The generalized proportional hazards model proposed by Peña and Rohatgi [8] assumed that X and  are independent and   where X and Y are two competing lifetimes with continuous survival functions  and  respectively, and b  is a nonnegative random variable with  When   is uniquely determined by an unknown parameter q with  a mild condition, they used n independent and identically distributed observations  taken from  and  to investigate estimators of  and q and their large sample properties. In this paper, we show that  is nondecreasing in t under the generalized proportional hazards model. As a consequence, we obtain that the odds ratio or the cross-product ratio  under the generalized proportional hazards model, where  for  We use this property to develop a method of testing  to determine when the generalized proportional hazards model is inappropriate for a data set. A similar result for the proportional odds ratio model that assumes the random variable b has a geometric distribution with the parameter q is also obtained. The result is also illustrated by an example.

Fisher’s exact test, generalized proportional hazards model, odds ratio, proportional odds ratio model.