When Is It Inappropriate to Use the Generalized Proportional Hazards Model?

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Jian-Lun Xu*+
• Companies: National Cancer Institute
• Keywords: Generalized proportional hazards model ; Positive covariance ; Fisher's exact test ; Pearson's Chi-squared test ; Proportional odds ratio model ; odds ratio

Abstract

Let $X$ and $Y$ be two competing lifetimes with continuous survival functions ${\overline F}(t)$ and ${\overline G}(t),$ respectively, and let $\beta$ be a nonnegative random variable with $B(b)=P[\,\beta\le b\,]. $ A generalized proportional hazards model proposed by Pe\~{n}a and Rohatgi (1989) assumed that $X$ and $(Y,\beta)$ are independent and ${\overline G}(t)=E_B[\,{\overline F}(t)\,]^{\beta}. $ When $B(b)$ is uniquely determined by an unknown parameter $\theta$ with a mild condition, they used $n$ independent and identically distributed observations $(Z_i, \delta_i)_{i=1}^n$ taken from $Z=\mbox{min}(X, Y)$ and $\delta=I(X\le Y)$ to investigate estimates of ${\overline F}(t)$ and $\theta$ and their large sample properties. In this paper we show that binary variables $I(Z>t)$ and $\delta$ under the generalized proportional hazards model are always positively correlated for any $t>0. $ We use this property to develop a method of testing when the generalized proportional hazards model is inappropriate for a data set. A similar result for the proportional odds ratio model is also obtained. Finally, examples to apply this testing method are considered.