---
title: "Package 'TGST'"
author: "Yizhen Xu, Tao Liu"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 3
vignette: >
  %\VignetteIndexEntry{Targeted Gold Standard Testing}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

**Type** Package

**Title** Targeted Gold Standard Testing

**Version** 1.0

**Date** "`r Sys.Date()`"

**Authors** Yizhen Xu, Tao Liu

**Maintainer** Yizhen (yizhen_xu@alumni.brown.edu)

**Description** This package implements the optimal allocation of gold standard testing under constrained availability.

**License** GPL

**URL**  https://github.com/yizhenxu/TGST

**Depends** R (>= 3.2.0)

**LazyData** true

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###TGST

*Create a TGST Object*

####Description

> Create a TGST object, usually used as an input for optimal rule search and ROC analysis. 

####Usage

> TGST( Z, S, phi, method="nonpar")

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; A vector of true disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.
> - **phi** Percentage of patients taking gold standard test. 
> - **method** Method for searching for the optimal tripartite rule, options are "nonpar" (default) and "semipar".

####Value

> An object of class TGST.The class contains 6 slots: phi (percentage of gold standard tests), Z (true failure status), S (risk score), Rules (all possible tripartite rules), Nonparametric (logical indicator of the approach), and FNR.FPR (misclassification rates).
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10% of patients taking viral load test
TGST( Z, S, phi, method="nonpar")
```

_____


###Check.exp.tilt

*Check exponential tilt model assumption*

####Description

> This function provides graphical assessment to the suitability of the exponential tilt model for risk score in finding optimal tripartite rules by semiparametric approach.
$$g_1(s) = exp(\beta_0^*+\beta_1*s)*g_0(s)$$

####Usage

> Check.exp.tilt( Z, S)


####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.

####Value

> Returns the plot of empirical density for risk score S, joint empirical density for (S,Z=1) and (S,Z=0), and the density under the exponential tilt model assumption for (S,Z=1) and (S,Z=0).

####Author(s)

> Yizhen Xu (yizhen_xu@alumni.brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
Check.exp.tilt( Z, S)
```
_____

###CV.TGST

*Cross Validation*

####Description

> This function allows you to compute the average of misdiagnoses rate for viral failure and the optimal risk under min $\lambda$ rules from K-fold cross-validation.

####Usage

> CV.TGST(Obj, lambda, K=10)


####Arguments

> - **Obj** &nbsp;&nbsp;&nbsp;&nbsp; An object of class TGST. 
> - **lambda** &nbsp;&nbsp;&nbsp;&nbsp; A user-specified weight that reflects relative loss for the two types of misdiagnoses, taking value in [0,1]. 
$Loss=\lambda*I(FN)+(1-\lambda)*I(FP)$.
> - **K**  &nbsp;&nbsp;&nbsp;&nbsp; Number of folds in cross validation. The default is 10.

 
####Value

> Cross validated results on false classification rates (FNR, FPR), $\lambda-$ risk, total misclassification rate and AUC.

####Author(s)

> Yizhen Xu (yizhen_xu@alumni.brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
data = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10% of patients taking viral load test
Obj = TVLT(Z, S, phi, method="nonpar")
CV.TGST(Obj, lambda, K=10)
```

_____

###OptimalRule

*Optimal Tripartite Rule*

###Description

> This function gives you the optimal tripartite rule that minimizes the min-$\lambda$ risk based on the type of user selected approach. It takes the risk score and true disease status from a training data set and returns the optimal tripartite rule under the specified proportion of patients able to take gold standard test.

####Usage

> OptimalRule(Obj, lambda)

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp;
> - **Obj** &nbsp;&nbsp;&nbsp;&nbsp; An object of class TGST. 
> - **lambda** &nbsp;&nbsp;&nbsp;&nbsp; A user-specified weight that reflects relative loss for the two types of misdiagnoses, taking value in [0,1]. $Loss=\lambda*I(FN)+(1-\lambda)*I(FP)$.

####Value

> Optimal tripartite rule.  

####Author(s)

> Yizhen Xu (yizhen_xu@alumni.brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10% of patients taking viral load test
lambda = 0.5
Obj = TGST(Z, S, phi, method="nonpar")
OptimalRule(Obj, lambda)
```

_____

###ROCAnalysis

*ROC Analysis*

####Description

> This function performs ROC analysis for tripartite rules. If 'plot=TRUE', the ROC curve is returned.

####Usage

> ROCAnalysis(Obj, plot=TRUE)

####Arguments

> - **Obj** &nbsp;&nbsp;&nbsp;&nbsp; An object of class TGST.
> - **plot**  &nbsp;&nbsp;&nbsp;&nbsp;  Logical parameter indicating if ROC curve should be plotted. Default is 'plot=TRUE'. If false, then only AUC is calculated.

