[R] Power analysis for Cox regression with a time-varying covariate

Marc Schwartz marc_schwartz at me.com
Tue Jul 17 21:54:23 CEST 2012

Hi Greg and Paul,

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:

  Sample-Size Formula for the Proportional-Hazards Regression Model
  David A. Schoenfeld
  Biometrics, Vol. 39, No. 2. (Jun., 1983), pp. 499-503.

Another reference would be:

Sample-Size Calculations for the Cox Proportional Hazards Regression Model with Nonbinary Covariates
F.Y. Hsieh and Philip W. Lavori
Controlled Clinical Trials 21:552–560 (2000

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


Marc Schwartz

On Jul 17, 2012, at 12:33 PM, Greg Snow wrote:

> 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@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

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