| Title: | Adaptive Lasso for the Cox Regression with Interval Censored and Possibly Left Truncated Data |
|---|---|
| Description: | Penalized variable selection tools for the Cox proportional hazards model with interval censored and possibly left truncated data. It performs variable selection via penalized nonparametric maximum likelihood estimation with an adaptive lasso penalty. The optimal thresholding parameter can be searched by the package based on the profile Bayesian information criterion (BIC). The asymptotic validity of the methodology is established in Li et al. (2019 <doi:10.1177/0962280219856238>). The unpenalized nonparametric maximum likelihood estimation for interval censored and possibly left truncated data is also available. |
| Authors: | Chenxi Li, Daewoo Pak and David Todem |
| Maintainer: | Daewoo Pak <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.1.1 |
| Built: | 2024-11-21 04:19:45 UTC |
| Source: | https://github.com/cran/ALassoSurvIC |
This package provides penalized variable selection tools for the Cox proportional hazards model with interval censored and possibly left truncated data. The main function alacoxIC performs the variable selection via a penalized nonparametric maximum likelihood estimation (PNPMLE) with an adaptive lasso penalty. The function also finds the optimal thresholding parameter automatically by minimizing the Bayesian information criterion (BIC). The unpenalized nonparametric maximum likelihood estimation for interval censored and possibly left truncated data is also available with the unpencoxIC function. The asymptotic validity of the methodology is established in Li et al. (2019).
| Package: | ALassoSurvIC |
| Type: | Package |
| Version: | 1.0.0 |
| Date: | 2019-8-28 |
| License: | GPL (>= 3) |
Chenxi Li, Daewoo Pak and David Todem
Li, C., Pak, D., & Todem, D. (2019). Adaptive lasso for the Cox regression with interval censored and possibly left truncated data. Statistical methods in medical research. doi:10.1177/0962280219856238
The alacoxIC function performs variable selection with an adaptive lasso penalty for interval censored and possibly left truncated data. It performs penalized nonparametric maximum likelihood estimation through a penalized EM algorithm by following Li et al. (2019). The function searches the optimal thresholding parameter automatically, based on BIC. The variable selection approach, implemented by the alacoxIC function, is proven to enjoy the desirable oracle property introduced by Fan & Li (2001). The full details are available in Li et al. (2019).
## Default S3 method: alacoxIC(lowerIC, upperIC, X, trunc, theta, normalize.X = TRUE, cl = NULL, max.theta = 1000, tol = 0.001, niter = 1e+05, string.cen = Inf, string.missing = NA, ...)## Default S3 method: alacoxIC(lowerIC, upperIC, X, trunc, theta, normalize.X = TRUE, cl = NULL, max.theta = 1000, tol = 0.001, niter = 1e+05, string.cen = Inf, string.missing = NA, ...)
... |
for S4 method only. |
lowerIC |
A numeric vector for the lower limit of the censoring interval. |
upperIC |
A numeric vector for the upper limit of the censoring interval. |
X |
A numeric matrix for the covariates that will be used for variable selection. |
trunc |
A numeric vector for left truncated times. If supplied, the function performs the variable selection for interval censored and left truncated data. If |
theta |
A numeric value for the thresholding parameter. If |
normalize.X |
A logical value: if |
cl |
A cluster object created by |
max.theta |
A numeric value for the maximum value that a thresholding parameter can take when searching the optimal one. The algorithm will look up an optimal tunning parameter below |
tol |
A numeric value for the absolute iteration convergence tolerance. |
niter |
A numeric value for the maximum number of iterations. |
string.cen |
A string indicating right censoring for |
string.missing |
A string indicating missing value. Default is |
The grid search algorithm is used to find the optimal thresholding parameter using a grid search algorithm, based on BIC. Specifically, the alacoxIC function first searches the smallest integer thresholding parameter which all coefficient estimates are zero beween and max.theta and then creates one hundred grid points by following the rule of Simon et al. (2011, Section 2.3). The one minimizing BIC among the one hundred candidates is chosen as the optimal thresholding parameter in the adaptive lasso estimation.
The cluster object, created by makeCluster in the parallel package, can be supplied with the cl argument to reduce computation time via parallel computing. The parallel computing will be used when searching the optimal thresholding parameter and calculating the hessian matrix of the log profile likelihood. How to use the parallel computing is illustrated in one of the examples given below.
