Abstract
In survival analysis, multiplicative and additive hazards models provide the two principal frameworks to study the association between the hazard and covariates. When these models are considered for analyzing a given survival dataset, it becomes relevant to evaluate the overall goodness-of-fit and how well each model can predict those subjects who subsequently will or will not experience the event. In this paper, this evaluation is based on a graphical representation of the Cox-Snell residuals and also on a time-dependent version of the area under the receiver operating characteristic (ROC) curve, denoted by AUC(t). A simulation study is carried out to evaluate the performance of the AUC(t) as a tool for comparing the predictive accuracy of survival models. A dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver is also considered to illustrate the usefulness of these tools to compare survival models formulated under distinct hazards frameworks.
Highlights
Data involving time to the occurrence of a certain event has been usually referred to as survival data
The most well-known regression model proposed for dealing with survival data is the Cox model (COX, 1972), whose validity relies on the assumption of
One of them is the impossibility of using statistical tests such as the likelihood ratio test, score test and Wald test since the models are not nested. Another is that the likelihood function is difficult to specify for additive hazards models containing nonparametric terms, which implies that likelihood based model selection criteria, such as Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and Schwarz’s Bayesian criterion (SBC) can not be used in this situation (HUFFER; McKEAGUE, 1991). With these statistical challenges in mind, the purpose of this paper was to consider a time-dependent version of the area under the receiver operating characteristic (ROC) curve, discussed by Heagerty and Zheng (2005) in the setting of survival models and denoted by AUC(t), as a procedure to assess the predictive accuracy of hazards models formulated under distinct frameworks
Summary
Data involving time to the occurrence of a certain event has been usually referred to as survival data. A complication in analyzing such data is that they are usually censored, meaning that the event time of interest is not fully observed on all subjects under study. The most well-known regression model proposed for dealing with survival data is the Cox model (COX, 1972), whose validity relies on the assumption of. As this assumption may not always be true (for example, the effect of a treatment may change over time), alternative models which allow non-proportional hazards (i.e., time-varying covariate effects) have been proposed
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