Copula Dependent Censoring Models for Survival Prognosis: Application to Lactylation-Related Genes

Survival for cancer patients is predictable by gene expressions obtained from DNA microarrays for tumor samples. For analyzing survival data with gene expressions, traditional survival analysis methods have been employed. However, these methods rely on the independent censoring model. In real survival data, dependent censoring arises, which violates the fundamental assumption of independent censorship. In addition, how to handle dependent censoring has not been clearly demonstrated for scientists working on molecular genetics. In this article, we review copula-based methods to handle dependent censoring, including the copula-graphic estimator and significance test. We illustrate the copula-based method by the prognostic analysis of the lactylation-related genes from 327 breast cancer tumor tissues. To justify the correctness of the copula-based significance test, we examine the performance of the copula-based methods using a simulation study. The results of our analysis indicate that the copula-based analyses may reverse the conclusions derived from the traditional independent censoring model.