Estimates of CVAUC

This function computes K-fold cross-validated estimates of the area under the receiver operating characteristics (ROC) curve (hereafter, AUC). This quantity can be interpreted as the probability that a randomly selected case will have higher predicted risk than a randomly selected control.

cv_auc(
  Y,
  X,
  K = 10,
  learner = "glm_wrapper",
  nested_cv = TRUE,
  nested_K = K - 1,
  parallel = FALSE,
  max_cvtmle_iter = 10,
  cvtmle_ictol = 1/length(Y),
  prediction_list = NULL,
  ...
)

Arguments

Y	A numeric vector of outcomes, assume to equal 0 or 1.
X	A data.frame or matrix of variables for prediction.
K	The number of cross-validation folds (default is 10).
learner	A wrapper that implements the desired method for building a prediction algorithm. See See ?glm_wrapper or read the package vignette for more information on formatting learners.
nested_cv	A boolean indicating whether nested cross validation should be used to estimate the distribution of the prediction function. Default (TRUE) is best choice for aggressive learner's, while FALSE is reasonable for smooth learner's (e.g., logistic regression).
nested_K	If nested cross validation is used, how many inner folds should there be? Default (K-1) affords quicker computation by reusing training fold learner fits.
parallel	A boolean indicating whether prediction algorithms should be trained in parallel. Default to FALSE.
max_cvtmle_iter	Maximum number of iterations for the bias correction step of the CV-TMLE estimator (default 10).
cvtmle_ictol	The CV-TMLE will iterate max_cvtmle_iter is reached or mean of cross-validated efficient influence function is less than cvtmle_ictol.
prediction_list	For power users: a list of predictions made by learner that has a format compatible with cvauc.
...	Other arguments, not currently used

Value

An object of class "cvauc".

est_cvtmle

cross-validated targeted minimum loss-based estimator of K-fold CV AUC

iter_cvtmle

iterations needed to achieve convergence of CVTMLE algorithm

cvtmle_trace

the value of the CVTMLE at each iteration of the targeting algorithm

se_cvtmle

estimated standard error based on targeted nuisance parameters

est_init

plug-in estimate of CV AUC where nuisance parameters are estimated in the training sample

est_empirical

the standard K-fold CV AUC estimator

se_empirical

estimated standard error for the standard estimator

est_onestep

cross-validated one-step estimate of K-fold CV AUC

se_onestep

estimated standard error for the one-step estimator

est_esteq

cross-validated estimating equations estimate of K-fold CV AUC

se_esteq

estimated standard error for the estimating equations estimator (same as for one-step)

folds

list of observation indexes in each validation fold

ic_cvtmle

influence function evaluated at the targeted nuisance parameter estimates

ic_onestep

influence function evaluated at the training-fold-estimated nuisance parameters

ic_esteq

influence function evaluated at the training-fold-estimated nuisance parameters

ic_empirical

influence function evaluated at the validation-fold estimated nuisance parameters

prediction_list

a list of output from the cross-validated model training; see the individual wrapper function documentation for further details

Details

To estimate the AUC of a particular prediction algorithm, K-fold cross-validation is commonly used: data are partitioned into K distinct groups and the prediction algorithm is developed using K-1 of these groups. In standard K-fold cross-validation, the AUC of this prediction algorithm is estimated using the remaining fold. This can be problematic when the number of observations is small or the number of cross-validation folds is large.

Here, we estimate relevant nuisance parameters in the training sample and use the validation sample to perform some form of bias correction -- either through cross-validated targeted minimum loss-based estimation, estimating equations, or one-step estimation. When aggressive learning algorithms are applied, it is necessary to use an additional layer of cross-validation in the training sample to estimate the nuisance parameters. This is controlled via the nested_cv option below.

Examples

# simulate data
n <- 200
p <- 10
X <- data.frame(matrix(rnorm(n*p), nrow = n, ncol = p))
Y <- rbinom(n, 1, plogis(X[,1] + X[,10]))

# get cv auc estimates for logistic regression
cv_auc_ests <- cv_auc(Y = Y, X = X, K = 5, learner = "glm_wrapper")

# get cv auc estimates for random forest
# using nested cross-validation for nuisance parameter estimation
fit <- cv_auc(Y = Y, X = X, K = 5,
              learner = "randomforest_wrapper",
              nested_cv = TRUE)