asy_var_vus: Asymptotic variance estimation for VUS

In bcROCsurface: Bias-Corrected Methods for Estimating the ROC Surface of Continuous Diagnostic Tests

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)
)

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.

Value

asy_var_vus returns a estimated value of the asymptotic variance.

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)

bcROCsurface documentation built on Sept. 9, 2023, 9:07 a.m.