Summary: The generalized proportional hazards model proposed by E. A. Peña and V. K. Rohatgi [J. Stat. Plann. Inference 22, No. 3, 371–389 (1989; Zbl 0671.62103)] assumed that \(X\) and \((Y, \beta)\) are independent and \(\overline{G}(t)=E_B[\overline{F}(t)]^\beta\) where \(X\) and \(Y\) are two competing lifetimes with continuous survival functions \(\overline{F}(t)\) and \(\overline{G}(t)\) respectively, and \(\beta\) is a nonnegative random variable with \(B(b)=P[\beta\leq b]\). When \(B(b)\) is uniquely determined by an unknown parameter \(\theta\) with a mild condition, they used \(n\) independent and identically distributed observations \((Z_i, \delta_i)^n_{i=1}\) taken from \(Z=\text{min}(X,Y)\) and \(\delta=I(X\leq Y)\) to investigate estimators of \(\overline{F}(t)\) and \(\theta\) and their large sample properties. In this paper, we show that \(m(t)=P[\delta=1|Z>t]\) is nondecreasing in \(t\) under the generalized proportional hazards model. As a consequence, we obtain that the odds ratio or the cross-product ratio \(OR(t)=P_{11}(t)P_{00}(t)/[P_{10}(t)P_{01}(t)]\geq 1\) under the generalized proportional hazards model, where \(P_{ij}(t)=P[I(Z>t)=i, \delta =j]\) for \(i, j=0,1\). 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 \(\beta\) has a geometric distribution with the parameter \(\theta\) is also obtained. The result is also illustrated by an example.