Sample size for two treatment effects with binary outcome using proc power

[Caetreviop543]

I am trying to run a power analysis with the following specifications to get the required sample size:

1. Model is logistic regression with binary outcome
2. Two separate treatments, and a control, with the following probabilities:
   1. Control: 0.30
   2. Treatment 1: 0.27
   3. Treatment 2: 0.14
3. 80% power, and 0.05 alpha

I’m not sure how to use proc power with three study arms. I could not figure out how to specify a non-ordinal, categorical variable in the vardist statement. I input each treatment effect as an ordinal dummy variable to compare to the control group. However, because proc power doesn’t allow for multiple odds ratios in the testoddsratio statement, I put the odds ratio for treatment two as a covariate effect. Here is my code:

proc power;
logistic
vardist("x1") = ordinal((0, 1) : (0.5, 0.5))
vardist("x2") = ordinal((0, 1) : (0.5, 0.5))
testpredictor = "x1"
covariates = "x2"
responseprob = 0.30
testoddsratio = 0.863
covoddsratios = 0.38
ntotal = .
power = 0.80;
run;

It gives me an N of 7,107; 2,369 for each group. Is there a way to specify a non-ordinal, categorical testpredictor in the vardist statement, and if so, how do I put two odds ratios in the testoddsratio statement?

[StatDave · Accepted solution]

If you just need the sample size for testing for any difference among the three treatment levels, as can be performed by a Pearson or likelihood ratio chi-square test, then this is easily done as discussed and illustrated in Example 3 in the Results tab of the PowerRxC macro, which shows how to do it with that macro or with the CUSTOM statement in PROC POWER.