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Paper IPM / M / 16548  


Abstract:  
A timedependent divergence measure is proposed to compare the survival functions of twolifetime random variables. It is shown that the proposed measure ranges between [0,1] and under some mild conditions has the metric properties. Several properties of the divergence measure are investigated, among others, it is shown the divergence between two survival functions does not depend on time if and only if they follow the proportional hazards model. The measure is also examined for various other wellknown survival models such as the proportional odds model. The estimation of the suggested divergence measure for survival data is also discussed and the asymptotic normal distribution of the resulting estimator is established. The proposed estimation is evaluated via simulation and further employed to compare the effects of two treatment groups on the overall survival times of kidney cancer patients.
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