vus_mar {bcROCsurface}

Estimation methods for volume under ROC surface (VUS) under MAR

Description

vus_mar computes bias-corrected estimates of the volume under the ROC surface for evaluating the accuracy of a continuous diagnostic test.

Usage

vus_mar(
  method = "full",
  diag_test,
  dise_vec,
  veri_stat,
  rho_est = NULL,
  pi_est = NULL,
  ci = TRUE,
  ci_level = ifelse(ci, 0.95, NULL),
  boot = FALSE,
  n_boot = ifelse(ci, 250, NULL),
  parallel = FALSE,
  ncpus = ifelse(parallel, detectCores()/2, NULL),
  trace = TRUE
)

Arguments

method

name of bias-corrected estimation method to be used for estimating the VUS in presence of verification bias. See rocs for more details.

diag_test

a numeric vector containing the diagnostic test values. NA values are not admitted.

dise_vec

a n * 3 binary matrix with the three columns, corresponding to 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.

ci

a logical value. If TRUE (default), computes an confidence interval of VUS and tests the null hypothesis H0: VUS = 1/6.

ci_level

an confidence level to be used for constructing the confidence interval; default 0.95.

boot

a logical value. Default = FALSE. If set to TRUE, a bootstrap resampling is employed to estimate the asymptotic variance of bias-corrected VUS estimates. See asy_var_vus.

n_boot

the number of bootstrap replicates, which is used for FULL or KNN estimator, or option boot = TRUE. Usually this will be a single positive integer.

parallel

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

ncpus

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

trace

a logical value. If TRUE, tracing information on the progress of the estimation is produced.

Details

The function implements five bias-corrected estimation methods in To Duc et al. (2016, 2020) for estimating VUS of a three-class continuous diagnostic test in presence of verification bias. The estimators are full imputation (FI), mean score imputation (MSI), inverse probability weighted (IPW), semiparametric efficient (SPE) and K nearest-neighbor (KNN), see rocs. These estimators work under MAR assumption.

The standard error of the estimates are obtained through the function asy_var_vus. In particular, the standard error of the FULL estimate is computed by bootstrap resampling method or by Jackknife approach proposed in Guangming et al. (2013). For the bias-corrected estimates, the standard errors are computed by using asymptotic theory (with respect to FI, MSI, IPW and SPE estimator) or bootstrap resampling method (with respect to KNN estimator). A confidence interval for VUS also is given. A logit transformation is also applied for obtaining the confidence interval.

The default value of the number of bootstrap replicates is 250.

Note that, before apply the functions vus_mar, the use of pre_data might be needed to check the monotone ordering disease classes and to create the matrix format for disease status.

Value

vus_mar returns an object of class inheriting from "vus_mar" class.

The function print.vus_mar can be used to print a summary of the results.

An object of class "vus_mar" is a list containing at least the following components:

vus_fit

the estimate of VUS.

std

the standard error, obtained by using asymptotic theory or bootstrap resampling method.

call

the matched call.

t_stat

t-statistic.

p_val_norm

p-value correspond to normal-test.

ci_norm

the confidence interval of VUS by using normal approximation.

ci_logit

the confidence interval of VUS via logit transform.

ci_level

the confidence level used.

boot

the value of boot.

n_boot

the number of bootstrap replicates used.

In addition, the name of method used to estimate VUS also is given as the attribute of vus_fit.

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)
head(EOC)


## Not run: 
# FULL data estimator
dise_full <- pre_data(EOC$D.full, EOC$CA125)
dise_vec_full <- dise_full$dise_vec
vus_mar("full", diag_test = EOC$CA125, dise_vec = dise_vec_full)

## End(Not run)

## Not run: 
# 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
# FI estimator
rho_out <- rho_mlogit(dise_fact_na ~ CA125 + CA153 + Age, data = EOC,
                      test = TRUE)

vus_mar("fi", diag_test = EOC$CA125, dise_vec = dise_vec_na,
        veri_stat = EOC$V, rho_est = rho_out)

# MSI estimator
vus_mar("msi", 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)
vus_mar("ipw", diag_test = EOC$CA125, dise_vec = dise_vec_na,
        veri_stat = EOC$V, pi_est = pi_out)

# SPE estimator
vus_mar("spe", diag_test = EOC$CA125, dise_vec = dise_vec_na,
        veri_stat = EOC$V, rho_est = rho_out, pi_est = pi_out)

# KNN estimator, K = 1, Mahalanobis distance
x_mat <- cbind(EOC$CA125, EOC$CA153, EOC$Age)
rho_maha_1nn <- rho_knn(x_mat = x_mat, dise_vec = dise_vec_na,
                        veri_stat = EOC$V, k = 1, type = "mahala")
vus_mar("knn", diag_test = EOC$CA125, dise_vec = dise_vec_na,
        veri_stat = EOC$V, rho_est = rho_maha_1nn)

## End(Not run)