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Hello,
I am trying to find the estimated relative risk given certain parameters in a power calculation. The example is for a randomized control trial with 5000 in the treatment group and 5000 in the placebo group with an estimated 2% of the placebo with the outcome.
To solve for the relative risk given these characteristics, I have tried the following code but there is an error message for the RR being missing...even though that is what I am trying to solve for. Any thoughts?
proc power;
twosamplefreq test=pchi
relativerisk= .
refproportion= 0.02
npergroup = 5000
power = 0.8;
run;
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Hello @jenoli525 and welcome to the SAS Support Communities!
You raise a good point. PROC POWER can solve only for power or sample size (be it total or per group), although asking for relative risk, given power, sample size and reference proportion, is an obvious, legitimate question, at least from a purely mathematical point of view. Maybe they want to nudge you towards specifying the relative risk based on subject-matter considerations, e.g., what is clinically relevant. Technically, it would be no problem at all to extend the capabilities of PROC POWER correspondingly.
You can still use the procedure to obtain the desired result:
- Set npergroup (or power) to missing and specify a range of relative risks.
- Refine and restrict the range to the interval in which the resulting npergroup in the previous step crossed 5000 (or the power crossed 0.8, resp.).
- Repeat step 2 until the desired precision is attained.
Of course, in your example there are two numeric solutions for the relative risk RR=p2/p1=p2/0.02, depending on whether the second proportion, p2, is less than or greater than reference proportion p1=0.02. In the latter case (the other case is done analogously) you could start with something like:
proc power;
twosamplefreq test=pchi
relativerisk= 1.1 to 2 by 0.1
refproportion= 0.02
npergroup = .
power = 0.8;
run;
In the results you see that the solution for relative risk must be between 1.4 and 1.5:
Computed N per Group Relative Actual N per Index Risk Power Group 1 1.1 0.800 80682 2 1.2 0.800 21109 3 1.3 0.800 9798 4 1.4 0.800 5745 5 1.5 0.800 3826 6 1.6 0.800 2760 7 1.7 0.800 2103 8 1.8 0.800 1668 9 1.9 0.800 1364 10 2.0 0.800 1141
So, in the next step you would use:
relativerisk= 1.4 to 1.5 by 0.01
and continue similarly with
relativerisk= 1.43 to 1.44 by 0.001
and
relativerisk= 1.431 to 1.432 by 0.0001
To see more decimals than in the default output of PROC POWER you may want to write the results to an ODS output dataset by using
ods output output=pow;
The final results, obtained with
proc print data=pow;
var rel: np:;
format relativerisk 6.4;
run;
are
Relative NPer Obs Risk Group 1 1.4310 5010 2 1.4311 5008 3 1.4312 5006 4 1.4313 5004 5 1.4314 5002 6 1.4315 5000 7 1.4316 4998 8 1.4317 4995 9 1.4318 4993 10 1.4319 4991 11 1.4320 4989
So, 1.4315 is the relative risk in question.
The solution with p2<p1 (obtained analogously) is 0.6438.