[S] AIC for survreg models

Paul Monaghan (pfm@scmp.scm.liv.ac.uk)
Mon, 16 Feb 1998 12:36:22 +0000 (GMT)

Thanks to Terry Therneau, Bill Venables and Brian Ripley who responded to my earlier query about
'residual deviance' for parametric survival modelling using the survreg function. I should have stated the
version of Splus I use, as pointed out by Prof. Ripley, this is 3.3 for Unix.

My main reason for considering deviance and log-likelihoods is an attempt to compare non-nested
parametric models using the Akaike Information Criteria. For example, I wish to compare fits using the
log-logistic, log-normal and Weibull models (the test of the exponential model versus the Weibull is
equivalent to the hypothesis test that the shape parameter is 1, or in the survreg fit that
Log(scale) is zero). The usual situation has AIC defined as

-2 log L + 2p *

where log L is the likelihood under the fitted model and p is the number of parameters in the model.
GIven the replies to my query, I am concerned about how this may apply to survreg fits. As the Weibull,
log-logistic and log-normal models all have 2 baseline parameters (shape and scale) using this definition
and assuming that the same covariates are included in each model the 'best' fitting model using this
criteria is that with the largest maximised log-likelihood.

My question is that since the 'residual deviance' depends on the estimate of the scale parameter, does
AIC hold for the comparison of survival models? Or is some correction to * based on the estimated scale
parameter required.

I would appreciate any help.

Paul Monaghan, University of Liverpool.
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