A Robust Parameterization for Unbounded Covariates Within the Cox Proportional Hazards Model

Richard J. Jackson, Trevor F. Cox

Abstract


The Cox proportional hazards model is widely used in the analysis of medical data either for survival or time to a particular event. Factors and continuous covariates can be easily incorporated into the model and hazard ratios calculated. The model can however be distorted when extreme value observations occur within a continuous covariate and the hazard ratio can become extremely large. To overcome this, transformations of the covariate are often made, which can be simple, e.g. log, or more sophisticated such as the fitting of a fractional polynomial. This paper takes a different approach and makes a transformation based on the logistic function that has the property that the hazard ratio is bounded. The models are introduced and discussed. Model diagnostics based on Schoenfeld residuals and the influence function are established and then data from a pancreatic cancer trial are used to illustrate the model.

Keywords


ESPAC 3 trial, hazard ratio, influence function, logistic function, Schoenfeld residuals.

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ISSN: 1929-6029