ROC632 (version 0.6)

boot.ROCt: Construction of a prognostic scoring system and estimation of its true diagnostic capacities when the data are incomplete (right censoring)

Description

This function allows the construction of a prognostic signature by using a Cox model with lasso penalty. This function also performs estimations of the corresponding time-dependent ROC curve according to different bootstrap-based approaches.

Usage

boot.ROCt(times, failures, features, N.boot, precision, prop, pro.time, fold.cv, lambda1)

Arguments

times

A numeric vector with the follow up times.

failures

A numeric vector with the event indicators (0=right censored, 1=event).

features

A matrix with the observed features. The number of raw is the number of individuals (equals to the length of the vectors times and failures).

N.boot

Number of bootstrap iterations.

precision

The quintiles of the predictor used for computing each point of the time dependent ROC curve.

prop

This is the proportion of the nearest neighbours used in the Akritas estimator. The estimation will be based on 2*lambda (1 lambda on the left and 1 lambda on the right) of the total sample size.

pro.time

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

lambda1

The fixed values of the tuning parameters for L1 (lasso). If NULL (default value), its value is obtained by cross-validation for the overall sample and at each bootstrap iteration. The reference approach is to re-estimate the tuning parameter and to select the features at each bootstrap iteration. Nevertheless, the 0.632+ estimator appeared to be robust when the tuning was estimated on the full data set and re-used at each step for the features selection. This assumption is associated to an important time-saving. Nevertheless, the complete re-estimation of the model at each iteration remains less open to criticism.

fold.cv

The fold for cross-validation which is only used if lambda1=NULL. By default, A 5-fold cross-validation is implemented.

Value

The function returns a list. AUC is a data frame. The raw(s) represent(s) the value(s) of the prognostic time. train is the mean of the areas obtained by using the individuals included in the bootstrap samples (training). valid is the mean of the areas obtained by using the individuals not included in the bootstrap samples (cross-validation). s632 is the mean of the areas obtained by using the simple 0.632 estimator. p632 is the mean of the areas obtained by using the 0.632+ estimator. ROC.Apparent, ROC.CV, ROC.632 and ROC.632p are 4 data frames in which the false negative and positive rates are presented respectively for the 4 estimators: apparent, bootstrap and cross-validation, bootstrap 0.632 and bootstrap 0.632+. These rates correspond to the thresholds defined in cut.values. Coef is a vector of the regression coefficients obtained in the Cox model with lasso penalty obtained by using all the subject. The value of the tuning parameter equals to Lambda. This model is contained in the object Model. This object is obtained by using the function penalized() in the R package penalized. Please, look at the corresponding help for more details about the object Model. Finally, the signature represents the prognostic score for each subject, i.e. the sum of the regression multiplied by the value of the features.

Details

This function deals with right-censored data. First, this function returns the results of the penalized Cox model. By default, all the corresponding parameters (including the tuning parameter obtained by cross-validation which defined the number of variables selected in the linear predictor) are obtained from the total sample. The user can also define the value of the tuning parameter. Second, because the resulting scoring system may be associated with overfitting, internal validation is needed. At each iteration and based on each bootstrap sample, a Cox model with lasso penalty is estimated. By default, the value of the tuning parameter is also determined by cross-validation on each bootstrap sample. Nevertheless, if lambda1 is defined by the user, the same value is used for all the iterations. The complete methodology is explained by Danger and Foucher (2012).

References

R. Danger and Y. Foucher. Time dependent ROC curves for the estimation of true prognostic capacity of microarray data. Statistical Applications in Genetics and Molecular Biology. 2012 Nov 22;11(6):Article 1.

Examples

# import and attach the data example

data(DLBCLpatients)
data(DLBCLgenes)

# In this exemple, we only reduce the number
# of features, threasholds and iterations for time-saving

DLBCLgenes <- DLBCLgenes[,1:500] # 500 first features
N.iterations <- 2

# If we define a priori the tuning parameter at 15.

res <- boot.ROCt(times=DLBCLpatients$t, failures=DLBCLpatients$f,
 features=DLBCLgenes, N.boot=N.iterations, precision=seq(0.05, 0.95, by=0.30),
 prop=0.02, pro.time=5, lambda1=15)

# The distribution of the prognostic score
hist(res$Signature, nclass=30, main="",
 xlab="Observed values of the multivariate signature")

# Illustrations of the ROC curve
plot(res$ROC.Apparent$FPR, 1-res$ROC.Apparent$FNR,
 type="b", pch=1, lty=1,
 ylab="True Positive Rates",
 xlab="False Positive Rates") 
lines(res$ROC.CV$FPR, 1-res$ROC.CV$FNR,
 type="b", pch=2, lty=2) 
lines(res$ROC.632$FPR, 1-res$ROC.632$FNR,
 type="b", pch=3, lty=3) 
lines(res$ROC.632p$FPR, 1-res$ROC.632p$FNR,
 type="b", pch=4, lty=4) 
legend("bottomright",
 paste(c("Apparent", "CV", "0.632", "0.632+"),
 "curve (AUC=", round(res$AUC,2), ")"), pch=1:4,
 lty=1:4)