####Value

AUC (the area under ROC curve) and ROC curve.
 
####Author(s)

Yizhen Xu (yizhen_xu@alumni.brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10% of patients taking viral load test
lambda = 0.5
Obj = TGST(Z, S, phi, method="nonpar")
ROCAnalysis(Obj, plot=TRUE)
```

_____

###nonpar.rules

*Nonparametric Rules Set*

####Description

> This function gives you all possible cutoffs [l,u] for tripartite rules, by applying nonparametric search to the given data.
$$P(S \in [l,u]) \le \phi$$

####Usage

> nonpar.rules( Z, S, phi)

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.
> - **phi**  &nbsp;&nbsp;&nbsp;&nbsp;  Percentage of patients taking viral load test.
 
####Value

> Matrix with 2 columns. Each row is a possible tripartite rule, with output on lower and upper cutoff.
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10\% of patients taking viral load test
nonpar.rules( Z, S, phi)
```

_____

###nonpar.fnr.fpr

*Nonparametric FNR FPR of the rules*

####Description

> This function gives you the nonparametric FNRs and FPRs associated with a given set of tripartite rules.

####Usage

> nonpar.fnr.fpr(Z,S,rules[1,1],rules[1,2])

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.
> - **l**  &nbsp;&nbsp;&nbsp;&nbsp;  Lower cutoff of tripartite rule. 
> - **u**  &nbsp;&nbsp;&nbsp;&nbsp;  Upper cutoff of tripartite rule. 

####Value

> Matrix with 2 columns. Each row is a set of nonparametric (FNR, FPR) on an associated tripartite rule.
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10\% of patients taking viral load test
rules = nonpar.rules( Z, S, phi)
nonpar.fnr.fpr(Z,S,rules[1,1],rules[1,2])
```

_____

###semipar.fnr.fpr

*Semiparametric FNR FPR of the rules*

####Description

> This function gives you the semiparametric FNR and FPR associated with a set of given tripartite rules.

####Usage

> semipar.fnr.fpr(Z,S,rules[1,1],rules[1,2])

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.
> - **l**  &nbsp;&nbsp;&nbsp;&nbsp;  Lower cutoff of tripartite rule. 
> - **u**  &nbsp;&nbsp;&nbsp;&nbsp;  Upper cutoff of tripartite rule. 
 
####Value

> Matrix with 2 columns. Each row is a set of semiparametric (FNR, FPR) on an associated tripartite rule.
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10\% of patients taking viral load test
rules = nonpar.rules( Z, S, phi)
semipar.fnr.fpr(Z,S,rules[1,1],rules[1,2])
```
_____

###cal.AUC

*Calculate AUC*

####Description

> This function gives you the AUC associated with the rules set.

####Usage

> cal.AUC(Z,S,rules[,1],rules[,2])

####Arguments

> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score.
> - **l**  &nbsp;&nbsp;&nbsp;&nbsp;  Lower cutoff of tripartite rule. 
> - **u**  &nbsp;&nbsp;&nbsp;&nbsp;  Upper cutoff of tripartite rule. 
 
####Value

> AUC.
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
d = Simdata
Z = d$Z # True Disease Status
S = d$S # Risk Score
phi = 0.1 #10% of patients taking viral load test
rules = nonpar.rules( Z, S, phi)
cal.AUC(Z,S,rules[,1],rules[,2])
```
_____

###Simdata

*Simulated data for package illustration*

####Description

> A simulated dataset containing true disease status and risk score. See details for simulation setting.

####Format

> A data frame with 8000 simulated observations on the following 2 variables.
> - **Z** &nbsp;&nbsp;&nbsp;&nbsp; True disease status (No disease / treatment success coded as Z=0, diseased / treatment failure coded as Z=1).
> - **S**  &nbsp;&nbsp;&nbsp;&nbsp;  Risk score. Higher risk score indicates larger tendency of diseased / treatment failure.
 
####Details

> We first simulate true failure status $Z$ assuming $Z\sim Bernoulli(p)$ with $p=0.25$; and then conditional on $Z$, simulate ${S|Z=z}=ceiling(W)$ with $W\sim Gamma(\eta_z,\kappa_z)$ where $\eta$ and $\kappa$ are shape and scale parameters.$(\eta_0,\kappa_0)=(2.3,80)$ and $(\eta_1,\kappa_1)=(9.2,62)$.
 
####Author(s)

> Yizhen Xu (yizhen_xu@brown.edu), Tao Liu, Joseph Hogan

####References

> T. Liu, J. Hogan, L. Wang, S. Zhang, R. Kantor (2013) *Journal of the American Statistical Association* Vol.108, No.504

####Examples

```{r,eval=FALSE}
data(Simdata)
summary(Simdata)
plot(Simdata)
```