Use the baseline function and the plot function to extract and plot the estimate of the baseline cumulative hazard function, respectively, from the object returned by the alacoxIC. The plot function also provides the plot of the estimated baseline survival function. See the usages in the examples given below.
Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456), 1348-1360
Simon, N., Friedman, J., Hastie, T., & Tibshirani, R. (2011). Regularization paths for Cox’s proportional hazards model via coordinate descent. Journal of statistical software, 39(5), 1.
Li, C., Pak, D., & Todem, D. (2019). Adaptive lasso for the Cox regression with interval censored and possibly left truncated data. Statistical methods in medical research. doi:10.1177/0962280219856238
unpencoxIC
library(ALassoSurvIC) ### Variable selection for interval censored data data(ex_IC) # the 'ex_IC' data having 100 subjects and 6 covariates lowerIC <- ex_IC$lowerIC upperIC <- ex_IC$upperIC X <- ex_IC[, -c(1:2)] ## Performing the variable selection algorithm using a single core system.time(result <- alacoxIC(lowerIC, upperIC, X)) ## Use parallel computing to reduce the computation time library(parallel) cl <- makeCluster(2L) # making the cluster object 'cl' with two CPU cores system.time(result <- alacoxIC(lowerIC, upperIC, X, cl = cl)) result # main result baseline(result) # obtaining the baseline cumulative hazard estimate plot(result) # plotting the baseline estimated cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function on.exit() ### Variable selection for interval censored and left truncated data ## Try following codes with the 'ex_ICLT' data example data(ex_ICLT) # the 'ex_ICLT' data having 100 subjects and 6 covariates lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result2 <- alacoxIC(lowerIC, upperIC, X, trunc) result2 baseline(result2) plot(result2) plot(result2, what = "survival")library(ALassoSurvIC) ### Variable selection for interval censored data data(ex_IC) # the 'ex_IC' data having 100 subjects and 6 covariates lowerIC <- ex_IC$lowerIC upperIC <- ex_IC$upperIC X <- ex_IC[, -c(1:2)] ## Performing the variable selection algorithm using a single core system.time(result <- alacoxIC(lowerIC, upperIC, X)) ## Use parallel computing to reduce the computation time library(parallel) cl <- makeCluster(2L) # making the cluster object 'cl' with two CPU cores system.time(result <- alacoxIC(lowerIC, upperIC, X, cl = cl)) result # main result baseline(result) # obtaining the baseline cumulative hazard estimate plot(result) # plotting the baseline estimated cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function on.exit() ### Variable selection for interval censored and left truncated data ## Try following codes with the 'ex_ICLT' data example data(ex_ICLT) # the 'ex_ICLT' data having 100 subjects and 6 covariates lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result2 <- alacoxIC(lowerIC, upperIC, X, trunc) result2 baseline(result2) plot(result2) plot(result2, what = "survival")
Internal functions for the ALassoSurvIC package.
Extracting the NPMLE for the baseline cumulative hazard function from the input object. The input object must be the objects returned by the alacoxIC function or the unpencoxIC function. The support set over which the cumulative hazard increases is the same as that of the nonparametric maximum likelihood estimator, characterized by Alioum and Commenges (1996). The full details are available in Li et al. (2019).
## Default S3 method: baseline(object, ...)## Default S3 method: baseline(object, ...)
... |
for S4 method only. |
object |
the |
The estimator for the baseline cumulative hazard function increases only on some support sets, so called maximal intersections, and the NPMLE is indifferent to how it increases on the support sets. The definition of maximal intersections and other details are available in Alioum and Commenges (1996) and Li et al. (2019).
A list with components:
support |
The maximal intersections with a finite upper endpoint. |
lambda |
The jump sizes over the support set. |
cum.lambda |
The NPMLE of the baseline cumulative hazard function. |
Alioum, A. and Commenges, D. (1996). A proportional hazards model for arbitrarily censored and truncated data. Biometrics 52, 512-524.
Li, C., Pak, D., & Todem, D. (2019). Adaptive lasso for the Cox regression with interval censored and possibly left truncated data. Statistical methods in medical research. doi:10.1177/0962280219856238
library(ALassoSurvIC) ### Display the hazard function for the interval censored data data(ex_ICLT) # the 'virtual' data having 100 subjects and 6 covariates lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- unpencoxIC(lowerIC, upperIC, X, trunc) baseline(result)library(ALassoSurvIC) ### Display the hazard function for the interval censored data data(ex_ICLT) # the 'virtual' data having 100 subjects and 6 covariates lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- unpencoxIC(lowerIC, upperIC, X, trunc) baseline(result)
The data ex_IC is a virtual data set created to show how to utilize the package. ex_IC is interval censored data. See ex_ICLT for interval censored and left truncated data.
data(ex_IC)data(ex_IC)
The data have the following columns:
lowerICThe lower limit of the censoring interval.
upperICThe upper limit of the censoring interval.
truncThe vector of left truncated points.
