Usage of Penalized Maximum Likelihood Estimation Method in Medical Research: An Alternative to Maximum Likelihood Estimation Method

Abstract

The present paper was to reduce biased estimation using new approach (Penalized Maximum Likelihood Estimation Method) in Logistic Regression. It was assumed in the present paper that four various data sets on coronary heart disease (CHD) and smoking (including separation case) were obtained. Maximum Likelihood Estimation and Penalized Maximum Likelihood Estimation Methods were applied and compared for separation case including biased estimation in Logistic Regression when one of the cells in 2 x 2 contingency tables becomes equal to zero (separation problem).The values of parameters and their standard error obtained by using Maximum Likelihood estimation for four data sets were found approximately: 12.56±257.8, 13.46±264.3, 13.42±210.3, and 13.41±180.4, respectively, meaning that Maximum likelihood Estimations are biased estimates. However, corresponding values for Penalized Maximum Likelihood Estimation Method were found 2.28 ± 1.81, 3.05 ± 1.59, 3.45± 1.53, and 3.45 ± 1.53, respectively, meaning that Penalized Maximum likelihood Estimations was unbiased estimates. For example, it is clear that standard error value for data set 1 reduced from 257.8 to 1.81 when using Penalized Maximum Likelihood Estimation Method for separation problem. According to the original approach, the odds of being coronary heart disease (CHD) risk for smoking were increased 21.08 times than that for no smoking in data set 2, which is statistically significant at 1% level. The odds of being coronary heart disease (CHD) risk for smoking were increased 31.63 times than that for no smoking in data set 3 (P < 0.001). The odds of being coronary heart disease (CHD) risk for smoking were increased 41.93 times than that for no smoking in data set 4.

When one of the cells in 2 x 2 contingency tables becomes equal to zero (separation problem), Penalized Maximum Likelihood Estimation Method was more superior to Maximum Likelihood Estimation Method because Penalized Maximum Likelihood Estimation Method may be performed unbiased (reliable) estimation.