Power analysis for Cox regression with a time-varying covariate

One quick (though probably not canned) approach to get a feel for what an
analysis might be like is to analyze a sample data set (from the survival
package, a textbook, or a past analysis).  Choose something that has some
similarity to the planned study.  Now look at the widths of the confidence
intervals from that analysis, that will give a feel for the effect size
that can be detected using the same sample size.  You could also analyze a
subset of the data to see what a smaller sample size would give and you
could sample with replacement to get a larger sample and analyze that to
get a feel for larger data sets (this will be more approximate than the
others since you will be reusing subjects and so they won't be as different
from each other as in a true data set).

Terry has also indicated that whether the predictors vary with time or not
should not affect the power/sample size calculations, so if you have a
canned approach (or just simpler approach) for non-varying predictors then
you could just use that.

On Sun, Jul 15, 2012 at 8:02 AM, Paul Miller <pjmiller_57 at yahoo.com> wrote:

Hi Greg,

Thanks for your response. So far I've just been asked to investigate what
the analysis likely would involve. The hope was that there were be some
sort of quick and easy "canned" approach. I don't really think this is the
case though. If I'm asked to do the actual analysis itself, I'll start out
using the steps you've listed and see where that takes me.

Paul

--- On *Fri, 7/13/12, Greg Snow <538280 at gmail.com>* wrote:


From: Greg Snow <538280 at gmail.com>
Subject: Re: [R] Power analysis for Cox regression with a time-varying
covariate
To: "Paul Miller" <pjmiller_57 at yahoo.com>
Cc: r-help at r-project.org
Received: Friday, July 13, 2012, 3:29 PM


For something like this the best (and possibly only reasonable) option
is to use simulation. I have posted on the general steps for using
simulation for power studies in this list and elsewhere before, but
probably never with coxph.

The general steps still hold, but the complicated part here will be to
simulate the data.  I would recommend something along the lines of:

1. generate a value for the censoring time, possibly exponential or
weibull (for simplicity I would make this not dependent on the
covariates if reasonable).
2. generate a value for the covariate for the given time period
(sample function possibly), then generate a survival time for this
covariate value (possibly weibull distribution, or lognormal,
exponential, etc.)  If the survival time is less than the time period
and censoring time then you have an event and a time to the event.  If
the survival time is longer than the censoring time, but not longer
than the time period (for the covariate), then you have censoring and
you can record the time to censoring.  If the survival time is longer
than the time period then you have the row information for that time
period and can move on to the next time period where you will first
randomly choose the covariate value again, then generate another
survival time based on the covariate and given that they have already
survived a given amount.  Continue with this until you have an event
or censoring time for each subject.

On Fri, Jul 13, 2012 at 9:17 AM, Paul Miller <pjmiller_57 at yahoo.com<http://ca.mc1616.mail.yahoo.com/mc/compose?to=pjmiller_57 at yahoo.com>>
wrote:

Hello All,

Does anyone know where I can find information about how to do a power

analysis for Cox regression with a time-varying covariate using R or  some
other readily available software? I've done some searching online but
haven't found anything.

Thanks,

Paul