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Posted 04-12-2018 12:27 PM
(1460 views)

I am doing a sample size calculation for two proportions (alpha=0.05, beta=0.2 (i.e. power=0.8)). Group proportions are fixed at 0.05 and 0.0375, respectively. If I decide on N=4555 subjects in one group how many subjects do I need to include in the other group ?

proc power; ods output Power.TwoSampleFreq.Output=out; twosamplefreq GROUPPROPORTIONS = (0.05 0.0375) groupns=(4555 .) power = 0.80 alpha = .05; run;

fails me. Any suggestions ?

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I suggest to simulate with different numbers, and find the right N for which the probability for rejecting becomes 80%. I assume it is a two side test, so we can test the hypothesis of equal proportions with a likelihood test.

The calculation of p-values so simple here that it can be calculated within a datastep. It turns out that about 3865 should be in the other group in order to get a probability of rejecting=80% (that is the power).

```
data simulation;
array n{2} _temporary_ (4555,3865);
array p{2} _temporary_ (0.05,0.0375);
array y_{2} _temporary_;
do i=1 to 1000000;
l0=0;
do k=1 to 2;
outcome=1;y=rand('binomial',p[k],n[k]);y_[k]=y;l0+y*log(y/n[k]);
outcome=0;y=n[k]-y; l0+y*log(y/n[k]);
end;
l1=(y_[1]+y_[2])*log((y_[1]+y_[2])/(n[1]+n[2]))+
(n[1]+n[2]-y_[1]-y_[2])*log(1-(y_[1]+y_[2])/(n[1]+n[2]));
minus2logQ=-2*(l1-l0);
pvalue=sdf('chisquare',minus2logQ,1);
reject=(pvalue<0.05);
output;
end;
keep minus2logQ reject;
run;
proc means data=simulation mean;
var reject;
run;
```

(I edited a bit, as first I said about 4000 in the other group. Increasing the number of simulations shows that 3865 is more accurate).

2 REPLIES 2

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I suggest to simulate with different numbers, and find the right N for which the probability for rejecting becomes 80%. I assume it is a two side test, so we can test the hypothesis of equal proportions with a likelihood test.

The calculation of p-values so simple here that it can be calculated within a datastep. It turns out that about 3865 should be in the other group in order to get a probability of rejecting=80% (that is the power).

```
data simulation;
array n{2} _temporary_ (4555,3865);
array p{2} _temporary_ (0.05,0.0375);
array y_{2} _temporary_;
do i=1 to 1000000;
l0=0;
do k=1 to 2;
outcome=1;y=rand('binomial',p[k],n[k]);y_[k]=y;l0+y*log(y/n[k]);
outcome=0;y=n[k]-y; l0+y*log(y/n[k]);
end;
l1=(y_[1]+y_[2])*log((y_[1]+y_[2])/(n[1]+n[2]))+
(n[1]+n[2]-y_[1]-y_[2])*log(1-(y_[1]+y_[2])/(n[1]+n[2]));
minus2logQ=-2*(l1-l0);
pvalue=sdf('chisquare',minus2logQ,1);
reject=(pvalue<0.05);
output;
end;
keep minus2logQ reject;
run;
proc means data=simulation mean;
var reject;
run;
```

(I edited a bit, as first I said about 4000 in the other group. Increasing the number of simulations shows that 3865 is more accurate).

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More complicated than I hoped for, but thanks

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