Improve The Odds Ratio Estimates In The Multi-classification Of The Continuous Response Variable

The loss of information from polychotomizing a continuous outcome is easy known. One advantage of polychotomizing is that it allows estimation of odds ratio through cumulative odds model. The objective of this paper is to develop a new estimatior of the same odds ratio parameters through regression analysis on the original continuous coutcome without the loss of information caused by polychotomizing. Through the large sample theory, we get the relative sample sizes of the polychotomiazing procedure and the proposed approach required to attain a specified power. The comparison highlights the substantial sample size saving attained by the proposed approach, particularly for large value of the odds ratio parameter and for different value of π_i. In a Monte Carlo simulations the absolute biases of the two odds ratio estimators and the length of their respective confidence intervals again demonstrate the improvement attained by the proposed approach. In addition, coverage probabilities of the confidence intervals of the proposed approach converge quickly to the nominal levels. The cost savings due to the reduction in required sample size when using this method make it a available tool.