Estimated ROC curves

Description

Plot of ROC curves estimated under parametric model assumptions on the continuous diagnostic marker.

Usage

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ROC.plot(ydat, xdat, distr = "exp", method = "RPstar", mc = 1)

Arguments

ydat

data vector of the diagnostic marker measurements on the sample of non-diseased individuals (from Y).

xdat

data vector of the diagnostic marker measurements on the sample of diseased individuals (from X).

distr

character string specifying the type of distribution assumed for Y and X. Possible choices for distr are "exp" (default) for the one-parameter exponential, "norm_EV" and "norm_DV" for the Gaussian distribution with, respectively, equal or unequal variances assumed for the two random variables.

method

character string specifying the methodological approach used for estimating the probability R, which is here interpreted as the area under the ROC curve (AUC). The argument method can be set equal to "Wald", "RP" or RPstar" (default), according as inference is based on the Wald statistic, the signed log-likelihood ratio statistic (directed likelihhod, r_p) or the modified signed log-likelihood ratio statistic (modified directed likelihood, r_p^*), respectively. For estimating the ROC curve parametrically, methods "Wald" and "RP" are equivalent and supply maximum likelihood estimation (MLE), whereas, by using method "RPstar", estimate of the ROC curve is based on the modified signed log-likelihood ratio statistic (r_p^*). See rpstar for details on this statistic.

mc

a numeric value indicating single or multiple plots in the same figure. In case mc is equal to 1 (default), only the method specified in method is applied and the corresponding estimated ROC curve is plotted. If mc is different from 1, both MLE and r_p^*-based methods are applied, and two differently estimated ROC curves are plotted.

Details

If mc is different from 1, method does not need to be specified.

Value

Plot of ROC curves

Note

The two independent random variables Y and X with given distribution distr are measurements of the diagnostic marker on the diseased and non-diseased subjects, respectively.
In "Wald" method, or equivalently "RP" method, MLEs for parameters of the Y and X distributions are computed and then used to estimate specificity and sensitivity. These measures are evaluated as P(Y<t) and P(X>t), respectively.
In "RPstar" method, parameters of the Y and X distributions are estimated from the r_p^*-based estimate of the AUC.

Author(s)

Giuliana Cortese

References

Cortese G., Ventura L. (2013). Accurate higher-order likelihood inference on P(Y<X). Computational Statistics, 28:1035-1059.

See Also

Prob

Examples

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	# data from the non-diseased population
	Y <- rnorm(15, mean=5, sd=1)       
	# data from the diseased population
	X <- rnorm(10, mean=7, sd=1.5)      
 	ROC.plot(Y, X, "norm_DV", method = "RP", mc = 2)