Sample size calculation based on discrete Weibull and zero-inflated discrete Weibull regression models

Abstract

In this paper, we present a sample size determination for count data based on discrete Weibull and zero-inflated discrete Weibull regression models. The discrete Weibull regression can be used under various dispersion of count data, but its attractive feature is not sufficiently revealed. Discrete Weibull regression has a desirable feature in that it can be used for both over and under dispersed data, and thus a researcher can use a unified model with having low risk of failing to cope with the dispersion type of the data. Although the sample size calculation for Poisson, negative binomial regression has been previously introduced in many papers, there is no study that deals with discrete Weibull or zero-inflated discrete Weibull regression. We modified the method by Channouf, Fredette, and MacGibbon (2014) to calculate the required sample size for the two models. By using these two models, one can incorporate the effect of skewness, dispersion type and zero-inflated structure of the data when calculating the required sample size. Through the simulation studies, it was shown that our proposed sample size calculation method gives accurate results and also sample size is affected by the skewness of the distribution, covariance structure of covariates and amount of zeros. For illustration of our methods, the hospital length of stay study was used.