R or Python, Is it possible to get the necessary sample size in a proportions power test calculation with ratio of sample sizes fixed?

Question

Given two proportions, p1 and p2,

I want to calculate the necessary samples of p1 I would need to do a Z-test of equivalence if:

1) alpha = .05
2) power = 0.9
3) n1/n2 = r

The Python stats models program gives something like this, but I think it is wrong because it gets drastically different answers from the STATA sampsi program.

The stata code is:

sampsi .01 .1, alpha(0.05) ratio(2)

which gives

Estimated sample size for two-sample comparison o

f proportions

Test Ho: p1 = p2, where p1 is the proportion in p

opulation 1 and p2 is the proportion in p opulation 2 Assumptions:

     alpha =   0.0500  (two-sided)
     power =   0.9000
        p1 =   0.0100
        p2 =   0.1000
     n2/n1 =   2.00

Estimated required sample sizes:

        n1 =      119
        n2 =      238

The python code is:

import statsmodels.stats.api as sms
es = sms.proportion_effectsize(0.01, 0.1)
sms.NormalIndPower().solve_power(es, power=0.9, alpha=0.05, ratio=2)

Which gives:

80.25164112946563

Answer 1

As @rawr says in comments above, bsamsize works (you need to set the frac argument to the fraction of samples in group 1)

library("Hmisc")
bsamsize(.01, .1, power=.9, frac=1/3)
      n1       n2 
102.8526 205.7051 

These are not the same numbers as Stata gives, but they're close. ?bsamsize gives details of the algorithm used.