bcROCsurface (version 1.0-6)

asy_var_vus: Asymptotic variance estimation for VUS

Description

asy_var_vus computes the asymptotic variance 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 VUS.

Usage

asy_var_vus(
  obj_vus,
  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)
)

Value

asy_var_vus returns a estimated value of the asymptotic variance.

Arguments

obj_vus

a result of a call to vus_mar.

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 of the bias-corrected VUS estimators.

n_boot

the number of bootstrap replicates, which is used for FULL or KNN estimators, or option boot = TRUE. The defaut is 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 the FULL estimator, a bootstrap resampling process or Jackknife approach is used to estimate the asymptotic variance, whereas, a bootstrap resampling process is employed to obtain the asymptotic variance of K nearest neighbor estimator.

For the full imputation, mean score imputation, inverse probability weighting and semiparametric efficient estimators of VUS, the asymptotic variances are computed by using the explicit form. Furthermore, a bootstrap procedure is also available, useful in case of small sample sizes.

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.

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.

Guangming, P., Xiping, W. and Wang, Z. (2013) Non-parameteric statistical inference for $P(X < Y < Z)$. Sankhya A, 75, 1, 118-138.

Examples

data(EOC)

# 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)
vus_fi <- vus_mar("fi", diag_test = EOC$CA125, dise_vec = dise_vec_na,
                  veri_stat = EOC$V, rho_est = rho_out, ci = FALSE)
var_fi <- asy_var_vus(vus_fi, diag_test = EOC$CA125, dise_vec = dise_vec_na,
                      veri_stat = EOC$V, rho_est = rho_out)