Re: Single-Factor-Cox-Regression

Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx> wrote in
news:grh1u25qmjbgaphi8d7ousfbrh6i8jitmf@xxxxxxx:

On 23 Feb 2007 12:08:09 -0800, patrick.ringsmoeller@xxxxxxxx wrote:

Hello everybody,

I would like to test the influence of a clinical parameter upon
patient survival by Cox-Regression. But I am not sure, whether this is
allowed (using only a single factor (covariate) within Cox-Regression)
or if Cox-Regression always needs a certain amount of different
covariates to be correct in a statistical sense. Moreover, I wondered
if there exists a rule of thumb how many covariates can be included in
a Cox-Regression at maximum for a given number of patients under
consideration.

The Cox proportionate hazard regression can is surely
safer with one variable than with several.

I have not seen mention of limits for covariates.
I have run a number of them, with fairly small N, and at some
point, it can fail to converge, or give bad numbers. Run some
with your own data -- Then try it with partial samples -- Does it
seem to work?


Like the logistic regression, which it is sort-of an extension
of, it is probably best used as a large sample procedure.
That is, there is a dichotomous criterion at each of the
multiple periods, and there is a further assumption that the
rates for two groups have the same Odds Ratio at each
of the several periods.

Cox regression models hazards and hazard ratios. No odds ratios. The goal
is to model probability of an event per unit time. Cox models do have
linear predictors inside exponential functions, but they are not
extensions of logistic models.

One conservative guideline that has been mentioned for
Logistic regression is to require at least 20 more cases in the
smaller category, for each additional covariate. (I think that
requiring "20" is being conservative; you are almost assured of
having no problems with an N that large, but you might do
pretty well with half that many... or, you might not.)

Logistic regression has one outcome; Cox regression has
outcomes at many periods. So it will need a bigger N.

I rather doubt that you can provide a citation or a mathematical
justification for that assertion.

Logistic regression has no representation of time or censoring.

Cox regression models time between events and calculates rates. It should
have more power, rather than less power to properly characterize risk in
cohorts.

I *think* that the Cox regressions are implemented around
discrete periods, so that you need cases in both groups at
every period. Thus, your N for Cox regression is probably
a multiple of what you need for Logistic regression, depending
on the number of periods.

No. Time is _not_ modeled as a discrete variable in Cox regression. There
are no "numbers of periods" that would affect the statistical power of
the procedure. You may be confusing Poisson regression with Cox
regression. In Poisson regression the assumption of constant hazards
during pre-specified intervals is often used. If you only measure time of
event to the nearest year, then that it your choice, not something
imposed by the Cox model. I suggest the OP completely ignore your
unsubstantiated hand-waving arguments.

Although I have not looked at it, not having access from home, I suspect
that persons with academic accounts may find this article interesting:
"Relaxing the Rule of Ten Events per Variable in Logistic and Cox
Regression" by Eric Vittinghoff and Charles E. McCulloch:

Abstract:
The rule of thumb that logistic and Cox models should be used with a
minimum of 10 outcome events per predictor variable (EPV), based on two
simulation studies, may be too conservative. The authors conducted a
large simulation study of other influences on confidence interval
coverage, type I error, relative bias, and other model performance
measures. They found a range of circumstances in which coverage and bias
were within acceptable levels despite less than 10 EPV, as well as other
factors that were as influential as or more influential than EPV. They
conclude that this rule can be relaxed, in particular for sensitivity
analyses undertaken to demonstrate adequate control of confounding.
<http://aje.oxfordjournals.org/cgi/reprint/kwk052v1>


If anyone knows something more definite about that, I will
be happy to hear it.

--
David Winsemius

.

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