Distribution-free Inference of Zero-inated Binomial Data for Longitudinal Studies

Relationship between political partisanship and COVID-19 deaths: future implications for public health

BACKGROUND

COVID-19 has impacted more than 200 countries. However in the USA, the response to the COVID-19 pandemic has been politically polarized. The objective of this study is to investigate the association between political partisanship and COVID-19 deaths rates in the USA.

METHODS

This study used longitudinal county-level panel data, segmented into 10 30-day time periods, consisting of all counties in the USA, from 22 January 2020 to 5 December 2020. The outcome measure is the total number of COVID-19 deaths per 30-day period. The key explanatory variable is county political partisanship, dichotomized as Democratic or Republican. The analysis used a ZINB regression.

RESULTS

When compared with Republican counties, COVID-19 death rates in Democratic counties were significantly higher (IRRs ranged from 2.0 to 18.3, P < 0.001) in Time 1-Time 5, but in Time 9-Time10, were significantly lower (IRRs ranged from 0.43 to 0.69, P < 0.001).

CONCLUSION

The reversed trend in COVID-19 death rates between Democratic and Republican counties was influenced by the political polarized response to the pandemic. The findings support the necessity of evidence-based public health leadership and management in maneuvering the USA out of the current COVID-19 pandemic and prepare for future public health crises.

Testing inflated zeros in binomial regression models

Binomial regression models are commonly applied to proportion data such as those relating to the mortality and infection rates of diseases. However, it is often the case that the responses may exhibit excessive zeros; in such cases a zero-inflated binomial (ZIB) regression model can be applied instead. In practice, it is essential to test if there are excessive zeros in the outcome to help choose an appropriate model. The binomial models can yield biased inference if there are excessive zeros, while ZIB models may be unnecessarily complex and hard to interpret, and even face convergence issues, if there are no excessive zeros. In this paper, we develop a new test for testing zero inflation in binomial regression models by directly comparing the amount of observed zeros with what would be expected under the binomial regression model. A closed form of the test statistic, as well as the asymptotic properties of the test, is derived based on estimating equations. Our systematic simulation studies show that the new test performs very well in most cases, and outperforms the classical Wald, likelihood ratio, and score tests, especially in controlling type I errors. Two real data examples are also included for illustrative purpose.

Semiparametric models for multilevel overdispersed count data with extra zeros

This study proposes semiparametric models for analysis of hierarchical count data containing excess zeros and overdispersion simultaneously. The methods discussed in this paper handle nonlinear covariate effects through flexible semiparametric multilevel regression techniques. This is performed by providing a comprehensive comparison of semiparametric multilevel zero-inflated negative binomial and semiparametric multilevel zero-inflated generalized Poisson models under the real and simulated data. An EM algorithm based on Newton–Raphson equations for maximum penalized likelihood estimation approach is developed. The performance of the proposed models is assessed by using a Monte Carlo simulation study. We also illustrated the methods by the analysis of decayed, missing, and filled teeth of children aged 5–14 years old.