AROC.sp {AROC} | R Documentation |
Semiparametric frequentist inference of the covariate-adjusted ROC curve (AROC).
Description
Estimates the covariate-adjusted ROC curve (AROC) using the semiparametric approach proposed by Janes and Pepe (2009).
Usage
AROC.sp(formula.healthy, group, tag.healthy, data,
est.surv.h = c("normal", "empirical"), p = seq(0, 1, l = 101), B = 1000)
Arguments
formula.healthy |
A |
group |
A character string with the name of the variable that distinguishes healthy from diseased individuals. |
tag.healthy |
The value codifying the healthy individuals in the variable |
data |
Data frame representing the data and containing all needed variables. |
est.surv.h |
A character string. It indicates how the conditional distribution function of the diagnostic test in healthy population is estimated. Options are "normal" and "empirical" (see Details). The default is "normal". |
p |
Set of false positive fractions (FPF) at which to estimate the covariate-adjusted ROC curve. |
B |
An integer value specifying the number of bootstrap resamples for the construction of the confidence intervals. By default 1000. |
Details
Estimates the covariate-adjusted ROC curve (AROC) defined as
AROC\left(t\right) = Pr\{1 - F_{\bar{D}}(Y_D | \mathbf{X}_{D}) \leq t\},
where F_{\bar{D}}(\cdot|\mathbf{X}_{\bar{D}})
denotes the conditional distribution function for Y_{\bar{D}}
conditional on the vector of covariates \mathbf{X}_{\bar{D}}
. In particular, the method implemented in this function estimates the outer probability empirically (see Janes and Pepe, 2008) and F_{\bar{D}}(\cdot|\mathbf{X}_{\bar{D}})
is estimated assuming a semiparametric location regression model for Y_{\bar{D}}
, i.e.,
Y_{\bar{D}} = \mathbf{X}_{\bar{D}}^{T}\mathbf{\beta}_{\bar{D}} + \sigma_{\bar{D}}\varepsilon_{\bar{D}},
such that, for a random sample \{(\mathbf{x}_{\bar{D}i})\}_{i=1}^{n_{\bar{D}}}
from the healthy population, we have
F_{\bar{D}}(y | \mathbf{X}_{\bar{D}}=\mathbf{x}_{\bar{D}i}) = F_{\bar{D}}\left(\frac{y-\mathbf{x}_{\bar{D}i}^{T}\mathbf{\beta}_{\bar{D}}}{\sigma_{\bar{D}}}\right),
where F_{\bar{D}}
is the distribution function of \varepsilon_{\bar{D}}
. In line with the assumptions made about the distribution of \varepsilon_{\bar{D}}
, estimators will be referred to as: (a) "normal", where Gaussian error is assumed, i.e., F_{\bar{D}}(y) = \Phi(y)
; and, (b) "empirical", where no assumption is made about the distribution (in this case, the distribution function F_{\bar{D}}
is empirically estimated on the basis of standardised residuals).
Value
As a result, the function provides a list with the following components:
call |
The matched call. |
p |
Set of false positive fractions (FPF) at which the pooled ROC curve has been estimated |
ROC |
Estimated covariate-adjusted ROC curve (AROC), and 95% pointwise confidence intervals (if required) |
AUC |
Estimated area under the covariate-adjusted ROC curve (AAUC), and 95% pointwise confidence intervals (if required). |
fit.h |
Object of class |
est.surv.h |
The value of the argument |
References
Janes, H., and Pepe, M.S. (2009). Adjusting for covariate effects on classification accuracy using the covariate-adjusted receiver operating characteristic curve. Biometrika, 96(2), 371 - 382.
See Also
AROC.bnp
, AROC.bsp
, AROC.sp
, AROC.kernel
, pooledROC.BB
or pooledROC.emp
.
Examples
library(AROC)
data(psa)
# Select the last measurement
newpsa <- psa[!duplicated(psa$id, fromLast = TRUE),]
# Log-transform the biomarker
newpsa$l_marker1 <- log(newpsa$marker1)
m3 <- AROC.sp(formula.healthy = l_marker1 ~ age,
group = "status", tag.healthy = 0, data = newpsa,
p = seq(0,1,l=101), B = 500)
summary(m3)
plot(m3)