To install the package from CRAN, type:

`install.packages("bcROCsurface")`

Next, load the package.

`library(bcROCsurface)`

`## Loading required package: nnet`

`## Loading required package: rgl`

`## Loading required package: boot`

`## Loading required package: parallel`

To illustrate the use of the package `bcROCsurface`

, we consisder an example, which presents the evaluation process for biomaker `CA125`

in the diagnosis of epithelial ovarian cancer (EOC).

`data(EOC)`

The data have 278 observations on the following 6 variables:

`head(EOC)`

```
## D.full V D CA125 CA153 Age
## 1 3 1 3 3.304971965 1.42822875 41
## 2 1 0 NA 0.112479444 0.11665310 52
## 3 2 1 2 2.375011262 -0.04096794 50
## 4 1 0 NA -0.001545381 0.32111633 66
## 5 1 0 NA 0.278200345 -0.14283052 52
## 6 2 0 NA 0.167645382 0.81470563 50
```

In data set, `CA125`

and `CA153`

are two biomarkers, `Age`

is the age of the patients. The variable `V`

is the verification status; 1 and 0 indicates verified and non-verified subject, respectively. `D.full`

is disease status, which consist of three classes, says, 1, 2, 3. These levels correspond to benign disease, early stage (I and II) and late stage (III and IV). On the other hand, `D`

is missing disease status.

The ROC surface and VUS are only applied when an monotone increasing ordering is of interest. Thus, before estimate ROC and also VUS, we have to be sure that the ordering of disease classes is monotone incresasing (with respect to the diagnostic test values). In order to do that, the function `preDATA()`

is usefull.

`Dfull <- preDATA(EOC$D.full, EOC$CA125)`

```
## The sample means of diagostic test based on three classes.
## ( 1 ) 1 : 0.192
## ( 2 ) 2 : 1.81
## ( 3 ) 3 : 3.214
## The sample median of diagostic test based on three classes.
## ( 1 ) 1 : 0.014
## ( 2 ) 2 : 1.499
## ( 3 ) 3 : 3.381
## The ordering based on median: 1 < 2 < 3
```

On the other hand, we describe the full diease status `D.full`

as the binary matrix having three columns, correspondings to three classes of the disease status. Each row corresponds to a trinomial vector, in which, 1 indicates the subject belongs to class j with j = 1,2,3. The function `preDATA()`

also done this work.

`head(Dfull$D)`

`## [1] 3 1 2 1 1 2`

`head(Dfull$Dvec)`

```
## D1 D2 D3
## [1,] 0 0 1
## [2,] 1 0 0
## [3,] 0 1 0
## [4,] 1 0 0
## [5,] 1 0 0
## [6,] 0 1 0
```

We construct the ROC surface of full data, and estimate the VUS.

```
Dvec.full <- Dfull$Dvec
ROCs(method = "full", T = EOC$CA125, Dvec = Dvec.full, ncp = 30, ellipsoid = TRUE,
cpst = c(-0.56, 2.31))
```

```
## Hmm, look likes the full data
## Number of observation: 278
## The verification status is not available
## You are working on FULL or Complete Case approach
## The diagnostic test: CA125
## Processing ....
## DONE
## ===============================================================
## Some values of TCFs:
## TCF1 TCF2 TCF3
## (0.4 , 2.627) 0.694 0.493 0.688
## (0.718 , 2.627) 0.769 0.418 0.688
## (0.4 , 2.945) 0.694 0.537 0.636
## (0.718 , 2.945) 0.769 0.463 0.636
## (0.4 , 1.991) 0.694 0.343 0.805
## (0.718 , 1.991) 0.769 0.269 0.805
##
## Some information for Ellipsoidal Confidence Region(s):
## Confidence level: 0.95
## TCFs at (-0.56, 2.31) are:
## TCF1 TCF2 TCF3
## 0.209 0.642 0.727
## ===============================================================
```

Here, we consider the full data, so we only need to put the arguments `T`

and `Dvec`

, and method is `full`

.

The FULL estimator of VUS is obtained by the following command:

`vus("full", T = EOC$CA125, Dvec = Dvec.full, ci = TRUE)`

```
## Hmm, look likes the full data
## The verification status is not available
## You are working on FULL or Complete Case approach
## Number of observation: 278
## The diagnostic test: CA125
## Processing ....
## DONE
##
## CALL: vus(method = "full", T = CA125, Dvec = Dvec.full, ci = TRUE,
## parallel = TRUE)
##
## Estimate of VUS: 0.5663
## Standard error: 0.0365
##
## Intervals :
## Level Normal Logit
## 95% ( 0.4946, 0.6379 ) ( 0.4937, 0.6360 )
## Estimation of Standard Error and Intervals are based on Bootstrap with 250 replicates
##
## Testing the null hypothesis H0: VUS = 1/6
## Test Statistic P-value
## Normal-test 10.596 < 2.2e-16 ***
## ---
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```

Now, we compute the FI and MSI estimator with missing data. First, we need to estimate the disease probabilities by using multnomial logistic model. In bcROCsurface package, this work is done by using `rhoMLogit()`

function.

`Dna <- preDATA(EOC$D, EOC$CA125)`

