R help - Jul 2012 - Power analysis for Cox regression with a time-varying covariate

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

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>
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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http://www.R-project.org/posting-guide.html
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-- 
Gregory (Greg) L. Snow Ph.D.
538280 at gmail.com

Marc gave the referencer for Schoenfeld's article.  It's actually quite 
simple.

Sample size for a Cox model has two parts:
  1. Easy part: how many deaths to I need

       d = (za + zb)^2 / [var(x) * coef^2]

       za = cutoff for your alpah, usually 1.96 (.05 two-sided)
       zb = cutoff for power, often 0.84 = qnorm(.8) = 80% power
       var(x) = variance of the covariate you are testing.  For a yes/no 
variable like treatment this would be p(1-p) where p = fraction on the 
first arm
       coef = the target coefficient in your Cox model.  For an 
"increase in survival of 50%" we need exp(coef)=1.5 or coef=.405

All leading to the value I've memorized by now of (1.96 + 0.84)^2 /(.25* 
.405^2) = 191 deaths for a balanced two arm study to detect a 50% 
increase in survival.

  2. Hard part: How many patients will I need to recruit, over what 
interval of time, and with how much total follow-up to achieve this 
number of events?
    I never use the canned procedures for sample size because this 
second part is so study specific.  And frankly, it's always a 
guesstimate.  Death rates for a condidtion will usually drop by 1/3 as 
soon as you start enrolling subjects.

Terry T.