tost_poisson_2indep(count1, exposure1, count2, exposure2, low, upp, method='score')¶
Equivalence test based on two one-sided test_proportions_2indep
This assumes that we have two independent binomial samples.
The Null and alternative hypothesis for equivalence testing are
H0: g1 / g2 <= low or upp <= g1 / g2
H1: low < g1 / g2 < upp
where g1 and g2 are the Poisson rates.
Number of events in first sample
Total exposure (time * subjects) in first sample
Number of events in second sample
Total exposure (time * subjects) in second sample
- low, upp :
equivalence margin for the ratio of Poisson rates
- method: string
Method for the test statistic and the p-value. Defaults to ‘score’. Current Methods are based on Gu et. al 2008 Implemented are ‘wald’, ‘score’ and ‘sqrt’ based asymptotic normal distribution, and the exact conditional test ‘exact-cond’, and its mid-point version ‘cond-midp’, see Notes
The two main attributes are test statistic statistic and p-value pvalue.
‘wald’: method W1A, wald test, variance based on separate estimates
‘score’: method W2A, score test, variance based on estimate under Null
‘wald-log’: W3A not implemented
‘score-log’ W4A not implemented
‘sqrt’: W5A, based on variance stabilizing square root transformation
‘exact-cond’: exact conditional test based on binomial distribution
‘cond-midp’: midpoint-pvalue of exact conditional test
The latter two are only verified for one-sided example.
Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008