timeROC (version 0.4)

SeSpPPVNPV: Time-dependent Sensitivity (Se), Specificity (Sp), Positive Predictive Value (PPV) and Negative Predictive Value (NPV) estimation

Description

This function aim at estimating time-dependent Sensitivity (Se), Specificity (Sp), Positive Predictive Value (PPV) and Negative Predictive Value (NPV) at a given cutpoint. Standard error computation via iid-representation of the estimator is also implemented.

Usage

SeSpPPVNPV(cutpoint, T, delta, marker, other_markers = NULL, cause,
           weighting = "marginal", times, iid = FALSE)

Arguments

cutpoint

The cutpoint for maker value at which we aim at estimating Se, Sp, PPV and NPV.

T

The vector of (censored) event-times.

delta

The vector of event indicators at the corresponding value of the vector T. Censored observations must be denoted by the value 0.

marker

The vector of the marker values for which we want to compute the time-dependent 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 method="marginal". Default value is other_markers=NULL.

cause

The value of the event indicator that represents the event of interest for which we aim to compute the time-dependent ROC curve. Without competing risks, it must be the value that indicates a non-censored obsevation (usually 1). With competing risks, subjects can undergo different type of events; then, it must be the value corresponding to the event of interest, for which we aim to compute the ROC curve (usually 1 or 2).

weighting

The method used to compute the weights. weighting="marginal" uses the Kaplan-Meier estimator of the censoring distribution. weighting="cox" and weighting="aalen" model the censoring by the Cox model and the additive Aalen model respectively. Default value is weighting="marginal".

times

The vector of times points "t" at which we want to compute the time-dependent ROC curve. If vector times contains only a single value, then value zero is added.

iid

A logical value that indicates if we want to compute the iid-representation of the area under time-dependent ROC curve estimator. iid = TRUE is required for computation of all inference procedures (Confidence intervals or test for comparing AUCs). For large sample size (greater than 2000, say) and/or large length of vector times, the computation of the iid representations might be time-consuming.

Value

Object of class "ipcwsurvivalSeSpPPVNPV" or "ipcwcompetingrisksSeSpPPVNPV", 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 "ipcwsurvivalSeSpPPVNPV" :

• TP : vector of time-dependent True Positive fraction (sensitivity) estimates at each time points.

• FP : vector of time-dependent False Positive fraction (1-specificity) estimates at each time points.

• PPV : vector of time-dependent Positive Predictive Value estimates at each time points.

• NPV : vector of time-dependent Negative Predictive Value estimates at each time points.

Specific objects of class "ipcwcompetingrisksSeSpPPVNPV" :

• TP : vector of time-dependent True Positive fraction (sensitivity) estimates at each time points.

• FP_1 : vector of time-dependent False Positive fraction (1-specificity) estimates at each time points with definition (i) of controls (see Details).

• FP_2 : vector of time-dependent False Positive fraction (1-specificity) estimates at each time points with definition (ii) of controls (see Details).

• PPV_1 : vector of time-dependent Positive Predictive Value estimates at each time points with definition (i) of controls (see Details).

• NPV_2 : vector of time-dependent Negative Predictive Value estimates at each time points with definition (ii) of controls (see Details).

Objects common to both classes :

• times : the time points for which Se, Sp, PPV, etc.. were computed.

• cutpoint : the cutpoint for which Se, Sp, PPV, etc.. 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.

• 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, iid-representations and estimated standard errors of the estimators.

• computation_time : the computation time, in seconds.

Details

This function computes Inverse Probability of Censoring Weighting (IPCW) estimates of Sensitivity (Se), Specificity (Sp), Positive Predictive Value (PPV) and Negative Predictive Value (NPV) for Cumulative/Dynamic definition of 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 \(T_i \leq t\). 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 \(\delta_i\) in the following. Let suppose that we are interested in the event \(\delta_i=1\). Then, a case is defined as a subject \(i\) with \(T_i \leq t\) and \(\delta_i=1\). 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 \(T_i \leq t\) and \(\delta_i \neq 1\). For all outputs of this package, objects named with _1 refer to definition (i). For instance AUC_1 or se_1 refer to time-dependent area under the ROC curve and its estimated standard error according to the definition (i). Objects named with _2 refer to definition (ii) .

References

Blanche, P., Dartigues, J. F., & Jacqmin-Gadda, H. (2013). Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks. Statistics in medicine, 32(30), 5381-5397.

See Also

timeROC

Examples

# NOT RUN {
##-------------Without competing risks-------------------
library(survival)
data(pbc)
head(pbc)
pbc<-pbc[!is.na(pbc$trt),] # select only randomised subjects
pbc$status<-as.numeric(pbc$status==2) # create event indicator: 1 for death, 0 for censored     
# Se, Sp, PPV and NPV computation for serum bilirunbin at threshold c=0.9(mg/dl) 
res.SeSpPPVNPV.bili <- SeSpPPVNPV(cutpoint=0.9,
                                  T=pbc$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)
res.SeSpPPVNPV.bili

##-------------With competing risks-------------------

#---------Example with Paquid data--------
data(Paquid)
# Se, Sp, PPV and NPV computation for DSST at threshold c=22
res.SeSpPPVNPV.DSST <- SeSpPPVNPV(cutpoint=22,
                                  T=Paquid$time,
                                  delta=Paquid$status,marker=Paquid$DSST,
                                  cause=1,weighting="cox",
                                  times=c(3,5,8,10))
res.SeSpPPVNPV.DSST

#---------Example with Melano data-------
data(Melano)
# Se, Sp, PPV and NPV computation for tumor thickness at threshold c=3 (1/100 mm)
res.SeSpPPVNPV.thick <- SeSpPPVNPV(cutpoint=3,
                                  T=Melano$time,delta=Melano$status,
                                  weighting="marginal",
                                  marker=Melano$thick,cause=1,
                                  times=c(1800,2000,2200),
                                  iid=TRUE)
res.SeSpPPVNPV.thick
# }