FROM Terry Therneau:
Consider a Cox model for the following data:
Treated Control
alive 40 35
dead 0 5
This might occur if treatment were effective and the analysis was done
very early. The true hazard ratio for this study is 0/something = 0
(where "something" depends on the actual pattern of death times, but
estimates the death rate in the control arm).
Since the Cox model assumes that hazard = exp(X beta), the MLE estimate
of beta is -infinity. The model is not invalid, and tests based on
either the log-likelihood or the score statistics are ok. However, the
Wald statistics (beta/se) for the infinite covariate are not correct, and
the program prints a warning message to alert the user.
This case occurs moderately often with categorical predictors, if the
model as a whole is able to isolate a subgroup with 0 events. Either a
categorical with lots of levels or interaction terms often cause it.
If stepAIC does not depend on Wald statistics (and I think it doesn't -- but
don't take my word on that) then all is well.
INSERT from Brian Ripley:
Terry is right: stepAIC just looks at the maximized partial likelihood.
What is in essence the same problem occurs with logistic regression and
log-linear models, including unreliable Wald statistics. The main
difference between step and stepAIC is that step does use the Wald
statistics, and by motivation for writing stepAIC was some examples
in which misled step quite seriously.
-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595
CONTINUATION of Terry Therneau's message:
Some people have urged me to remove the warning message entirely as a "confounded nuisance". In particular, skewed or correlated covariates can sometimes trigger the message inappropriately.
Terry M. Therneau, Ph.D. (507) 284-3694 Head, Section of Biostatistics (507) 284-9542 FAX Mayo Clinic therneau.terry@mayo.edu Rochester, Minn 55905
Melania Pintilie ext 4886 PMH Biostatistics
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