compute.threshold.cROC {ROCnReg}

Covariate-specific ROC based threshold values.

Description

This function implements methods for estimating covariate-specific ROC-based threshold values.

Usage

compute.threshold.cROC(object, criterion = c("FPF", "TPF", "YI"), FPF, TPF, newdata,
  ci.level = 0.95, parallel = c("no", "multicore", "snow"), ncpus = 1, cl = NULL)

Arguments

object

An object of class cROC as produced by cROC.bnp(), cROC.sp(), or cROC.kernel().

criterion

A character string indicating whether the covariate-specific threshold values should be computed based on the Youden index (“YI”) or for fixed false positive fractions (“FPF”) or true positive fractions (“TPF”).

FPF

For criterion = "FPF", a numeric vector with the FPF at which to calculate the covariate-specific threshold values. Atomic values are also valid.

TPF

For criterion = "TPF", a numeric vector with the TPF at which to calculate the covariate-specific threshold values. Atomic values are also valid.

newdata

Optional data frame containing the values of the covariates at which the covariate-specific threshold values will be computed. If not supplied, the function cROCData is used to build a default dataset.

ci.level

An integer value (between 0 and 1) specifying the confidence level. The default is 0.95.

parallel

A characters string with the type of parallel operation: either "no" (default), "multicore" (not available on Windows) or "snow".

ncpus

An integer with the number of processes to be used in parallel operation. Defaults to 1.

cl

An object inheriting from class cluster (from the parallel package), specifying an optional parallel or snow cluster if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the call.

Details

Estimates covariate-specific ROC-based threshold values based on three different criteria, namely, the Youden index (YI), one that gives rise to a pre-specified FPF, and one that gives rise to a pre-specified TPF.

In the conditional case, the Youden index is defined as

YI(\mathbf{x}) = \max_{c}|TPF(c|\mathbf{x}) - FPF(c|\mathbf{x})| = \max_{c}|F_{\bar{D}}(c|\mathbf{x}) - F_{D}(c|\mathbf{x})|,

where

F_{D}(y|\mathbf{x}) = Pr(Y_{D} \leq y | \mathbf{X}_{D} = \mathbf{x}),

F_{\bar{D}}(y|\mathbf{x}) = Pr(Y_{\bar{D}} \leq y | \mathbf{X}_{\bar{D}} = \mathbf{x}).

The value c^{*}_{\mathbf{x}} that achieves the maximum is called the optimal covariate-specific YI threshold. Regarding the criterion for a fixed FPF, the covariate-specific threshold values are obtained as follows

c^{*}_{\mathbf{x}} = F_{\bar{D}}^{-1}(1-FPF|\mathbf{x}),

and for a fixed TPF we have

c^{*}_{\mathbf{x}} = F_{D}^{-1}(1-TPF|\mathbf{x}),

In all cases, we use the notation c^{*}_{\mathbf{x}} to emphasise that this value depends on covariate \mathbf{x}.

Value

As a result, the function provides a list with the following components:

call

The matched call.

newdata

Data frame containing the values of the covariates at which the covariate-specific thresholds were computed.

thresholds

If method = "YI", the estimated covariate-specific (optimal) threshold corresponding to the covariate-specific Youden index (the one that maximises TPF/sensitivity + TNF/specificity). If method = "FPF", the covariate-specific threshold corresponding to the specified FPF, and if method = "TPF", the covariate-specific threshold corresponding to the specified TPF. For the Bayesian approach (cROC.bnp), in addition to the posterior mean, the ci.level*100% pointwise credible band is also returned.

YI

If method = "YI", the estimated covariate-specific Youden index. For the Bayesian approach (cROC.bnp), in addition to the posterior mean, the ci.level*100% pointwise credible band is also returned.

FPF

If method = "YI" or method = "TPF", the FPF corresponding to the estimated (optimal) covariate-specific thresholds (for the Bayesian approach (cROC.bnp), in addition to the posterior mean, the ci.level*100% pointwise credible band is also returned.). If method = "FPF", the supplied FPF argument.

TPF

If method = "YI" or method = "FPF", the covariate-specific TPF/sensitivity corresponding to the estimated covariate-specific (optimal) threshold. For the Bayesian approach (AROC.bnp), in addition to the posterior mean, the ci.level*100% pointwise credible band is also returned. If method = "TPF", the supplied TPF argument.

References

Inacio de Carvalho, V., de Carvalho, M. and Branscum, A. J. (2017). Nonparametric Bayesian Covariate-Adjusted Estimation of the Youden Index. Biometrics, 73, 1279-1288.

Rodriguez-Alvarez, M. X., Roca-Pardinas, J., and Cadarso-Suarez, C. (2011). ROC curve and covariates: extending induced methodology to the non-parametric framework. Statistics and Computing, 21, 483–499.

Rutter, C.M. and Miglioretti, D. L. (2003). Estimating the Accuracy of Psychological Scales Using Longitudinal Data. Biostatistics, 4, 97–107.

Youden, W. J. (1950). Index for rating diagnostic tests. Cancer, 3, 32–35.

See Also

cROC.bnp, cROC.kernel or cROC.sp

Examples

library(ROCnReg)
data(psa)
# Select the last measurement
newpsa <- psa[!duplicated(psa$id, fromLast = TRUE),]

# Log-transform the biomarker
newpsa$l_marker1 <- log(newpsa$marker1)

cROC_bnp <- cROC.bnp(formula.h = l_marker1 ~ f(age, K = 0),
			  formula.d = l_marker1 ~ f(age, K = 0),
              group = "status", 
              tag.h = 0, 
              data = newpsa,
              standardise = TRUE,
              p = seq(0,1,l=101),
              mcmc = mcmccontrol(nsave = 500, nburn = 100, nskip = 1))

### Threshold values based on the YI
th_cROC_bnp_yi <- compute.threshold.cROC(cROC_bnp, criterion = "YI")

# Plot results
	# Threshold values
	plot(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$thresholds[,"est"], 
		type = "l", xlab = "Age", 
		ylab = "log(PSA)", ylim = c(0,3), 
		main = "Threshold values based on the Youden Index")
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$thresholds[,"qh"], lty = 2)
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$thresholds[,"ql"], lty = 2)

	# Youden Index
	plot(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$YI[,"est"], 
		type = "l", xlab = "Age", 
		ylab = "log(PSA)", ylim = c(0,1), 
		main = "Threshold values based on the Youden Index")
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$YI[,"qh"], lty = 2)
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_yi$YI[,"ql"], lty = 2)

### Threshold values for a fixed FPF
th_cROC_bnp_fpf <- compute.threshold.cROC(cROC_bnp, criterion = "FPF", FPF = 0.1)

# Plot results
	# Threshold values
	plot(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_fpf$thresholds[["0.1"]][,"est"], 
		type = "l", xlab = "Age", 
		ylab = "log(PSA)", ylim = c(0,3), main = "Threshold values for a FPF = 0.1")
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_fpf$thresholds[["0.1"]][,"qh"], lty = 2)
	lines(th_cROC_bnp_yi$newdata$age, th_cROC_bnp_fpf$thresholds[["0.1"]][,"ql"], lty = 2)