Power analysis for Cox regression with a time-varying covariate

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Power analysis for Cox regression with a time-varying covariate

Paul Miller
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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Re: Power analysis for Cox regression with a time-varying covariate

glsnow
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]> 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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.



--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

______________________________________________
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Re: Power analysis for Cox regression with a time-varying covariate

Paul Miller
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]> 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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.


--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

        [[alternative HTML version deleted]]


______________________________________________
[hidden email] mailing list
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and provide commented, minimal, self-contained, reproducible code.
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Re: Power analysis for Cox regression with a time-varying covariate

glsnow
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
> >
> > ______________________________________________
> > [hidden email]<http://ca.mc1616.mail.yahoo.com/mc/compose?to=R-help@...>mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> > and provide commented, minimal, self-contained, reproducible code.
>
>
>
> --
> Gregory (Greg) L. Snow Ph.D.
> [hidden email]<http://ca.mc1616.mail.yahoo.com/mc/compose?to=538280@...>
>
>


--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

        [[alternative HTML version deleted]]

______________________________________________
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Re: Power analysis for Cox regression with a time-varying covariate

Marc Schwartz-3
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.

Regards,

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 <[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

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.