A new biased estimator for the gamma regression model: Some applications in medical sciences

Abstract

The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator’s performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators.

Keywords:

• Gamma regression model
• James-Stein estimator
• shrinkage estimator
• MSE
• ridge regression

Acknowledgements

The authors thank the Associate Editor and anonymous referees for their valuable comments and suggestions that improved the quality of this paper greatly.

Notes

1 GRM is a special form of the GLM.

2 “Oklahoma and Mississippi states were excluded.”

3 “Expected deaths per standard million population.”

4 “The proportion of the population living in cities of 25,000 or over.”

5 “Wine and spirits consumption figures were taken from “Alcohol Statistics Letters.”

6 “In the literature, many studies found that a greater proportion of heavy drinkers died of cirrhosis than would be expected based on rates of cirrhosis deaths in the general population (i.e., liver cirrhosis deaths among heavy drinkers ranged from 2 to 23 times higher than the rate that would be expected in the general population).”