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

[Terry Therneau-2]

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.

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[Paul Miller]

Hi Terry, Greg, and Marc,
 
Thanks for your advice about this. I think I have a pretty good starting point now for the analysis.
 
Appreciate your help.
 
Paul

--- On Wed, 7/18/12, Terry Therneau <[hidden email]> wrote:


From: Terry Therneau <[hidden email]>
Subject: Re: [R] Power analysis for Cox regression with a time-varying covariate
To: "Marc Schwartz" <[hidden email]>, "Greg Snow" <[hidden email]>, [hidden email], "Paul Miller" <[hidden email]>
Received: Wednesday, July 18, 2012, 8:24 AM


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.


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