I had initially contemplated a solution similar to Greg's, which is simulation.

However, I might just throw out, that if based upon Terry's comments, time varying covariates do not impact the power/sample size considerations for the Cox model, then Schoenfeld's 1983 article in Biometrics would be of value:

David A. Schoenfeld

Biometrics, Vol. 39, No. 2. (Jun., 1983), pp. 499-503.

Sample-Size Calculations for the Cox Proportional Hazards Regression Model with Nonbinary Covariates

F.Y. Hsieh and Philip W. Lavori

A skillful Google search will find both available online if you don't have access otherwise.

> 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 <

[hidden email]> 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 <

[hidden email]>* wrote:

>>

>>

>> From: Greg Snow <

[hidden email]>

>> Subject: Re: [R] Power analysis for Cox regression with a time-varying

>> covariate

>> To: "Paul Miller" <

[hidden email]>

>> Cc:

[hidden email]
>> 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 <

[hidden email]<

http://ca.mc1616.mail.yahoo.com/mc/compose?to=pjmiller_57@...>>

>> 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