Copula modeling of receiver operating characteristic and predictiveness curves

Abstract

Receiver operating characteristic (ROC) and predictiveness curves are graphical tools to study the discriminative and predictive power of a continuous-valued marker in a binary outcome. In this paper, a copula-based construction of the joint density of the marker and the outcome is developed for plotting and analyzing both curves. The methodology only requires a copula function, the marginal distribution of the marker, and the prevalence rate for the model to be characterized. The adoption of the Gaussian copula and the customization of the margin for the marker are proposed for such characterization. The computation of both curves is numerically more feasible than methods that attempt to obtain one curve in terms of the other. Estimation is carried out using maximum likelihood and resampling-based methods. Randomized quantile residuals from each conditional distribution are employed for both assessing the adequacy of the model and identifying outliers. The performance of the estimators of both curves and their underlying quantities is evaluated in simulation studies that assume different dependence structures and sample sizes. The methods are illustrated with an analysis of the level of progesterone receptor gene expression for the diagnosis and prediction of estrogen receptor-positive breast cancer.

Comparison of generalized estimating equations and Gaussian copula regression results using data from the randomized control trial

“…GEE estimates using autoregressive correlation structure was compared to verify with estimates obtained from Gaussian copula regression with autoregressive correlation structure [24]. Misleading estimates can be avoided when using maximum likelihood estimation by Gaussian copula regression which is a major strength [37].…”

Copula modeling for the estimation of measures of marker classification and predictiveness performance with survival outcomes

“…In this paper, two copula-based approaches are proposed to characterize such joint model. The first model is an extension of the model for cross-sectional data in Escarela et al., 5 which is conveniently constructed by customizing and linking with a copula a parametric marginal continuous cumulative distribution function (CDF) for M and a parametric marginal survival distribution function for T, leading to a fully parametric (FP) formulation. Such construction is appealing since the copula that characterizes the joint behavior of monotone increasing transforms of M and T is exactly the same copula as for the original pair false( M , T false); that is, the unique copula associated with false( M , T false) is invariant under monotone increasing transformations of the margins, 6 which clearly benefits both the modeling and the inference process.…”