WDBC

This repository provides the R code used for the real data studies in the below two papers:

1. (wdbc.YI.R) Wang S, Shi S, Qin G. Interval estimation for the Youden index of a continuous diagnostic test with verification biased data. Statistical Methods in Medical Research 2025; 34: 796-811.
2. (wdbc.AUC.R) Wang S, Shi S, Qin G. Empirical likelihood inference for the area under the ROC curve with verification biased data. (2025, Manuscript Under Review)

About WDBC dataset

Wisconsin Diagnostic Breast Cancer (WDBC) dataset was created by Dr. William H. Wolberg, W. Nick Street and Olvi L. Mangasarian from University of Wisconsin in 1995. In this dataset, features were computed from a digitized image of a fine needle aspirate (FNA) of breast masses and the verified diagnosis (malignant or benign) of breast masses were recorded. They describe characteristics of the cell nuclei present in the image. There are 569 instances of breast masses (357 benign, 212 malignant), each has 32 attributes, including their IDs, true diagnoses and 30 real-valued input features. There is no missing value in the dataset. This database is also available on UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29.

Attribute Information:

Column 1: ID number

Column 2: Diagnosis (M = malignant, B = benign)

Column 3-32: Ten real-valued features computed for each cell nucleus, including:

a) radius (mean of distances from center to points on the perimeter)

b) texture (standard deviation of gray-scale values)

c) perimeter

d) area

e) smoothness (local variation in radius lengths)

f) compactness (perimeter^2 / area - 1.0)

g) concavity (severity of concave portions of the contour)

h) concave points (number of concave portions of the contour)

i) symmetry

j) fractal dimension ("coastline approximation" - 1)

The mean, standard error and "worst" or largest (mean of the three largest values) of these features were computed for each image, resulting in 30 features. For instance, field 3 is Mean Radius, field 13 is Radius SE, field 23 is Worst Radius.

All feature values are recoded with four significant digits.

wdbc.new is a subset of the WDBC dataset that we create to be used in our real data study, with 344 benign subjects and 86 malignant subjects, so the disease prevalence is 0.2.

wdbc.YI.R

wdbc.YI.R is the R code for calculating the confidence intervals for the Youden Index with verification biased data.

1. To run the code and replicate our results in the paper (1), first install and load R packages rocbc, ThresholdROC and dplyr.
2. Load dataset 'wdbc.new'.
3. Calculate jc, which contains the estimates of J and cutoff point for all biomarkers using complete data.
4. wdbc.ci is the main function to compute the CIs. It requires 5 arguments:
   • seed : An integer that specifies the seed used to generate random numbers. We use 123 (default) in the paper.
   • k : A numerical value that specifies the parameter used to control the missing proportion, default value is 1.
   • bio : An integer between 3 to 32. It specifies the biomarkers considered in the study, in the paper we use 4, 25, 29.
   • a : Valid inputs are "FI", "MSI", "IPW" and "SPE"(by default). It indicates the bias-corrected estimator used to compute the CIs.
   • misv : Boolean. It indicates if the verification model is misspecified. Default value is FALSE.
5. The function returns a list that contains the estimates of J, verification proportion for both diseased and healthy groups, 95% CIs computed from packages rocbc and ThresholdROC and 95% CIs computed using our proposed methods.

wdbc.AUC.R

wdbc.AUC.R is the R code for calculating the confidence intervals for the AUC with verification biased data.

1. To run the code and replicate our results in the paper (2), first install and load R packages rocbc, pROC, dplyr, MASS and emplik.
2. Load dataset 'wdbc.new'.
3. Calculate wdbc_auc, which contains the estimates of AUCs for all biomarkers using complete data.
4. auc_vb_ci is the main function to compute the CIs. It requires 4 arguments:
   • bmk : An integer selected from 1 to 30. It specifies the biomarkers considered in the study, in the paper we use bmk = 2, 5, 7.
   • k : A numerical value that specifies the parameter used to control the missing proportion, in the paper we use k = 1 or -1.
   • a : An integer selected from 1 to 30. It specifies the biomarkers considered as covariate in the study, in the paper we use a = 6.
   • misv : Boolean. It indicates if the verification model is misspecified. Default value is FALSE.
5. To reproduce our results in the paper, use set.seed(123).
6. The function returns a list that contains two integrated matrices: CIs shows estimated AUC using complete data, verification proportion, numbers of verified diseased and healthy subjects, 95% CIs computed from packages rocbc and pROC and 95% CIs computed using our proposed methods ( with FI, MSI, IPW and SPE estimators). The other matrix CI_comp shows their corresponding length and coverage (0 or 1).