| Title: | Estimating Time-Dependent ROC Curve and AUC for Censored Data |
|---|---|
| Description: | Contains functions to estimate a smoothed and a non-smoothed (empirical) time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve and the optimal cutoff point for the right and interval censored survival data. See Beyene and El Ghouch (2020)<doi:10.1002/sim.8671> and Beyene and El Ghouch (2022) <doi:10.1002/bimj.202000382>. |
| Authors: | Kassu Mehari Beyene [aut, cre], Anouar El Ghouch [aut, ths] |
| Maintainer: | Kassu Mehari Beyene <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.0.0 |
| Built: | 2024-12-14 06:50:39 UTC |
| Source: | CRAN |
This function computes the time-dependent ROC curve for right censored survival data using the cumulative sensitivity and dynamic specificity definitions. The ROC curves can be either empirical (non-smoothed) or smoothed with/wtihout boundary correction. It also calculates the time-dependent area under the ROC curve (AUC).
cenROC(Y, M, censor, t, U = NULL, h = NULL, bw = "NR", method = "tra", ktype = "normal", ktype1 = "normal", B = 0, alpha = 0.05, plot = "TRUE")cenROC(Y, M, censor, t, U = NULL, h = NULL, bw = "NR", method = "tra", ktype = "normal", ktype1 = "normal", B = 0, alpha = 0.05, plot = "TRUE")
Y |
The numeric vector of event-times or observed times. |
M |
The numeric vector of marker values for which the time-dependent ROC curves is computed. |
censor |
The censoring indicator, |
t |
A scaler time point at which the time-dependent ROC curve is computed. |
U |
The vector of grid points where the ROC curve is estimated. The default is a sequence of |
h |
A scaler for the bandwidth of Beran's weight calculaions. The defualt is the value obtained by using the method of Sheather and Jones (1991). |
bw |
A character string specifying the bandwidth estimation method for the ROC itself. The possible options are " |
method |
The method of ROC curve estimation. The possible options are " |
ktype |
A character string giving the type kernel distribution to be used for smoothing the ROC curve: " |
ktype1 |
A character string specifying the desired kernel needed for Beran weight calculation. The possible options are " |
B |
The number of bootstrap samples to be used for variance estimation. The default is |
alpha |
The significance level. The default is |
plot |
The logical parameter to see the ROC curve plot. The default is |
The empirical (non-smoothed) ROC estimate and the smoothed ROC estimate with/without boundary correction can be obtained using this function.
The smoothed ROC curve estimators require selecting two bandwidth parametrs: one for Beran’s weight calculation and one for smoothing the ROC curve.
For the latter, three data-driven methods: the normal reference "NR", the plug-in "PI" and the cross-validation "CV" were implemented.
To select the bandwidth parameter needed for Beran’s weight calculation, by default, the plug-in method of Sheather and Jones (1991) is used but it is also possible introduce a numeric value.
See Beyene and El Ghouch (2020) for details.
Returns the following items:
ROC The vector of estimated ROC values. These will be numeric numbers between zero
and one.
U The vector of grid points used.
AUC A data frame of dimension . The columns are: AUC, standard error of AUC, the lower
and upper limits of bootstrap CI.
bw The computed value of bandwidth. For the empirical method this is always NA.
Dt The vector of estimated event status.
M The vector of Marker values.
Kassu Mehari Beyene and Anouar El Ghouch
Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.
Sheather, S. J. and Jones, M. C. (1991). A Reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological) 53(3): 683–690.
library(cenROC) data(mayo) est = cenROC(Y=mayo$time, M=mayo$mayoscore5, censor=mayo$censor, t=365*6) est$AUClibrary(cenROC) data(mayo) est = cenROC(Y=mayo$time, M=mayo$mayoscore5, censor=mayo$censor, t=365*6) est$AUC
This function computes the data-driven bandwidth for smoothing the ROC (or distribution) function using the CV method of Beyene and El Ghouch (2020). This is an extension of the classical (unweighted) cross-validation bandwith selection method to the case of weighted data.
