statsmodels.stats.rates.power_equivalence_neginb_2indep

statsmodels.stats.rates.power_equivalence_neginb_2indep(rate1, rate2, nobs1, low, upp, nobs_ratio=1, exposure=1, alpha=0.05, dispersion=0, method_var='alt', return_results=False)

Power of equivalence test of ratio of 2 indep. negative binomial rates

Parameters:

rate1float

Poisson rate for the first sample, treatment group, under the alternative hypothesis.

rate2float

Poisson rate for the second sample, reference group, under the alternative hypothesis.

nobs1float or array_like

Number of observations in sample 1.

lowfloat or array_like

Lower equivalence margin for the rate ratio, rate1 / rate2.

uppfloat or array_like

Upper equivalence margin for the rate ratio, rate1 / rate2.

nobs_ratiofloat or array_like, optional

Sample size ratio, nobs2 = nobs_ratio * nobs1. All values must be positive and finite.

Changed in version 0.15.1: A nobs_ratio that is not positive and finite raises a ValueError. Previously it returned nan or raised a ZeroDivisionError.

exposurefloat, optional

Exposure for each observation. Total exposure is nobs1 * exposure and nobs2 * exposure.

alphafloat or array_like in interval (0,1), optional

Significance level, e.g., 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true.

dispersionfloat or array_like >= 0., optional

Dispersion parameter for Negative Binomial distribution. The Poisson limiting case corresponds to dispersion=0.

method_var{“score”, “alt”, “ftotal”}, optional

The variance of the test statistic for the null hypothesis given the rates under the alternative, can be either equal to the rates under the alternative method_var="alt", or estimated under the constrained of the null hypothesis, method_var="score", or based on a moment constrained estimate, method_var="ftotal". see references.

return_resultsbool, optional

If true, then a results instance with extra information is returned, otherwise only the computed power is returned.

Returns:

PowerEquivalenceResult or float

If return_results is False (default), then only the power is returned as a float. If return_results is True, then a PowerEquivalenceResult result object is returned; it behaves like the scalar power in numeric comparisons (e.g. assert_allclose), while also exposing std_null_low, std_null_upp, std_alt and other attributes.

Notes

Changed in version 0.15.1: The power is changed if nobs_ratio is not equal to 1. The variances of the test statistic used the wrong sample size and, for method_var="alt", the rates of the two samples were interchanged. For method_var="ftotal" the variance under the null hypothesis used the wrong sample size ratio; with dispersion=0 it is now equal to method_var="score". Results for nobs_ratio=1 are unchanged.

References

[1]

Zhu, Haiyuan. 2017. “Sample Size Calculation for Comparing Two Poisson or Negative Binomial Rates in Noninferiority or Equivalence Trials.” Statistics in Biopharmaceutical Research, March. https://doi.org/10.1080/19466315.2016.1225594

[2]

Zhu, Haiyuan, and Hassan Lakkis. 2014. “Sample Size Calculation for Comparing Two Negative Binomial Rates.” Statistics in Medicine 33 (3): 376-87. https://doi.org/10.1002/sim.5947.

[3]

PASS documentation