# statsmodels.stats.rates.tost_poisson_2indep¶

statsmodels.stats.rates.tost_poisson_2indep(count1, exposure1, count2, exposure2, low, upp, method=`'score'`, compare=`'ratio'`)[source]

Equivalence test based on two one-sided test_proportions_2indep

This assumes that we have two independent poisson samples.

The Null and alternative hypothesis for equivalence testing are

for compare = ‘ratio’

• H0: rate1 / rate2 <= low or upp <= rate1 / rate2

• H1: low < rate1 / rate2 < upp

for compare = ‘diff’

• H0: rate1 - rate2 <= low or upp <= rate1 - rate2

• H1: low < rate - rate < upp

Parameters:
count1`int`

Number of events in first sample

exposure1`float`

Total exposure (time * subjects) in first sample

count2`int`

Number of events in second sample

exposure2`float`

Total exposure (time * subjects) in second sample

low, upp

equivalence margin for the ratio or difference of Poisson rates

method: string

TOST uses `test_poisson_2indep` and has the same methods.

ratio:

• ‘wald’: method W1A, wald test, variance based on observed rates

• ‘score’: method W2A, score test, variance based on estimate under the Null hypothesis

• ‘wald-log’: W3A, uses log-ratio, variance based on observed rates

• ‘score-log’ W4A, uses log-ratio, variance based on estimate under the Null hypothesis

• ‘sqrt’: W5A, based on variance stabilizing square root transformation

• ‘exact-cond’: exact conditional test based on binomial distribution

This uses `binom_test` which is minlike in the two-sided case.

• ‘cond-midp’: midpoint-pvalue of exact conditional test

• ‘etest’ or ‘etest-score: etest with score test statistic

• ‘etest-wald’: etest with wald test statistic

diff:

• ‘wald’,

• ‘waldccv’

• ‘score’

• ‘etest-score’ or ‘etest: etest with score test statistic

• ‘etest-wald’: etest with wald test statistic

Returns:
results`instance` `of` `HolderTuple` `class`

The two main attributes are test statistic statistic and p-value pvalue.

References

Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008

Last update: Oct 29, 2023