# statsmodels.stats.rates.power_negbin_ratio_2indep¶

statsmodels.stats.rates.power_negbin_ratio_2indep(rate1, rate2, nobs1, nobs_ratio=`1`, exposure=`1`, value=`1`, alpha=`0.05`, dispersion=`0.01`, alternative=`'two-sided'`, method_var=`'alt'`, return_results=`True`)[source]

Power of test of ratio of 2 independent negative binomial rates.

Parameters:
rate1`float`

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

rate2`float`

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

nobs1

Number of observations in sample 1.

low`float`

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

upp`float`

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

nobs_ratio`float`

Sample size ratio, nobs2 = nobs_ratio * nobs1.

exposure`float`

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

value`float`

Rate ratio, rate1 / rate2, under the null hypothesis.

alpha`float` `in` `interval` (0,1)

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

dispersion`float` >= 0.

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

method_var{“score”, “alt”}

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.

alternative`str`, ‘two-sided’ (`default`), ‘larger’, ‘smaller’

Alternative hypothesis whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either ‘larger’, ‘smaller’.

return_resultsbool

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

Returns:
results`results` `instance` or `float`

If return_results is False, then only the power is returned. If return_results is True, then a results instance with the information in attributes is returned.

powerfloat

Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true.

Other attributes in results instance include :

std_null

standard error of difference under the null hypothesis (without sqrt(nobs1))

std_alt

standard error of difference under the alternative hypothesis (without sqrt(nobs1))

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

Last update: Jul 16, 2024