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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, November 7, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Jane L. Hutton}
\centerline{\sl University of Warwick, UK}
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\centerline{\bf Models for survival data: choice between accelerated life 
and proportional hazards models}
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In medical, engineering and economic applications, the choice between the
proportional hazards or the accelerated life families of models is rarely
discussed.  The proportional hazards family is widely used in medicine.
Accelerated life  models have conventionally been used in reliability and
economic applications. 

We discuss the impact of misspecifying  fully parametric proportional
hazards and accelerated life models. For the uncensored case, misspecified
accelerated life models give asymptotically unbiased estimates of covariate
effect, but the shape and scale parameters depend on the misspecification.
The covariate, shape and scale parameters differ in the censored case.
Asymptotic and first order results are compared. Simulation is used to
investigate whether the asymptotic results hold for small samples.

Accelerated life models are more robust to misspecification than
proportional hazards.
Parametric proportional hazards models do not have a sound justification
for general use: estimates from misspecified models can be very biased,
there is a loss of power, and misleading results for the shape of the
hazard function can arise. Misspecified survival functions are more biased
at the extremes than the centre. Estimates of covariate effects for
misspecified fully parametric models are compared with those from a Cox
proportional hazards model, and survivor function estimates compared with
Cox and Kaplan-Meier
estimators.  The comparative robustness, in terms of estimation of
covariate effect, and size and power of tests of effect, of the Weibull
model and the Cox proportional hazards model merit further investigation. 

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