# Re: st: Cox reg sample size formula in our book

 From ymarchenko@stata.com (Yulia Marchenko, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: Cox reg sample size formula in our book Date Sat, 14 Mar 2009 14:10:03 -0500

```Enzo Coviello <enzo.coviello@tin.it> asks:

> making use of -stpower- I noted the formula at the bottom of pag 338 of
> "An intoduction to survival analysis using Stata" 2nd ed., where to
> compute the required number of events the estimates of sigma_squared
> (the variance) and of R_squared are at the denominator.  In the next
> page the comment is "The terms ... (above mentioned) ...  accounts for
> the the variability in the estimate of beta ... the larger the variance
> ..., the larger the required number of events ", as it should be.
> ...
> This conclusion seems inconsistent with the fact that the terms for
> the variability of the estimate are at denominator where  the larger
> values  should correspond  to lesser value of the required number of
> events. Do I (or does the formula) miss something ?

The sentence Enzo is referring to states the following:

"The term {sigma^2(1-R^2)}^(-1) accounts for the variability in the
estimate of beta_1 -- the larger the variance of the estimate, the
larger the required number of events and sample size."

The denominator of the formula for the required number of events, ignoring the
estimate of the coefficient, is sigma^2(1-R^2).  The word "term" above refers
to the 1/denominator.  So, the conclusion is consistent with the formula: as
1/denominator gets larger, the number of events gets larger.

-- Yulia
ymarchenko@stata.com
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