Description Usage Arguments Details Value Author(s) References See Also Examples
Inverse Probability of Censoring Weighting (IPCW) estimation of Cumulative/Dynamic timedependent ROC curve. The function works in the usual survival setting as well as in the competing risks setting. Computation of the iidrepresentation of areas under timedependent ROC curves is implemented. This enables computation of inference procedures: Confidence intervals and tests for comparing two AUCs of two different markers measured on the same subjects.
1 2 
T 
The vector of (censored) eventtimes. 
delta 
The vector of event indicators at the corresponding value of the vector 
marker 
The vector of the marker values for which we want to compute the timedependent ROC curves. Without loss of generality, the function assumes that larger values of the marker are associated with higher risks of events. If lower values of the marker are associated with higher risks of events, then reverse the association adding a minus to the marker values. 
other_markers 
A matrix that contains values of other markers that we want to take into account for computing the inverse probability of censoring weights. The different columns represent the different markers. This argument is optional, and ignored if 
cause 
The value of the event indicator that represents the event of interest for which we aim to compute the timedependent ROC curve. Without competing risks, it must be the value that indicates a noncensored obsevation (usually 
weighting 
The method used to compute the weights. 
times 
The vector of times points "t" at which we want to compute the timedependent ROC curve. If vector 
ROC 
A logical value that indicates if we want to save the estimates of
sensitivities and specificties. Default value is 
iid 
A logical value that indicates if we want to compute the iidrepresentation of the area under timedependent ROC curve estimator. 
This function computes Inverse Probability of Censoring Weighting (IPCW) estimates of Cumulative/Dynamic timedependent ROC curve.
By definition, timedependent ROC curve intrinsically depends on the definitions of timedependent cases and controls.
Let T_i denote the event time of the subject i.
Without competing risks : A case is defined as a subject i with T_i <=t. A control is defined as a subject i with T_i > t.
With competing risks : In this setting, subjects may undergo different type of events, denoted by δ_i in the following. Let suppose that we are interested in the event δ_i=1. Then, a case is defined as a subject i with T_i <=t and δ_i = 1.
With competing risks, two definitions of controls were suggested: (i) a control is defined as a subject i that is free of any event, i.e with T_i > t, and (ii) a control is defined as a subject i that is not a case, i.e with T_i > t or with T_i <=t and δ_i != 1 .
For all outputs of this package, objects named with _1
refer to definition (i). For instance AUC_1
or se_1
refer to timedependent area under the ROC curve and its estimated standard error according to the definition (i). Objects named with _2
refer to definition (ii) .
Object of class "ipcwsurvivalROC" or "ipcwcompetingrisksROC", depending on if there is competing risk or not, that is a list. For these classes, there are print, plot and confint methods. Most objects that they contain are similar, but some are specific to each class.
Specific objects of class "ipcwsurvivalROC" :
AUC
: vector of timedependent AUC estimates at each time points.
TP
: matrix of timedependent True Positive fraction (sensitivity) estimates.
FP
: matrix of timedependent False Positive fraction (1specificity) estimates.
Specific objects of class "ipcwcompetingrisksROC" :
AUC_1
: vector of timedependent AUC estimates at each time points with definition (i) of controls (see Details).
AUC_2
: vector of timedependent AUC estimates at each time points with definition (ii) of controls (see Details).
TP
: matrix of timedependent True Positive fraction (sensitivity) estimates.
FP_1
: matrix of timedependent False Positive fraction (1specificity) estimates with definition (i) of controls (see Details).
FP_2
: matrix of timedependent False Positive fraction (1specificity) estimates with definition (ii) of controls (see Details).
Objects common to both classes :
times
: the time points for which the timedependent ROC curves were computed.
weights
: a object of class "IPCW", containing all informations about the weights. See ipcw
function of pec
package.
computation_time
: the total computation time.
CumulativeIncidence
: the vector of estimated probabilities of being a case at each time points.
survProb
: the vector of estimated probabilities of being eventfree at each time points.
Stats
: a matrix containing descriptive statistics at each time points (like numbers of observed cases or censored observations before each time points).
iid
: the logical value of parameter iid
used in argument.
n
: the sample size, after having omitted missing vaues.
inference
: a list that contains, among other things, iidrepresentations and estimated standard errors of the estimators, and that is used for computation of comparison tests and confidence intervals.
computation_time
: the computation time, in seconds.
Paul Blanche pabl@sund.ku.dk
Hung, H. and Chiang, C. (2010). Estimation methods for timedependent AUC with survival data. Canadian Journal of Statistics, 38(1):826
Uno, H., Cai, T., Tian, L. and Wei, L. (2007). Evaluating prediction rules for tyears survivors with censored regression models. Journal of the American Statistical Association, 102(478):527537.
Blanche, P., Dartigues, J. F., & JacqminGadda, H. (2013). Estimating and comparing timedependent areas under receiver operating characteristic curves for censored event times with competing risks. Statistics in medicine, 32(30), 53815397.
