You're welcome. I was busy with other things, too.
@Skillside wrote:
So if i understood it correctly the following proc will be correct for noninferiority sample size calculation,
proc power;
twosamplefreq groupps=(0.97 0.95) alpha=0.025 nullpdiff=0.02 power=0.9
test=fm sides=1 npergroup=.;
run;
That gives 535 ...
Correct.
so i cannot set nullpdiff below 2%
Not correct. Null proportion differences less than 2% are no problem since the difference 0.95-0.97=-0.02 is still less than any positive number. NULLPDIFF values <=-0.02 would be invalid (but for negative values we would be in the situation of a superiority test anyway).
and for nullpdiff is more optimistic 356.
This is the result for nullpdiff=0.03.
But then when i calcualte power for Chi-square test it doesn't give the sufficient power.
Sure, because this means nullpdiff=0, which is much closer to the assumed true difference 0.95-0.97=-0.02 than the nullpdiff=0.02 we used for the non-inferiority test.
Well, they differ between endpoints but i assume that in real life scenario and on the bigger sample it will be the same as first drug or even better.
I meant that i assume the margin which will show equality or even superiority.
Since a superiority test would require an even larger sample size than the equality (chi-square) test, I'd say that we can focus on equality or non-inferiority.
Could you provide some simulations, please?
Here they are: Let's start with the non-inferiority studies corresponding to your PROC POWER step above.
%let nsim=10000; /* number of simulated studies */
%let n=535; /* sample size per group */
%let p1=0.97; /* success probability in group 1 */
%let p2=0.95; /* success probability in group 2 */
%let m=0.02; /* non-inferiority margin (absolute value of the null proportion difference) */
/* Simulate the results of &NSIM studies */
data sim;
call streaminit(3141592);
do i=1 to ≁
do grp=1, 2;
success=1;
k=rand('binom', choosen(grp, &p1, &p2), &n);
output;
success=0;
k=&n-k;
output;
end;
end;
run;
/* Perform non-inferiority (Farrington-Manning score) test for each study */
ods select none;
ods noresults;
ods output pdiffnoninf=pdni;
proc freq data=sim;
by i;
weight k;
tables grp*success / riskdiff(column=2 method=fm noninf margin=&m);
run;
ods select all;
ods results;
/* Determine the proportion of studies with a significant test result
(i.e., showing non-inferiority of the treatment in group 1)
*/
proc format;
value pvone
low-0.025='significant'
0.025<-high='not significant';
run;
ods exclude binomialtest;
proc freq data=pdni;
format pvalue pvone.;
tables pvalue / binomial;
run;
ods exclude none;
Result: Point estimate of the power: 0.9123 (exact 95%-CI: 0.9066, 0.9178).
For an equality test the required sample size would be much larger:
proc power;
twosamplefreq groupps=(0.97 0.95) alpha=0.05 power=0.9
test=pchi sides=2 npergroup=.;
run; /* --> npergroup=2016 */
The corresponding simulation is similar to the one above:
%let nsim=10000; /* number of simulated studies */
%let n=2016; /* sample size per group */
%let p1=0.97; /* success probability in group 1 */
%let p2=0.95; /* success probability in group 2 */
/* Simulate the results of &NSIM studies */
data sim;
call streaminit(31415927);
do i=1 to ≁
do grp=1, 2;
success=1;
k=rand('binom', choosen(grp, &p1, &p2), &n);
output;
success=0;
k=&n-k;
output;
end;
end;
run;
/* Perform Pearson chi-square test for each study */
ods select none;
ods noresults;
ods output chisq=csq(where=(statistic='Chi-Square'));
proc freq data=sim;
by i;
weight k;
tables grp*success / chisq;
run;
ods select all;
ods results;
/* Determine the proportion of studies with a significant test result
(i.e., showing a significant difference between the success rates)
*/
proc format;
value pvtwo
low-0.05='significant'
0.05<-high='not significant';
run;
ods exclude binomialtest;
proc freq data=csq;
format prob pvtwo.;
tables prob / binomial;
run;
ods exclude none;
Result: Point estimate of the power: 0.9040 (exact 95%-CI: 0.8981, 0.9097).
So, in both cases the intended power of 0.9 was achieved.
And thank you for providing the link to documentation, but unfortunately, i don't understand most of the equations, i am not mathematician
The important parts at the top of the page are relatively simple. The actual sample size formulas are a bit complicated, but you don't need them as long as you trust PROC POWER. Also, if in doubt, you can ask me. I am a mathematician. 🙂
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