { LR.example <- rbind(LR.example,c(max(obsT[obsT<T.example[i]]), min(obsT[obsT>=T.example[i]]))) } } # Generate interval-censored failure times # Fit Cox's model with penalized estimation model1 <- CoxICPen.XZ(LR = LR.example, x = x.example, z = z.example, lamb = 100, pen = "RIDGE") beta.initial <- model1$beta model2 <- CoxICPen.XZ(LR = LR.example, x = x.example, z = z.example, beta.initial = beta.initial, pen = "BAR") model2$beta # Plots of covariate effects of z par(mfrow=c(1,2)) plot(model2$f.est.all$z1, model2$f.est.all$f1, type="l", ylim=c(-1,2), xlab="z1", ylab="f1") lines(model2$f.est.all$z1, f1(model2$f.est.all$z1), col="blue") legend("topright", col=c("black","blue"), lty=rep(1,2), c("Estimate", "True")) plot(model2$f.est.all$z2, model2$f.est.all$f2, type="l", ylim=c(-1,2), xlab="z2", ylab="f2") lines(model2$f.est.all$z2, f2(model2$f.est.all$z2), col="blue") legend("topright", col=c("black","blue"), lty=rep(1,2), c("Estimate", "True"))