X1 - X6The covariate vectors used for variable selection.
library(ALassoSurvIC) data(ex_IC) # 100 subjects and 6 covariates print(ex_IC)library(ALassoSurvIC) data(ex_IC) # 100 subjects and 6 covariates print(ex_IC)
The data ex_ICLT is a virtual data set created to show how to utilize the package. ex_ICLT is interval censored and left truncated data. See ex_IC for interval censored data.
data(ex_ICLT)data(ex_ICLT)
The data have the following columns:
lowerICThe lower limit of the censoring interval.
upperICThe upper limit of the censoring interval.
truncThe vector of left truncated points.
X1 - X6The covariate vectors used for variable selection.
library(ALassoSurvIC) data(ex_IC) # 100 subjects and 6 covariates print(ex_IC)library(ALassoSurvIC) data(ex_IC) # 100 subjects and 6 covariates print(ex_IC)
alacoxIC objectThe plot method for alacoxIC object for plotting the estimated baseline culmulative function and the estimated baseline survival function.
## S3 method for class 'alacoxIC' plot(x, what = "cum.hazard", xlim, ylim, xlab, ylab, axes = FALSE, ...)## S3 method for class 'alacoxIC' plot(x, what = "cum.hazard", xlim, ylim, xlab, ylab, axes = FALSE, ...)
... |
for S4 method only. |
x |
An object of class |
what |
A character string specifying which function will be plotted. Default is "cum.hazard", which plots the estimated baseline cumulative hazard function. Set to "survival" to plot the estimated baseline survival function. |
xlim |
A vector with two elements for the limits of follow-up time. |
ylim |
A vector with two elements for the limits of y-axis. |
xlab |
A label for the x axis. |
ylab |
A label for the y axis. |
axes |
A logical value drawing both axes. Default is |
The x argument must be the object returned by the alacoxIC function. Note that plot provides the conditional survival function for left truncated data, which is analogous to the function (5) of Alioum and Commenges (1996). See the usages in the examples given below.
Alioum, A. and Commenges, D. (1996). A proportional hazards model for arbitrarily censored and truncated data. Biometrics 52, 512-524.
library(ALassoSurvIC) data(ex_ICLT) # interval censored and left truncated data lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- alacoxIC(lowerIC, upperIC, X, trunc, theta = 1.5) plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival functionlibrary(ALassoSurvIC) data(ex_ICLT) # interval censored and left truncated data lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- alacoxIC(lowerIC, upperIC, X, trunc, theta = 1.5) plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function
unpencoxIC objectPlot method for unpencoxIC object for plotting the estimated baseline culmulative function and the estimated baseline survival function.
## S3 method for class 'unpencoxIC' plot(x, what = "cum.hazard", xlim, ylim, xlab, ylab, axes = FALSE, ...)## S3 method for class 'unpencoxIC' plot(x, what = "cum.hazard", xlim, ylim, xlab, ylab, axes = FALSE, ...)
... |
for S4 method only. |
x |
An object of class |
what |
A character string specifying which function will be plotted. Default is "cum.hazard", which plots the estimated baseline cumulative hazard function. Set to "survival" to plot the estimated baseline survival function. |
xlim |
A vector with two elements for the limits of follow-up time. |
ylim |
A vector with two elements for the limits of y-axis. |
xlab |
A label for the x axis. |
ylab |
A label for the y axis. |
axes |
A logical value drawing both axes. Default is |
The x argument must be the object returned by the unpencoxIC function. Note that plot provides the conditional survival function for left truncated data, which is analogous to the function (5) of Alioum and Commenges (1996). See the usages in the examples given below.
