Re: st: detectable alternative/effect size;

[Steven Samuels <sjhsamuels@earthlink.net>]

On Sep 16, 2008, at 4:18 PM, Elliott Dasenbrook wrote:
> I am trying to calculate the detectable alternative for a  
> dichotomous outcome expressed as a relative risk given my sample  
> size and a power of 0.90; Is there a command/package in STATA that  
> does this? [i saw that this can be calculated for Cox proportions] 
> The sampsi command only allows calculation of power or sample size  
> as far as I can tell;
Here is a do file which will calculate minimum detectable RR for a  
series of baseline values for the smaller probability for power =90%  
and 2-sided alpha =.05. The code uses the angular transformation to  
stabilize the variance.  I added a purely ad-hoc continuity  
correction to bring the actual power to detect the "minimum  
detectable" differences closer to the 90%, so use at your own risk.  
(Use -sampsi- to see the actual power to detect the listed "minimum- 
detectable" alternatives.  Be sure to zap gremlins before inserting  
the code into Stata.


*******************Code Starts******************************
/* File minimum detectable risks for test of proportion:
   H0: P= P0 H1: P=P1>P02 2-sided 0.05 test  Power =90%
   Uses the angular (arcsine) transformation to stabilize variances.
   A purely ad-hoc continuity correction is added to make the power
   closer to the nominal value of 90%*/
clear
capture drop _all

set obs 1
// Set up initial values
local n1 = 200  //Set sample sizes per group
local n2 = 200
local base_val .05 .1 .15 .2 .3 // list of values for smaller  
proportion P0

local power =  0.90
local alpha=.05

local zz = (invnorm(1-`alpha'/2) + invnorm(`power'))
local se = 0.5*(1/`n1' + 1/`n2')^.5
local delta= `zz'*`se'   //Detectable difference on Z scale


foreach x of numlist 1 {
di  _newline(1)  _col(12)  " N1 = " `n1'  _col(25) "N2 = " `n2'   ///
 _newline _col(5) "P0" _col(15) "Min P1"  _col(30) "Min Detec RR"
foreach p0 of numlist `base_val'{
local h0 = asin(sqrt(`p0'))       // angular transformation
local cc = .75*(1/`n1' +1/`n2')   //continuity correction
local h1 = `delta' + `h0' + `cc'  // detectable alternative
local p1 = (sin(`h1'))^2         //back transform to proportion
local rr = `p1'/`p0'
di  _col(5) round(`p0',.01) _col(15) round(`p1',.001)   _col(30) round 
(`rr',.01)
}
}
***********************Code Ends*****************************


 
 
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