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 array_like

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 or array_like, optional

Rate ratio, rate1 / rate2, under the null hypothesis. The value must be positive and finite because the test is based on the log of the rate ratio.

Changed in version 0.15.1: Values that are not positive and finite now raise a ValueError. A rate ratio of 0 previously gave a divide by zero warning and a power of 1 or nan.

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.

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.

Raises:

ValueError

If nobs1 is not positive, value is not positive and finite, alpha is not in the interval (0, 1), or dispersion is negative.

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