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Biometrika 1995 82(2):251-261; doi:10.1093/biomet/82.2.251
© 1995 by Biometrika Trust
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Testing the hypothesis of proportional hazards in two populations

JAYANT V. DESHPANDE and DEBASIS SENGUPTA

Department of Statistics, University of Poona Pune 411 007, India
Computer Science Unit, Indian Statistical Institute Calcutta 700 035, India

The assumption of proportional hazards in different populations leads to elegant analysis of survival data as initiated by Cox (1972). However, this model is not appropriate in all situations. In recent literature there have been several instances of crossing hazards, which may be modelled by an increasing hazard ratio. We present a U-statistic test for checking constancy of the hazard ratio against this alternative. The test is suitable for censored data and is found to have reasonable power in certain parametric families. Next we propose a test for checking proportionality of the hazards of two competing risks, in the presence of a third risk, against the alternative of increasing hazard ratio. Analyses of a few real data sets and some results based on computer simulations are also given.

Key Words: Asymptotic relative efficiency • Censoring • Competing risks • Counting process • Increasing failure rate • Proportional hazards model


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