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Connections between cure rates and survival probabilities in proportional hazards models
Author(s) -
Lin LiHsiang,
Huang LiShan
Publication year - 2019
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.255
Subject(s) - proportional hazards model , statistics , survival analysis , econometrics , mathematics , model selection , regression analysis , inference , cure rate , computer science , medicine , artificial intelligence
The Cox regression model has been widely used to assess proportional hazards in survival analysis, and the Yakovlev model for analysing cure rates also possesses the PH structure. In this paper, we present some connections that link the Cox model to the Yakovlev model. These connections suggest we may not only estimate proportional hazards rates but also assess cure rates when fitting a Cox model. The connections also motivate us to investigate the effects on estimated cure rates with different values of the cure threshold, which is used to identify cured subjects in the Yakovlev model, and the Cox model may be considered “theoretically” as a limiting case of the Yakovlev model with the cure threshold tending to infinity. The finite sample properties of the results are investigated in a simulation study, and an analysis of a classical dataset concerning malignant melanoma illustrates interpreting cure rates when fitting a Cox model. In addition, through using these connections, we find that many statistical inference tools developed for the Cox model, such as variable selection methods, can be directly applied to the Yakovlev model, and we use a breast cancer dataset to demonstrate the application.