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Abstract Details
Activity Number:
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32
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Type:
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Contributed
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Date/Time:
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Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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Abstract - #306263 |
Title:
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When Is It Inappropriate to Use the Generalized Proportional Hazards Model?
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Author(s):
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Jian-Lun Xu*+
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Companies:
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National Cancer Institute
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Address:
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EPN-3131, Bethesda, MD, 20892-7354, United States
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Keywords:
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Generalized proportional hazards model ;
Positive covariance ;
Fisher's exact test ;
Pearson's Chi-squared test ;
Proportional odds ratio model ;
odds ratio
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Abstract:
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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.
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Authors who are presenting talks have a * after their name.
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