Title:Sample Size Estimation for Negative Binomial Regression Models with Distinct Shape Parameters
Volume: 3
Issue: 2
Author(s): Yongming Qu and Junxiang Luo
Affiliation:
Keywords:
Hypoglycemia, overdispersion, statistical power.
Abstract: Background: Negative bionmial regression is a common statistical
model for analyzing count data. For example, hypoglycemic events occurred in
clinical trials studying anti-diabetes therapies are often analyzed using negative binomial
regression. Recently, methods have been developed for calculating statistical
power and sample size needed for negative binomial regression with a common
shape parameter across treatment groups. Real data examples suggest that the
shape parameters are often distinct when the hypoglycemia event rates between
two treatment groups are different. This article extended the existing method of
negative binomial regression for distinct shape parameters.
Methods: Three new methods are proposed for sample size calculation based on estimating the variance
under null hypothesis: (1). Using the true rate and shape parameter based on the reference
group; (2) Using the true rates and shape parameters under the alternative hypothesis; (3). Using the
true shape parameters under alternative hypothesis and maximum likelihood estmator for the rate
under the null hypothesis.
Results: Simulations were performed for various mean and shape parameters based on previous publications
and based on hypoglycemic events data from clinical trials in diabetes. Results show that
Methods (2) and (3) provided satisfactory estimation of sample size in which the simulated statistical
power approximated the desired statistical power. In each case, the analysed sample size based on
Method 2 was not smaller than the sample size based on Method 1.
Conclusion: Two methods for estimating the statistical power using negative binomial regression
with distinct shape parameters are proposed and simulations show that they had satistifactory performance.