Alioum, A. and Commenges, D. (1996). A proportional hazards model for arbitrarily censored and truncated data. Biometrics 52, 512-524.
library(ALassoSurvIC) data(ex_ICLT) # interval censored and left truncated data lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- unpencoxIC(lowerIC, upperIC, X, trunc) plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival functionlibrary(ALassoSurvIC) data(ex_ICLT) # interval censored and left truncated data lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result <- unpencoxIC(lowerIC, upperIC, X, trunc) plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function
The unpencoxIC function performs unpenalized nonparametric maximum likelihood estimation. The function provides unpenalized nonparametric maximum likelihood estimates, standard errors, and 95% confidence intervals. The full details are available in Li et al. (2019).
## Default S3 method: unpencoxIC(lowerIC, upperIC, X, trunc = NULL, normalize.X = TRUE, covmat = TRUE, cl = NULL, tol = 0.001, niter = 1e+05, string.cen = Inf, string.missing = NA, ...)## Default S3 method: unpencoxIC(lowerIC, upperIC, X, trunc = NULL, normalize.X = TRUE, covmat = TRUE, cl = NULL, tol = 0.001, niter = 1e+05, string.cen = Inf, string.missing = NA, ...)
... |
for S4 method only. |
lowerIC |
A numeric vector for the lower limit of the censoring interval. |
upperIC |
A numeric vector for the upper limit of the censoring interval. |
X |
A numeric matrix for the covariates that will be used for variable selection. |
trunc |
A numeric vector for left truncated time. If supplied, the function performs the variable selection for interval censored and left truncated data. If |
normalize.X |
A logical value: if |
covmat |
Controlling the estimation of the covariance matrix |
cl |
A cluster object created by |
tol |
A numeric value for the absolute iteration convergence tolerance. |
niter |
A numeric value for the maximum number of iterations. |
string.cen |
A string indicating right censoring for |
string.missing |
A string indicating missing value. Default is |
The cluster object, created by makeCluster in the parallel package, can be supplied with the cl argument to reduce computation time via parallel computing. The parallel computing will be used when calculating the hessian matrix of the estimates. How to use the parallel computing is illustrated in one of the examples given below.
Use the baseline function and the plot function to extract and plot the estimate of the baseline cumulative hazard function, respectively, from the object returned by the unpencoxIC. The plot function also provides the plot for estimated baseline survival function. See the usages in the examples given below.
Li, C., Pak, D., & Todem, D. (2019). Adaptive lasso for the Cox regression with interval censored and possibly left truncated data. Statistical methods in medical research. doi:10.1177/0962280219856238
alacoxIC
library(ALassoSurvIC) ### Getting the unpenalized NPMLE for interval censored data data(ex_IC) lowerIC <- ex_IC$lowerIC upperIC <- ex_IC$upperIC X <- ex_IC[, -c(1:2)] system.time(result <- unpencoxIC(lowerIC, upperIC, X)) result # main result baseline(result) # obtaining the baseline cumulative hazard estimate plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function ## Use the parallel computing to reduce computational times library(parallel) cl <- makeCluster(2L) # making the cluster object 'cl' with two CPU cores system.time(result <- unpencoxIC(lowerIC, upperIC, X, cl = cl)) on.exit() ### Getting the unpenalized NPMLE for interval censored and left truncated data ## Try following codes with the 'ex_ICLT' data example data(ex_ICLT) lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result2 <- unpencoxIC(lowerIC, upperIC, X, trunc) result2 baseline(result2) plot(result2) plot(result2, what = "survival")library(ALassoSurvIC) ### Getting the unpenalized NPMLE for interval censored data data(ex_IC) lowerIC <- ex_IC$lowerIC upperIC <- ex_IC$upperIC X <- ex_IC[, -c(1:2)] system.time(result <- unpencoxIC(lowerIC, upperIC, X)) result # main result baseline(result) # obtaining the baseline cumulative hazard estimate plot(result) # plotting the estimated baseline cumulative hazard function by default plot(result, what = "survival") # plotting the estimated baseline survival function ## Use the parallel computing to reduce computational times library(parallel) cl <- makeCluster(2L) # making the cluster object 'cl' with two CPU cores system.time(result <- unpencoxIC(lowerIC, upperIC, X, cl = cl)) on.exit() ### Getting the unpenalized NPMLE for interval censored and left truncated data ## Try following codes with the 'ex_ICLT' data example data(ex_ICLT) lowerIC <- ex_ICLT$lowerIC upperIC <- ex_ICLT$upperIC trunc <- ex_ICLT$trunc X <- ex_ICLT[, -c(1:3)] result2 <- unpencoxIC(lowerIC, upperIC, X, trunc) result2 baseline(result2) plot(result2) plot(result2, what = "survival")