Cox Model Predicting Covariate Subject to Right Censoring
Time-to-event endpoints are frequently used as outcomes in oncology and other disease areas where the outcome of interest may not be observed within a predetermined period. Although many analytical methods address the challenges of censoring in outcomes, limited research has focused on censored covariates. Conventional methods such as the complete case (CC) analysis, where data from patients with censored covariates are discarded, suffer from efficiency loss and potential bias due to reduced sample size. Alternatively, imputing censored covariates with a constant value can underestimate variability. Recognizing these limitations, novel estimation procedures within the generalized linear model framework have been proposed, with some research emerging in time-to-event outcomes. In this paper, we investigate the association between progression-free survival and overall survival using a semi-parametric Cox model framework. We modify the Cox model's partial likelihood function to account for censored covariates by replacing the relative risk associated with censored covariates with a weighted average of patients with observed covariates. The performance of the proposed method is demonstrated through simulations and applications to two oncology clinical trials. Results indicate that the proposed method offers improved estimation efficiency and better utilization of available data compared to other approaches.