```
## There are missing disease status.
## The sample means of diagostic test based on three classes.
## ( 1 ) 1 : 0.555
## ( 2 ) 2 : 2.112
## ( 3 ) 3 : 3.347
## The sample median of diagostic test based on three classes.
## ( 1 ) 1 : 0.286
## ( 2 ) 2 : 1.972
## ( 3 ) 3 : 3.439
## The ordering based on median: 1 < 2 < 3
```

```
Dvec.na <- Dna$Dvec
D.na <- Dna$D
rho.out <- rhoMLogit(D.na ~ CA125 + CA153 + Age, data = EOC, test = TRUE, trace = TRUE)
```

```
## # weights: 15 (8 variable)
## initial value 195.552987
## iter 10 value 134.148494
## final value 133.798546
## converged
## Fitting the disease model by using multinomial logistic model via nnet package.
## FORMULAR: Disease ~ CA125 + CA153 + Age
##
## ====================================================================
## The p-value calculation for the regression coefficients:
## 1 2
## (Intercept) 1.708e-05 0.0008529
## CA125 1.303e-08 0.0417717
## CA153 6.543e-02 0.0216723
## Age 1.635e-03 0.0031442
## ====================================================================
```

The following command provides the ROC surface of FI esimator:

```
ROCs(method = "fi", T = EOC$CA125, Dvec = Dvec.na, V = EOC$V, rhoEst = rho.out, ncp = 30,
ellipsoid = TRUE, cpst = c(-0.56, 2.31))
```

```
## Hmm, look likes the incomplete data
## Number of observation: 278
## 64% of the subjects receive disease verification.
## You required estimate ROC surface using FI approach
## The diagnostic test: CA125
## The ellipsoidal confidence region(s) of TCFs are also constructed
## Processing ....
## DONE
## ===============================================================
## Some values of TCFs:
## TCF1 TCF2 TCF3
## (1.036 , 2.945) 0.820 0.362 0.606
## (0.718 , 2.945) 0.747 0.433 0.606
## (1.354 , 2.945) 0.876 0.291 0.606
## (1.036 , 2.627) 0.820 0.312 0.637
## (0.4 , 2.945) 0.670 0.492 0.606
## (0.718 , 2.627) 0.747 0.383 0.637
##
## Some information for Ellipsoidal Confidence Region(s):
## Confidence level: 0.95
## TCFs at (-0.56, 2.31) are:
## TCF1 TCF2 TCF3
## 0.195 0.586 0.680
## ===============================================================
```

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And, for VUS:

`vus(method = "fi", T = EOC$CA125, Dvec = Dvec.na, V = EOC$V, rhoEst = rho.out, ci = TRUE)`

```
## Hmm, look likes the incomplete data
## Number of observation: 278
## 64% of the subjects receive disease verification.
## You required estimate VUS using FI approach
## The diagnostic test: CA125
## Processing ....
## DONE
##
## CALL: vus(method = "fi", T = CA125, Dvec = Dvec.na, V = V, rhoEst = rho.out,
## ci = TRUE)
##
## Estimate of VUS: 0.515
## Standard error: 0.0404
##
## Intervals :
## Level Normal Logit
## 95% ( 0.4357, 0.5942 ) ( 0.4360, 0.5932 )
## Estimation of Standard Error and Intervals are based on Asymptotic Theory
##
## Testing the null hypothesis H0: VUS = 1/6
## Test Statistic P-value
## Normal-test 8.6168 < 2.2e-16 ***
## ---
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```

For MSI estimator, we could do that to plot ROC surface

```
ROCs(method = "msi", T = EOC$CA125, Dvec = Dvec.na, V = EOC$V, rhoEst = rho.out, ncp = 30,
ellipsoid = TRUE, cpst = c(-0.56, 2.31))
```

```
## Hmm, look likes the incomplete data
## Number of observation: 278
## 64% of the subjects receive disease verification.
## You required estimate ROC surface using MSI approach
## The diagnostic test: CA125
## The ellipsoidal confidence region(s) of TCFs are also constructed
## Processing ....
## DONE
## ===============================================================
## Some values of TCFs:
## TCF1 TCF2 TCF3
## (0.4 , 2.945) 0.676 0.504 0.612
## (0.4 , 2.627) 0.676 0.455 0.655
## (0.718 , 2.945) 0.741 0.419 0.612
## (0.718 , 2.627) 0.741 0.370 0.655
## (0.081 , 2.945) 0.544 0.608 0.612
## (0.4 , 1.991) 0.676 0.315 0.769
##
## Some information for Ellipsoidal Confidence Region(s):
## Confidence level: 0.95
## TCFs at (-0.56, 2.31) are:
## TCF1 TCF2 TCF3
## 0.200 0.609 0.688
## ===============================================================
```