CV(X, wt, ktype = "normal")CV(X, wt, ktype = "normal")
X |
The numeric data vector. |
wt |
The non-negative weight vector. |
ktype |
A character string giving the type kernel to be used: " |
Bowman et al (1998) proposed the cross-validation bandwidth selection method for unweighted kernal smoothed distribution function. This method is implemented in the R package kerdiest.
We adapted this for the case of weighted data by incorporating the weight variable into the cross-validation function of Bowman's method. See Beyene and El Ghouch (2020) for details.
Returns the computed value for the bandwith parameter.
Kassu Mehari Beyene and Anouar El Ghouch
Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.
Bowman A., Hall P. and Trvan T.(1998). Bandwidth selection for the smoothing of distribution functions. Biometrika 85:799-808.
Quintela-del-Rio, A. and Estevez-Perez, G. (2015). kerdiest: Nonparametric kernel estimation of the distribution function, bandwidth selection and estimation of related functions. R package version 1.2.
library(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Cross-validation bandwidth selection CV(X = X, wt = wt)$bwlibrary(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Cross-validation bandwidth selection CV(X = X, wt = wt)$bw
This data contains the marker values with the left and right limits of the observed time for the subjects in NASA Hypobaric Decompression Sickness Data.
data(hds)data(hds)
This is a data frame with 238 observations and 3 variables: L (left limit of the observed time), R (right limit of the observed time) and M (marker). The marker is a score derived by combining the covariates Age, Sex, TR360, and Noadyn.
Beyene, K. M. and El Ghouch A. (2022). Time-dependent ROC curve estimation for interval-censored data. Biometrical Journal, 64, 1056– 1074.
This function computes the time-dependent ROC curve for interval censored survival data using the cumulative sensitivity and dynamic specificity definitions. The ROC curves can be either empirical (non-smoothed) or smoothed with/without boundary correction. It also calculates the time-dependent AUC.
IntROC(L, R, M, t, U = NULL, method = "emp", method2 = "pa", dist = "weibull", bw = NULL, ktype = "normal", len = 151, B = 0, alpha = 0.05, plot = "TRUE")IntROC(L, R, M, t, U = NULL, method = "emp", method2 = "pa", dist = "weibull", bw = NULL, ktype = "normal", len = 151, B = 0, alpha = 0.05, plot = "TRUE")
L |
The numericvector of left limit of observed time. For left censored observations |
R |
The numericvector of right limit of observed time. For right censored observation |
M |
The numeric vector of marker values. |
t |
A scaler time point used to calculate the ROC curve. |
U |
The numeric vector of cutoff values. |
method |
The method of ROC curve estimation. The possible options are " |
method2 |
A character indication type of modeling. This include nonparametric |
dist |
A character incating the type of distribution for parametric model. This includes are |
bw |
A character string specifying the bandwidth estimation method. The possible options are " |
ktype |
A character string giving the type kernel distribution to be used for smoothing the ROC curve: " |
len |
The length of the grid points for ROC estimation. Default is |
B |
The number of bootstrap samples to be used for variance estimation. The default is |
alpha |
The significance level. The default is |
plot |
The logigal parameter to see the ROC curve plot. Default is |
This function implments time-dependent ROC curve and the corresponding AUC using the model-band and nonparametric for the estimation of conditional survival function. The empirical (non-smoothed) ROC estimate and the smoothed ROC estimate with/without boundary correction can be obtained using this function.
The smoothed ROC curve estimators require selecting a bandwidth parametr for smoothing the ROC curve. To this end, three data-driven methods: the normal reference "NR", the plug-in "PI" and the cross-validation "CV" were implemented.
See Beyene and El Ghouch (2020) for details.
Returns the following items:
ROC The vector of estimated ROC values. These will be numeric numbers between zero
and one.
U The vector of grid points used.
AUC A data frame of dimension . The columns are: AUC, standard error of AUC, the lower
and upper limits of bootstrap CI.
bw The computed value of bandwidth. For the empirical method this is always NA.
Dt The vector of estimated event status.
M The vector of Marker values.
Beyene, K. M. and El Ghouch A. (2022). Time-dependent ROC curve estimation for interval-censored data. Biometrical Journal, 64, 1056– 1074.
Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.
library(cenROC) data(hds) est = IntROC(L=hds$L, R=hds$R, M=hds$M, t=2) est$AUClibrary(cenROC) data(hds) est = IntROC(L=hds$L, R=hds$R, M=hds$M, t=2) est$AUC
Two marker values with event time and censoring status for the subjects in Mayo PBC data.
data(mayo)data(mayo)
A data frame with 312 observations and 4 variables: time (event time/censoring time), censor (censoring indicator), mayoscore4, mayoscore5. The two scores are derived from 4 and 5 covariates respectively.
Heagerty, P. J., and Zheng, Y. (2005). Survival model predictive accuracy and ROC curves. Biometrics, 61(1), 92-105.
This function computes the data-driven bandwidth for smoothing the ROC (or distribution) function using the NR method of Beyene and El Ghouch (2020). This is an extension of the classical (unweighted) normal reference bandwith selection method to the case of weighted data.
NR(X, wt, ktype = "normal")NR(X, wt, ktype = "normal")
X |
The numeric data vector. |
wt |
The non-negative weight vector. |
ktype |
A character string giving the type kernel to be used: " |
See Beyene and El Ghouch (2020) for details.
Returns the computed value for the bandwith parameter.
Kassu Mehari Beyene and Anouar El Ghouch
Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.
library(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Normal reference bandwidth selection NR(X = X, wt = wt)$bwlibrary(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Normal reference bandwidth selection NR(X = X, wt = wt)$bw
This function computes the data-driven bandwidth for smoothing the ROC (or distribution) function using the PI method of Beyene and El Ghouch (2020). This is an extension of the classical (unweighted) direct plug-in bandwith selection method to the case of weighted data.
PI(X, wt, ktype = "normal")PI(X, wt, ktype = "normal")
X |
The numeric vector of random variable. |
wt |
The non-negative weight vector. |
ktype |
A character string giving the type kernel to be used: " |
See Beyene and El Ghouch (2020) for details.
Returns the computed value for the bandwith parameter.
Kassu Mehari Beyene and Anouar El Ghouch
Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.
library(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Plug-in bandwidth selection PI(X = X, wt = wt)$bwlibrary(cenROC) X <- rnorm(100) # random data vector wt <- runif(100) # weight vector ## Plug-in bandwidth selection PI(X = X, wt = wt)$bw
This function computes the optimal cutoff point using the Youden index criteria of both right and interval censored time-to-event data. The Youden index estimator can be either empirical (non-smoothed) or smoothed with/without boundary correction.
youden(est, plot = "FALSE")youden(est, plot = "FALSE")
est |
The object returned either by |
plot |
The logical parameter to see the ROC curve plot along with the Youden inex. The default is |
In medical decision-making, obtaining the optimal cutoff value is crucial to identify subject at high risk of experiencing the event of interest. Therefore, it is necessary to select a marker value that classifies subjects into healthy and diseased groups. To this end, in the literature, several methods for selecting optimal cutoff point have been proposed. In this package, we only included the Youden index criteria.
Returns the following items:
Youden.index The maximum Youden index value.
cutopt The optimal cutoff value.
sens The sensitivity corresponding to the optimal cutoff value.
spec The specificity corresponding to the optimal cutoff value.
Beyene, K. M. and El Ghouch A. (2022). Time-dependent ROC curve estimation for interval-censored data. Biometrical Journal, 64, 1056– 1074.
Youden, W.J. (1950). Index for rating diagnostic tests. Cancer 3, 32–35.
library(cenROC) # Right censored data data(mayo) resu <- cenROC(Y=mayo$time, M=mayo$mayoscore5, censor=mayo$censor, t=365*6, plot="FALSE") youden(resu, plot="TRUE") # Interval censored data data(hds) resu1 = IntROC(L=hds$L, R=hds$R, M=hds$M, t=2) youden(resu1, plot="TRUE")library(cenROC) # Right censored data data(mayo) resu <- cenROC(Y=mayo$time, M=mayo$mayoscore5, censor=mayo$censor, t=365*6, plot="FALSE") youden(resu, plot="TRUE") # Interval censored data data(hds) resu1 = IntROC(L=hds$L, R=hds$R, M=hds$M, t=2) youden(resu1, plot="TRUE")