Quantifying time-varying cause-specific hazard and subdistribution hazard ratios with competing risks data

A robust hazard ratio for general modeling of survival-times

Hazard ratios (HR) associated with the well-known proportional hazard Cox regression models are routinely used for measuring the impact of one factor of interest on a time-to-event outcome. However, if the underlying real model does not fit with the theoretical requirements, the interpretation of those HRs is not clear. We propose a new index, gHR, which generalizes the HR beyond the underlying survival model. We consider the case in which the study factor is a binary variable and we are interested in both the unadjusted and adjusted effect of this factor on a time-to-event variable, potentially, observed in a right-censored scenario. We propose non-parametric estimations for unadjusted gHR and semi-parametric regression-induced techniques for the adjusted case. The behavior of those estimators is studied in both large and finite sample situations. Monte Carlo simulations reveal that both estimators provide good approximations of their respective inferential targets. Data from the Health and Lifestyle Study are used for studying the relationship of the tobacco use and the age of death and illustrate the practical application of the proposed technique. gHR is a promising index which can help facilitate better understanding of the association of one study factor on a time-dependent outcome.

Analysis of Prognostic Factors of Low-Grade Gliomas in Adults Using Time-Dependent Competing Risk Models: A Population Study Based on the Surveillance, Epidemiology, and End Results Database

BACKGROUND

Because of multiple competing death outcomes and time-varying coefficients, using a Cox regression model to analyze the prognostic factors of low-grade gliomas (LGG) may lead to a possible bias. Therefore, we adopted time-dependent competing risk models to obtain accurate prognostic factors for LGG.

METHODS

In this retrospective cohort study, data were extracted from patients enrolled in the Surveillance, Epidemiology, and End Results (SEER) database between 2000 and 2018. Univariate analysis was performed using the cumulative incidence function (CIF) and Kaplan-Meier (KM) function. Time-dependent competing risk and Cox regression models were used in the multivariable analysis.

RESULTS

A total of 2581 patients were diagnosed with low-grade glioma, among whom 889 died from low-grade glioma, 114 died from other causes, and the rest were alive. The time-dependent competing risk models indicated that age, sex, marital status, primary tumor site, histological type, tumor diameter, surgery, and year of diagnosis were significantly associated with low-grade glioma-specific death, and the relative effect of age, tumor diameter, surgery, oligodendroglioma, and mixed glioma on low-grade glioma-specific death changed over time. Compared with the competing risk models, the Cox regression model misestimated the hazard ratio (HR) of covariates on the outcome and even produced false-negative results.

CONCLUSIONS

The time-dependent competing risk models were better than the Cox regression model for evaluating the impact of covariates on low-grade glioma-specific mortality in the presence of competing risks and time-varying coefficients. The models identified the prognostic factors of LGG more accurately than the Cox regression model.