P. Blanche, A. Latouche, V. Viallon (2013). Timedependent AUC with rightcensored data: A Survey. Risk Assessment and Evaluation of Predictions, 239251, Springer, http://arxiv.org/abs/1210.6805.
compare
for testing a difference of timedependent AUCs.
confint
for confidence intervals of timedependent AUC.
SeSpPPVNPV
for estimating Sensitivity (Se), Specificity (Sp), Positive Predictive
Value (PPV) and Negative Predictive Value (NPV) at a given cutpoint
marker value.
plot
for plotting timedependent ROC curves.
plotAUCcurve
for plotting timedependent AUC curve.
plotAUCcurveDiff
for plotting the curve of the
difference of two timedependent AUCs over time.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51  ##Without competing risks
library(survival)
data(pbc)
head(pbc)
pbc<pbc[!is.na(pbc$trt),] # select only randomised subjects
pbc$status<as.numeric(pbc$status==2) # create event indicator: 1 for death, 0 for censored
# we evaluate bilirubin as a prognostic biomarker for death.
# 1) with the KaplanMeier estimator for computing the weights (default).
ROC.bili.marginal<timeROC(T=pbc$time,
delta=pbc$status,marker=pbc$bili,
cause=1,weighting="marginal",
times=quantile(pbc$time,probs=seq(0.2,0.8,0.1)),
iid=TRUE)
ROC.bili.marginal
# 2) with a Cox model (with covariates bili, chol and albumin) for computing the weights.
ROC.bili.cox<timeROC(T=pbc$time,
delta=pbc$status,marker=pbc$bili,
other_markers=as.matrix(pbc[,c("chol","albumin")]),
cause=1,weighting="cox",
times=quantile(pbc$time,probs=seq(0.2,0.8,0.1)))
ROC.bili.cox
##With competing risks
#Example with Melano data
data(Melano)
# Evaluate tumor thickness as a prognostic biomarker for
# death from malignant melanoma.
ROC.thick<timeROC(T=Melano$time,delta=Melano$status,
weighting="aalen",
marker=Melano$thick,cause=1,
times=c(1800,2000,2200))
ROC.thick
#Example with Paquid data
data(Paquid)
# evaluate DDST cognitive score as a prognostic tool for
# dementia onset, accounting for death without dementia competing risk.
ROC.DSST<timeROC(T=Paquid$time,delta=Paquid$status,
marker=Paquid$DSST,cause=1,
weighting="cox",
other_markers=as.matrix(Paquid$MMSE),
times=c(3,5,10),ROC=TRUE)
ROC.DSST
plot(ROC.DSST,time=5)

id time status trt age sex ascites hepato spiders edema bili chol
1 1 400 2 1 58.76523 f 1 1 1 1.0 14.5 261
2 2 4500 0 1 56.44627 f 0 1 1 0.0 1.1 302
3 3 1012 2 1 70.07255 m 0 0 0 0.5 1.4 176
4 4 1925 2 1 54.74059 f 0 1 1 0.5 1.8 244
5 5 1504 1 2 38.10541 f 0 1 1 0.0 3.4 279
6 6 2503 2 2 66.25873 f 0 1 0 0.0 0.8 248
albumin copper alk.phos ast trig platelet protime stage
1 2.60 156 1718.0 137.95 172 190 12.2 4
2 4.14 54 7394.8 113.52 88 221 10.6 3
3 3.48 210 516.0 96.10 55 151 12.0 4
4 2.54 64 6121.8 60.63 92 183 10.3 4
5 3.53 143 671.0 113.15 72 136 10.9 3
6 3.98 50 944.0 93.00 63 NA 11.0 3
TimedependentRoc curve estimated using IPCW (n=312, without competing risks).
Cases Survivors Censored AUC (%) se
t=999.2 53 249 10 83.96 2.91
t=1307.4 68 218 26 85.66 2.56
t=1839.5 86 156 70 88.03 2.25
t=2555.7 102 94 116 83.41 3.17
t=3039 108 63 141 80.79 3.48
Method used for estimating IPCW:marginal
Total computation time : 0.55 secs.
TimedependentRoc curve estimated using IPCW (n=284, without competing risks).
Cases Survivors Censored AUC (%)
t=999.2 48 226 10 83.90
t=1307.4 60 198 26 86.07
t=1839.5 76 139 69 87.57
t=2555.7 92 83 109 82.81
t=3039 98 57 129 80.11
Method used for estimating IPCW:cox
Total computation time : 1.27 secs.
TimedependentRoc curve estimated using IPCW (n=205, with competing risks).
Cases Survivors Other events Censored AUC_1 (%) AUC_2 (%)
t=1800 45 124 9 27 76.60 75.71
t=2000 46 103 10 46 76.19 74.97
t=2200 50 83 11 61 73.43 72.45
Method used for estimating IPCW:aalen
Total computation time : 0.06 secs.
TimedependentRoc curve estimated using IPCW (n=2561, with competing risks).
Cases Survivors Other events Censored AUC_1 (%) AUC_2 (%)
t=3 70 2117 194 180 80.83 79.85
t=5 122 1834 313 292 79.55 77.65
t=10 318 1107 545 591 76.40 71.93
Method used for estimating IPCW:cox
Total computation time : 1.16 secs.
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