RISCA (version 0.9)

roc.summary: Summary ROC Curve For Aggregated Data.

Description

This function computes summary ROC curve (Combescure et al., 2016).

Usage

roc.summary(study.num, classe, n, year, surv, nrisk, proba, marker.min,
 marker.max, init.nlme1, precision, pro.time, time.cutoff)

Arguments

study.num

A numeric vector (1,2,3,...) with the study identification.

classe

A numeric vector with integers (1,2,3,...) for identifying the groups defined using the studied marker. 1 is the first group with the lowest values of the marker.

n

A numeric vector with the number of subjects at the baseline (date of marker collection).

year

A numeric vector with the survival times.

surv

A numeric vector with the survival probabilities corresponding to the previous times (often obtained graphically using the published survival curves).

nrisk

A numeric vector with the number of subjects at-risk of the event at the corresponding year.

proba

This numeric vector represents the proportion of the patients in a center which belong to the corresponding group.

marker.min

A numeric vector with the minimum values of the marker interval corresponding to the previous class.

marker.max

A numeric vector with the maximum values of the marker interval corresponding to the previous class.

init.nlme1

A numeric vector with the initiate values (mean, sd) of the maker distribution which is assumed to be Gaussian. Default is (0,1).

precision

A numeric vector with the initiate values (mean, sd) of the maker distribution which is assumed to be Gaussian. Default is \(10^{-6}\).

pro.time

The value of prognostic time is the maximum delay for which the capacity of the variable is evaluated. The same unit than the one used in the argument time.

time.cutoff

The value of internal threasholds for the definition of the piecewise hazard function (3 values for a 4-piece constant function and 4 values for a 5-piece constant function).

Value

nlme1

An object of class nlme representing the nonlinear mixed-effects model of the marker distribution. The marker is assumed Gaussian distributed. mu and sigma represent the mean and the standard deviation. The inter-study variability is modeled with a random effect on the mean. See nlmeObject for the components of the fit.

nlme2

An object of class nlme representing the nonlinear mixed-effects model of the time distribution. The hazard function is a stepwise function with 5 intervals. exp(beta0.1) and exp(beta0.2) represent the baseline hazard and the hazard ratio in the first interval. exp(beta1.1) and exp(beta1.2) represent the corrections of these parameters for the second interval... The inter-study variability is modeled with a random effect on the baseline parameter beta0.1. See nlmeObject for the components of the fit.

table

This data frame presents the sensitivities (se) and specificities (sp) associated with the cut-off values (cut.off).

auc

The area under the SROC curve for a prognostic up to prognostic time.

Details

This function computes summary ROC curve. The hazard function associated with the time-to-event was defined as a 4-piece or a 5-piece constant function with a specific association with the marker at each interval. The maker distribution is assumed to be Gaussian distributed.

References

Combescure et al. A literature-based approach to evaluate the predictive capacity of a marker using time-dependent Summary Receiver Operating Characteristics. Stat Methods Med Res, 25(2):674-85, 2016. <doi: 10.1177/ 0962280212464542>

Examples

# NOT RUN {
# The example is too long to compute for a submission on the CRAN
# Remove the characters '#'

### import and attach the data example
#data(dataKi67)

### Compute the SROC curve for a prognostic up to 9 years
#roc9y<-roc.summary(dataKi67$study.num, dataKi67$classe, dataKi67$n,
# dataKi67$year, dataKi67$surv, dataKi67$nrisk, dataKi67$proba,
# dataKi67$log.marker.min, dataKi67$log.marker.max,
# init.nlme1=c(2.55, -0.29), precision=50, pro.time=9,
# time.cutoff=c(2, 4, 6, 8))

### Compute the SROC curve for a prognostic up to 3 years
#roc3y<-roc.summary(dataKi67$study.num, dataKi67$classe, dataKi67$n,
# dataKi67$year, dataKi67$surv, dataKi67$nrisk, dataKi67$proba,
# dataKi67$log.marker.min, dataKi67$log.marker.max,
# init.nlme1=c(2.55, -0.29), precision=50, pro.time=3,
# time.cutoff=c(2, 4, 6, 8))

### The ROC graph associated to these to SROC curves
#plot(c(1,1-roc9y$table$sp,0), c(1,roc9y$table$se,0),
# xlab="1-specificity", ylab="sensitivity", type="l",
# col=1, lty=1, lwd=2)

#lines(c(1,1-roc3y$table$sp,0), c(1,roc3y$table$se,0), type="l",
# col=2, lty=2, lwd=2)

#legend("bottomright", c(paste("Prognostic up to 9 years (AUC=",
#  round(roc9y$auc,2), ")", sep=""), paste(
#  "Prognostic up to 3 years (AUC=",  round(roc3y$auc,2), ")",
#  sep="")), col=c(1, 2), lty=c(1, 2), lwd=c(2, 2))

### Check of the goodness-of-fit: the observed proportions of
### patients in the $g$th interval of the study $k$ versus the
### fitted proportions (equation 3).
#plot(roc9y$data.marker$proba, roc9y$data.marker$fitted,
# xlab="Observed probabilities", ylab="Fitted probabilities",
# ylim=c(0,1), xlim=c(0,1))
#abline(0,1)

### Check of the goodness-of-fit: the observed bivariate
### probabilities versus the fitted bivariate
### probabilities (equation 4).

#plot(roc9y$data.surv$p.joint, roc9y$data.surv$fitted,
# xlab="Observed probabilities", ylab="Fitted probabilities",
# ylim=c(0,1), xlim=c(0,1))
#abline(0,1)

### Check of the goodness-of-fit: the residuals of the bivariate
### probabilities (equation 4) versus the times.

#plot(roc9y$data.surv$year, roc9y$data.surv$resid,
# xlab="Survival time (years)", ylab="Residuals")
#lines(lowess(roc9y$data.surv$year,
# I(roc9y$data.surv$resid), iter=0))
# }