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A semi-parametric generalization of the Cox proportional hazards regression model: inference and applications. (English) Zbl 1247.62247

Summary: The assumption of proportional hazards (PH) fundamental to the Cox PH model sometimes may not hold in practice. We propose a generalization of the Cox PH model in terms of the cumulative hazard function taking a form similar to the Cox PH model, with the extension that the baseline cumulative hazard function is raised to a power function. Our model allows for interactions between covariates and the baseline hazard and also includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach can not be applied here to estimate the model parameters. We use the full likelihood approach via a cubic B-spline approximation for the baseline hazard to estimate the model parameters. A semi-automatic procedure for knot selection based on Akaike’s information criterion is developed. We illustrate the applicability of our approach using real-life data.

MSC:

62N02 Estimation in survival analysis and censored data
62N01 Censored data models
65C60 Computational problems in statistics (MSC2010)
62G32 Statistics of extreme values; tail inference
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References:

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