pooledROC.BB {ROCnReg}

Bayesian bootstrap estimation of the pooled ROC curve.

Description

This function estimates the pooled ROC curve using the Bayesian bootstrap estimator proposed by Gu et al. (2008).

Usage

pooledROC.BB(marker, group, tag.h, data, 
	p = seq(0, 1, l = 101), B = 5000, ci.level = 0.95, pauc = pauccontrol(),
  	parallel = c("no", "multicore", "snow"), ncpus = 1, cl = NULL)

Arguments

marker

A character string with the name of the diagnostic test variable.

group

A character string with the name of the variable that distinguishes healthy from diseased individuals.

tag.h

The value codifying healthy individuals in the variable group.

data

Data frame representing the data and containing all needed variables.

p

Set of false positive fractions (FPF) at which to estimate the pooled ROC curve.

B

An integer value specifying the number of Bayesian bootstrap resamples. By default 5000.

ci.level

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

pauc

A list of control values to replace the default values returned by the function pauccontrol. This argument is used to indicate whether the partial area under the pooled ROC curve should be computed, and in case it is computed, whether the focus should be placed on restricted false positive fractions (FPFs) or on restricted true positive fractions (TPFs), and the upper bound for the FPF (if focus is FPF) or the lower bound for the TPF (if focus is TPF).

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 the pooled ROC curve (ROC) defined as

ROC(p) = 1 - F_{D}\{F_{\bar{D}}^{-1}(1-p)\},

where

F_{D}(y) = Pr(Y_{D} \leq y),

F_{\bar{D}}(y) = Pr(Y_{\bar{D}} \leq y).

The method implemented in this function makes use of the equivalence (see Gu et al., 2008)

ROC(p) = 1 - F_{D}\{F_{\bar{D}}^{-1}(1-p)\} = 1 - Pr(1 - F_{\bar{D}}(Y_D) \leq p),

and estimates both F_{\bar{D}} and the outer probability using the Bayesian bootstrap resampling distribution.

Regarding the area under the curve, we note that

AUC = \int_{0}^{1}ROC(p)dp = 1 - E\{U_D\},

where U_D = 1 - F_{\bar{D}}(Y_D). In our implementation, the expectation is computed using the Bayesian bootstrap (using the same weights as those used to estimate the pooled ROC). As far as the partial area under the curve is concerned, when focus = "FPF" and assuming an upper bound u_1 for the FPF, what it is computed is

pAUC_{FPF}(u_1)=\int_0^{u_1} ROC(p)dp = u_1 - E\{U_{D,u_1}\},

where U_{D,u_1} = \min\{u_1, 1 - F_{\bar{D}}(Y_D)\}. Again, the expectation is computed using the Bayesian bootstrap. The returned value is the normalised pAUC, pAUC_{FPF}(u_1)/u_1 so that it ranges from u_1/2 (useless test) to 1 (perfect marker). Conversely, when focus = "TPF", and assuming a lower bound for the TPF of u_2, the partial area corresponding to TPFs lying in the interval (u_2,1) is computed as

pAUC_{TPF}(u_2)=\int_{u_2}^{1}ROC_{TNF}(p)dp,

where ROC_{TNF}(p) is a 270^\circ rotation of the ROC curve, and it can be expressed as ROC_{TNF}(p) = F_{\bar{D}}\{F_{D}^{-1}(1-p)\}. Thus

pAUC_{TPF}(u_2)=\int_{u_2}^{1}ROC_{TNF}(p)dp = E\{U_{\bar{D}, u_2} - u_2\},

where U_{\bar{D}, u_2} = \max\{u_2, 1 - F_{D}(Y_{\bar{D}})\}, and the expectation is computed using the Bayesian bootstrap. The returned value is the normalised pAUC, pAUC_{TPF}(u_2)/(1-u_2), so that it ranges from (1-u_2)/2 (useless test) to 1 (perfect test).

Value

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

call

The matched call.

marker

A list with the diagnostic test outcomes in the healthy (h) and diseased (d) groups.

missing.ind

A logical value indicating whether missing values occur.

p

Set of false positive fractions (FPF) at which the pooled ROC curve has been estimated.

ci.level

The value of the argument ci.level used in the call.

ROC

Estimated pooled ROC curve, and corresponding ci.level*100% pointwise credible band.

AUC

Estimated pooled AUC, and corresponding ci.level*100% credible interval.

pAUC

If computed, estimated partial area under the pooled ROC curve (posterior mean) and ci.level*100% credible interval. Note that the returned values are normalised, so that the maximum value is one (see more on Details).

weights

list with the Dirichlet weights (involved in the estimation) in the healthy (h) and diseased (d) groups. These are matrices of dimension n0 x B and n1 x B, where n0 is the number of healthy individuals and n1 is the number of diseased individuals.

References

Gu, J., Ghosal, S., and Roy, A. (2008). Bayesian bootstrap estimation of ROC curve. Statistics in Medicine, 27, 5407–5420.

See Also

AROC.bnp, AROC.sp, AROC.kernel, pooledROC.BB, pooledROC.emp, pooledROC.kernel, pooledROC.dpm, cROC.bnp, cROC.sp or AROC.kernel.

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)

m0_BB <- pooledROC.BB(marker = "l_marker1", group = "status",
tag.h = 0, data = newpsa, p = seq(0,1,l=101), B = 5000)

summary(m0_BB)

plot(m0_BB)