statsmodels.stats.rates.power_poisson_ratio_2indep

statsmodels.stats.rates.power_poisson_ratio_2indep(rate1, rate2, nobs1, nobs_ratio=1, exposure=1, value=1, alpha=0.05, dispersion=1, alternative='smaller', method_var='alt', return_results=True)

Power of test of ratio of 2 independent poisson rates

This is based on Zhu and Zhu and Lakkis. It does not directly correspond to test_poisson_2indep.

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 default of 1 is the null hypothesis that both rates are equal. 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: The default was changed from 0 to 1. A rate ratio of 0 made the power 0, 1 or nan with a divide by zero warning. Values that are not positive and finite now raise a ValueError.

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, optional

Dispersion coefficient for quasi-Poisson. Dispersion different from one can capture over or under dispersion relative to Poisson distribution.

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

Alternative hypothesis whether the power is calculated for a one-sided or two-sided test. Default is ‘smaller’.

method_var{“score”, “alt”}, 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".

return_resultsbool, optional

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

Returns:

PowerRatioResult or float

If return_results is False, then only the power is returned as a float. If return_results is True (default), then a PowerRatioResult 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