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 – equivalence margin for the ratio or difference of Poisson rates

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

Return type:

instance of HolderTuple class

References

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

See also

test_poisson_2indep, confint_poisson_2indep