asy_cov_tcf {bcROCsurface}

Asymptotic variance-covariance estimation for True Class Fractions (TCFs) at the cut point (c_1, c_2)

Description

asy_cov_tcf computes the asymptotic variance-covariance matrix of full data (FULL) and bias-corrected estimators (i.e. full imputation, mean score imputation, inverse probability weighting, semiparametric efficient and K nearest neighbor) of TCFs.

Usage

asy_cov_tcf(
  obj_tcf,
  diag_test,
  dise_vec,
  veri_stat = NULL,
  rho_est = NULL,
  pi_est = NULL,
  boot = FALSE,
  n_boot = 250,
  parallel = FALSE,
  ncpus = ifelse(parallel, detectCores()/2, NULL)
)

Arguments

obj_tcf

a result of a call to rocs.tcf.

diag_test

a numeric vector containing the diagnostic test values. NA values of diag_test are not accepted.

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).

rho_est

a result of a call to rho_mlogit of rho_knn to fit the disease model.

pi_est

a result of a call to psglm to fit the verification model.

boot

a logical value. Default = FALSE. If set to TRUE, a bootstrap resampling is employed to estimate the asymptotic variance-covariance matrix of bias-corrected TCFs.

n_boot

the number of bootstrap replicates, used when boot = TRUE or for FULL estimator. Usually this will be a single positive integer. Default 250.

parallel

a logical value. If TRUE, a parallel computing is employed in the bootstrap resampling process.

ncpus

number of processes to be used in parallel computing. Default is half of available cores.

Details

For bias-corrected estimators of TCFs, the asymptotic variance-covariance matrix at a fixed cut point is estimated by using the Delta method. The function asy_cov_tcf implements the explicit forms presented in To Duc et al. (2016, 2020). In addition, the bootstrap procedure is also available.

For FULL estimator, the asymptotic variance-covariance matrix is computed via bootstrap only.

Value

This function returns an estimated asymptotic variance-covariance matrix for FULL estimator and bias-corrected estimators of TCFs at a fixed cut point.

References

To Duc, K., Chiogna, M. and Adimari, G. (2016) Bias-corrected methods for estimating the receiver operating characteristic surface of continuous diagnostic tests. Electronic Journal of Statistics, 10, 3063-3113.

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)

# FULL data estimator
dise_full <- pre_data(EOC$D.full, EOC$CA125)
dise_vec_full <- dise_full$dise_vec

full_tcf <- rocs.tcf("full", diag_test = EOC$CA125, dise_vec = dise_vec_full,
                     cps = c(2, 4))
full_var <- asy_cov_tcf(full_tcf, diag_test = EOC$CA125,
                        dise_vec = dise_vec_full)

# Preparing the missing disease status
dise_na <- pre_data(EOC$D, EOC$CA125)
dise_vec_na <- dise_na$dise_vec
dise_fact_na <- dise_na$dise

rho_out <- rho_mlogit(dise_fact_na ~ CA125 + CA153 + Age, data = EOC,
                      test = TRUE)

## FI estimator
fi_tcf <- rocs.tcf("fi", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                   veri_stat = EOC$V, rho_est = rho_out, cps = c(2, 4))
fi_var <- asy_cov_tcf(fi_tcf, diag_test = EOC$CA125, dise_vec = dise_vec_na,
                      veri_stat = EOC$V, rho_est = rho_out)

## MSI estimator
msi_tcf <- rocs.tcf("msi", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                    veri_stat = EOC$V, rho_est = rho_out, cps = c(2, 4))
msi_var <- asy_cov_tcf(msi_tcf, diag_test = EOC$CA125,
                       dise_vec = dise_vec_na, veri_stat = EOC$V,
                       rho_est = rho_out)

## IPW estimator
pi_out <- psglm(V ~ CA125 + CA153 + Age, data = EOC, test = TRUE)

ipw_tcf <- rocs.tcf("ipw", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                    veri_stat = EOC$V, pi_est = pi_out, cps = c(2, 4))
ipw_var <- asy_cov_tcf(ipw_tcf, diag_test = EOC$CA125,
                       dise_vec = dise_vec_na, veri_stat = EOC$V,
                       pi_est = pi_out)

## SPE estimator
spe_tcf <- rocs.tcf("spe", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                    veri_stat = EOC$V, rho_est = rho_out, pi_est = pi_out,
                    cps = c(2, 4))
spe_var <- asy_cov_tcf(spe_tcf, diag_test = EOC$CA125,
                       dise_vec = dise_vec_na, veri_stat = EOC$V,
                       rho_est = rho_out, pi_est = pi_out)

## KNN estimators
x_mat <- cbind(EOC$CA125, EOC$CA153, EOC$Age)
rho_1nn <- rho_knn(x_mat = x_mat, dise_vec = dise_vec_na, veri_stat = EOC$V,
                   k = 1, type = "mahala")
knn_tcf <- rocs.tcf("knn", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                    veri_stat = EOC$V, rho_est = rho_1nn, cps = c(2, 4))
knn_var <- asy_cov_tcf(knn_tcf, diag_test = EOC$CA125,
                       dise_vec = dise_vec_na, veri_stat = EOC$V,
                       rho_est = rho_1nn)