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
floatorint 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
floatininterval(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.
- rate1
- Returns:¶
- results
resultsinstanceorfloat 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))
- results
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