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)

Power of test of ratio of 2 independent 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 int

Number of observations in sample 1.

nobs_ratiofloat, optional

Sample size ratio, nobs2 = nobs_ratio * nobs1.

exposurefloat, optional

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

valuefloat, optional

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

alphafloat 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 >= 0., optional

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

alternative{‘two-sided’, ‘larger’, ‘smaller’}, optional

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’.

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:

PowerNegbinRatioResult or float

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

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