rho_knn {bcROCsurface}

K nearest-neighbor (KNN) regression

Description

rho_knn uses the KNN approach to estimate the probabilities of the disease status in case of three categories.

Usage

rho_knn(
  x_mat,
  dise_vec,
  veri_stat,
  k,
  type = c("eucli", "manha", "canber", "lagran", "mahala"),
  trace = FALSE
)

Arguments

x_mat

a numeric design matrix.

dise_vec

a n * 3 binary matrix with three columns, corresponding to the three classes of the disease status. In row i, 1 in column j indicates that the i-th subject belongs to class j, with j = 1, 2, 3. A row of NA values indicates a non-verified subject.

veri_stat

a binary vector containing the verification status (1 verified, 0 not verified).

k

an integer value/vector, which indicates the number of nearest neighbors. It should be less than the number of the verification subjects.

type

a distance measure.

trace

switch for tracing estimation process. Default FALSE.

Details

type should be selected as one of "eucli", "manha", "canber", "lagran", "mahala" corresponding to Euclidean, Manhattan, Canberra, Lagrange and Mahalanobis distance. In practice, the selection of a suitable distance is typically dictated by features of the data and possible subjective evaluations. For example, if the covariates are heterogeneous with respect to their variances (which is particularly true when the variables are measured on heterogeneous scales), the choice of the Mahalanobis distance may be a good choice.

For the number of nearest neighbors, a small value of k, within the range 1-3, may be a good choice. In general, the choice of k may depend on the dimension of the feature space, and propose to use cross–validation to find k in case of high–dimensional covariate. See cv_knn.

Value

rho_knn returns a list containing the following components:

values

estimates of the probabilities.

X

a design model matrix.

K

the number of nearest neighbors.

type

the chosen distance.

References

To Duc, K., Chiogna, M. and Adimari, G. (2020) Nonparametric estimation of ROC surfaces in presence of verification bias. REVSTAT-Statistical Journal. 18, 5, 697–720.

Examples

data(EOC)
x_mat <- cbind(EOC$CA125, EOC$CA153, EOC$Age)
dise_na <- pre_data(EOC$D, EOC$CA125)
dise_vec_na <- dise_na$dise_vec

## Euclidean distance, k = 1
out_ecul_1nn <- rho_knn(x_mat, dise_vec_na, EOC$V, k = 1, type = "eucli")

## Manhattan distance, k = 1
out_manh_1nn <- rho_knn(x_mat, dise_vec_na, EOC$V, k = 1, type = "manha")

## Canberra distance, k = 3
out_canb_1nn <- rho_knn(x_mat, dise_vec_na, EOC$V, k = 3, type = "canber")

## Lagrange distance, k = 3
out_lagr_1nn <- rho_knn(x_mat, dise_vec_na, EOC$V, k = 3, type = "lagran")

## Mahalanobis distance, k = c(1,3)
out_maha_13nn <- rho_knn(x_mat, dise_vec_na, EOC$V, k = c(1, 3),
                         type = "mahala")