Gaussian Copula Regression Modeling for Marker Classification Metrics with Competing Risk Outcomes

Alejandro Román Vásquez, Gabriel Escarela, Hortensia Josefina Reyes-Cervantes, Gabriel Núñez-Antonio and Niansheng Tang

International Journal of Mathematics and Mathematical Sciences, 2024, vol. 2024, 1-13

Abstract: Decisions regarding competing risks are usually based on a continuous-valued marker toward predicting a cause-specific outcome. The classification power of a marker can be summarized using the time-dependent receiver operating characteristic curve and the corresponding area under the curve (AUC). This paper proposes a Gaussian copula-based model to represent the joint distribution of the continuous-valued marker, the overall survival time, and the cause-specific outcome. Then, it is used to characterize the time-varying ROC curve in the context of competing risks. Covariate effects are incorporated by linking linear components to the skewed normal distribution for the margin of the marker, a parametric proportional hazards model for the survival time, and a logit model for the cause of failure. Estimation is carried out using maximum likelihood, and a bootstrap technique is implemented to obtain confidence intervals for the AUC. Information-criteria strategies are employed to find a parsimonious model. The performance of the proposed model is evaluated in simulation studies, considering different sample sizes and censoring distributions. The methods are illustrated with the reanalysis of a prostate cancer clinical trial. The joint regression strategy produces a straightforward and flexible model of the time-dependent ROC curve in the presence of competing risks, enhancing the understanding of how covariates may affect the discrimination of a marker.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1671254

DOI: 10.1155/2024/1671254

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